circuits and analog electronics 电路与模拟电子技术

Circuits and Analog ElectronicsCircuits and Analog Electronics

电路与模拟电子技术电路与模拟电子技术

Prof Li Chen School of Information Science and Technology Sun Yat-sen University

中山大学信息科学与技术学院陈立副教授

Email chenli55mailsysueducn

10 10 级计算机科学级计算机科学 22 ＋＋ 22

References bull W H Hayt Jr J E Kemmerly and S M Durbin Engineering

Circuit Analysis McGraw-Hill 2005 ISBN 978-7-121-01667-7

bull R L Boylestad and L Nashelsky Electronic Devices and Circuit Theory Pearson Education 2007 ISBN 978-7-121-04396-3

bull 高玉良电路与模拟电子技术高教出版社 2004 ISBN 7-04-014536-7


Handouts available at

sistsysueducn~chenli

References bull W H Hayt Jr J E Kemmerly and S M Durbin Engineering Circuit

Analysis McGraw-Hill 2005 ISBN 978-7-121-01667-7




Weeks Chapters References

1 2 Basis concepts and laws of electronics Hayt Ch 1 2 5

3 4 Basis analysis methods to circuits Hayt Ch 3 4

5 Basis RL amp RC circuits Hayt Ch 6

6 7 8 Sinusoidal steady state analysis Hayt Ch 7

9 Midterm

10 Diodes and diodes circuits Boylestad Ch 1 2

11 12 13 Basic BJT amplifier circuits Boylestad Ch 3-6

14 15 16 Operational amplifier and Op Amp circuits Boylestad Ch 11

17 Review

Teaching ScheduleTeaching Schedule

Ch1 Ch1 Basic Concepts and Laws of Electric Basic Concepts and Laws of Electric CircuitsCircuits

11 Basic Concepts and Electric Circuits

12 Basic Quantities

13 Circuit ElementsCircuit Elements

14 Kirchhoffs Current and Voltage Laws

References Hayt Ch1 2 5 Gao Ch1


Signal processing and transmissiontransmission

Amplifiers


Electrical powerElectrical power conversion and transmissiontransmission

Power Supplies

TransmissionTransmission Loads

Circuits KinescopeAntenna

Speakertransmitter

11 Basic Concepts and Electric Circuits Electrical power conversion and transmission


Question What is the current through the bulb

Concept of Abstraction

Solution

In order to calculate the current we can replace the bulb with a resistor

R is the only subject of interest which serves as an abstraction of the bulb


Lumped circuit abstraction

bull A resistor is a circuit element that transforms the electrical energy (eg electricity heat)

bull Commonly used devices that are modeled as resistors include incandescent heaters wires and etc

bull A circuit consists of sources resistors capacitors inductors and conductors

bull Elements are lumped

bull Conductors are perfect

Resistance R = VI 1 =1VA ohm

Conductance G = 1R = 1AV siemens (S)

1S = 1AV i(t) = G times v(t) Instantaneous current and voltage at time t


Understanding the AM radio requires knowledge of several concepts

bull Communicationssignal processing (frequency domain analysis)

bull Electromagnetics (antennas high-frequency circuits)

bull Power (batteries power supplies)

bull Solid state (miniaturization low-power electronics)

The AM Radio SystemThe AM Radio System

Transmitter Receiver

Example 1 The AM audio system

Example 2 The telephone system



The AM Radio SystemThe AM Radio System A signal is a quantity that may vary with time

Voltage or current in a circuit

Sound (sinusoidal wave traveling through air)

Light or radio waves (electromagnetic energy traveling through free space)

The analysis and design of AM radios (and communication systems in general) is usually conducted in the frequency domain using Fourier analysis which allows us to represent signals as combinations of sinusoids (sines and cosines)



Frequency is the rate at which a signal oscillatesDuration of the signal T frequency of the signal f = 1T

High Frequency Low Frequency



Visible light is the electromagnetic energy with frequency between 380THz (Terahertz) and 860THz Our visual system perceives the frequency of the electromagnetic energy as color is 460THz is 570THz and is 630THz An AM radio signal has a frequency of between 500kHz and 18MHz

FM radio and TV uses different frequencies

Mathematical analysis of signals in terms of frequency

Most commonly encountered signals can be represented as a Fourier series or a Fourier transform A Fourier series is a weighted sum of cosines and sines

red green blue


The AM Radio SystemThe AM Radio SystemFourier Series A Fourier series decomposes a periodic function (or signal) into the sum of a set of sines and cosines Given function f(t) with angular frequency ω and period T its Fourier series can be written as

f(t) = A0 + A1msin(ωt + ψ1) + A2msin(2ωt + ψ2) +

=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t

ttfExample Given function during a period

2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0

2 2 2A f t d t d t d t

2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0

kmC f t k td t k td t k td t

k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k

B f t k td t k td t k td t

k td t k t kk k

k is even

k is odd



Example-Fourier SeriesExample-Fourier Series

基波

3次谐波

基波＋3 次谐波

bull Signals can be represented in terms of their frequency components

bull The AM transmitter and receiver are analyzed in terms of their effects on the frequency components signals

1st series + 3rd series

1st series (k = 1)

3rd series (k = 3)



The modulator converts the frequency of the input signal from the audio range (0-5kHz) to the carrier frequency of the station (ie 605kHz-615kHz)

freq5kHz

Frequency domain representation of input

Frequency domain representation of output

freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna

Transmitter Block DiagramTransmitter Block Diagram



Input Signal

Output Signal

Modulator Time DomainModulator Time Domain



bull A typical AM station broadcasts several kWndash Up to 50kW-Class I or Class II stationsndash Up to 5kW-Class III stationndash Up to 1kW-Class IV station

bull Typical modulator circuit can provide at most a few mWbull Power amplifier takes modulator output and increases its magnitude

Power AmplifierPower Amplifier

The antenna converts a current or a voltage signal to an electromagnetic signal which is radiated through the space

AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker

Receiver Block DiagramReceiver Block Diagram



bull The antenna captures electromagnetic energy and converts it to a small voltage or current

bull In the frequency domain the antenna output is

0 frequency

Undesired SignalsDesired Signal

Carrier Frequencyof desired station

AntennaAntenna

interferences interferences



bull RF Amplifier amplifies small signals from the antenna to voltage levels appropriate for transistor circuits

bull RF Amplifier also performs as a Bandpass filter for the signal

ndash Bandpass filter attenuates the other components outside the frequency range that contains the desired station

RF (Radio Frequency) AmplifierRF (Radio Frequency) Amplifier

0 frequency

Undesired Signals

Desired Signal

Carrier Frequency of desired station


0 frequency

Undesired Signals

Desired Signal

455 kHz

IF (Intermediate Frequency) MixerIF (Intermediate Frequency) Mixerbull The IF Mixer shifts its input in the frequency domain from the carrier

frequency to an intermediate frequency of 455kHz

bull The IF amplifier bandpass filters the output of the IF mixer eliminating all of the undesired signals

IF AmplifierIF Amplifier

0 frequency

Desired Signal

455 kHz



bull Computes the envelope of its input signal

Envelope DetectorEnvelope Detector

Output Signal

Input Signal


The AM Radio SystemThe AM Radio SystemAudio AmplifierAudio Amplifier

bull Amplifies signal from envelope detector

bull Provides power to drive the speaker

Hierarchical System ModelsHierarchical System Modelsbull Modelling at different levels of abstraction

bull Higher levels of the model describe overall function of the system

bull Lower levels of the model describe necessary details to implement the system

bull In the AM receiver the input is the antenna voltage and the output is the sound energy produced by the speaker

bull In EE a system is an electrical andor mechanical device a process or a mathematical model that relates one or more inputs to one or more outputs

SystemInputs Outputs


The AM Radio SystemThe AM Radio SystemTop Level ModelTop Level Model

AM ReceiverInput Signal Sound

Second Level ModelSecond Level Model

RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter

Low Level Model Envelope DetectorLow Level Model Envelope Detector

Circuit Level Model Envelope DetectorCircuit Level Model Envelope Detector

+

-R C

+

-VoutVin

12 Basic Quantities

UnitsUnitsbull Standard SI Prefixes

ndash 10-12 pico (p)

ndash 10-9 nano (n)

ndash 10-6 micro ()

ndash 10-3 milli (m)

ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)

bull Electric charge (q)

ndash in Coulombs (C)

bull Current (I)

ndash in Amperes (A)

bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent

bull Time rate of change of charge t

qI Constant current tIq

dttdqti )()( Time varying current

t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities

bull Notation Current flow represents the flow of positive chargebull Alternating versus direct current (AC vs DC)

i(t) i(t)

t t

DCACTime ndash varying current Steady current

bull A mount of electric charges flowing through the surface per unit time

CurrentCurrent

Positive versus negative currentPositive versus negative current

2 A -2 A

P11 In the wire electrons moving left to right to create a current of 1 mA Determine I1 and I2

Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities

Current is always associated with arrows (directions)

Negative charge of -2Cs moving

Positive charge of 2Cs moving or



Voltage(Potential)Voltage(Potential)

baab VVV

b

a

b

aab ldE

q

ldF

q

WV

VoltageVoltage Units 1 V = 1 JC

Positive versus negative voltagePositive versus negative voltage

+

ndash

ndash

+

2 V -2 V

12 Basic Quantities

bull Energy per unit chargebull It is an electrical force drives an electric current

+- of voltage (V) tell the actual polarity of a certain point DN

Two ldquoDo Not (DN)rdquo

+- of current (I) tell the actual direction of particlersquos movement DN

Voltage (Potential)Voltage (Potential)

a

b

VVab 5 a b which pointrsquos potential is higher

b

a

V6aV V4bV Vab =

a b +Q from point b to point a get energy Point a is

Positive or Positive or negativenegative

12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa

v E v E v E v E R R R E R R R E R R Rv

R R R R R R R R R R R R R R R R

PowerPower

bull One joules of energy is expanded per second

bull Rate of change of energy

P = Wt )()()()()( titVdt

dqtVdttdwtp abab

bull Used to determine the electrical power is being absorbed or supplied

ndash if P is positive (+) power is absorbed

ndash if P is negative (ndash) power is supplied

+

ndash

v(t)

i(t)p(t) = v(t) i(t)

v(t) is defined as the voltage with positive reference at the same terminal that the current i(t) is entering

12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash

-5V 5 2 10WP Power is supplied delivered power to external element

+

ndash

5V

2A

5 2 10WP Power is absorbed Power delivered to

Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower

bull Power absorbed by a resistor

)()()( titvtp )(2 tiR

Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-

P15 Find the power absorbed by each element in the circuit

12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP

Supply energy element 1 3 4 Absorb energy element 2 5

Open CircuitOpen Circuit R=

I=0 V=E P=0E

R0

Short CircuitShort Circuit R=0

E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI

Loaded CircuitLoaded Circuit

E

R0 R

I

0PPP E

12 Basic Quantities


Key Words Resistors Capacitors Inductors Resistors Capacitors Inductors voltage source current source

bull Passive elements (cannot generate energy)

ndash eg resistors capacitors inductors etc

bull Active elements (capable of generating energy)

ndash batteries generators etc

bull Important active elements

ndash Independent voltage source

ndash Independent current source

ndash Dependent voltage source

bull voltage dependent and current dependent

ndash Dependent current source



ResistorsResistors

Dissipation ElementsElements

S

lR v=iR P=vi=Ri2=v2R gt0

v-i relationship

v

i


Resistors connected in series

ndash Equivalent Resistance is found by Req= R1 + R2 + R3 + hellip

R1 R2 R3

Resistors connected in parallel 1Req=1R1 + 1R2 + 1R3 + hellip

R1 R2 R3

Capacitors

bull Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator)

bull Charge on the two conductors creates an electric field that stores energy

bull The voltage difference between the two conductors is proportional to the charge q = C v

bull The proportionality constant C is called capacitance

bull Units of Farads (F) - CV

bull 1F= one coulomb of charge of each conductor causes a voltage of one volt across the device

1F=106F 1F=106PF


Capacitors

store energy in an electric field

v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2

1cvcvdvpdtwEnergy stored


Capacitors connected in seriesndash Equivalent capacitance is found

by 1Ceq=1C1 + 1C2 + 1C3 + hellip

series

parallel

Capacitors connected in parallel Ceq= C1 + C2 + C3 + hellip

vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors

store energy in a magnetic field that is created by electric passing through it

v-i relationship i(t) +

-

v(t)L

Inductors connected in series Leq= L1 + L2 + L3 + hellip

Inductors connected in parallel 1Leq=1L1 + 1L2 + 1L3 + hellip


dt

diLiivP )(

2

1)( 2 tLitwL Energy stored

022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)

Independent voltage source

+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical


Independent current source

I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1

Voltage source connected in series

n

kSkS RR

1

Voltage source connected in parallel

n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21


Voltage controlled (dependent) voltage source (VCVS)

+_

_

+

Sv Svv

Current controlled (dependent) voltage source (CCVS)

+_ Sriv Si

Q What are the units for and r


Voltage controlled (dependent) current source (VCCS)

Current controlled (dependent) current source (CCCS)

_

+

SvSgvi

Si Sii

Q What are the units for and g


Independent source

dependent source

Can provide power to the circuit

Excitation to circuit

Output is not controlled by external

Can provide power to the circuit No excitation to circuit

Output is controlled by external


bull So far we have talked about two kinds of circuit elements

ndash Sources (independent and dependent)

bull active can provide power to the circuit

ndash Resistors

bull passive can only dissipate power

Review

The energy supplied by the active elements is equivalent to the energy absorbed by the passive elements



Key Words Nodes Branches Loops KCL KVL

Nodes Branches Loops mesh

Node point where two or more elements are joined (eg big node 1)

Loop A closed path that never goes twice over a node (eg the blue line)

Branch Component connected between two nodes (eg component R4)

The red path is NOT a loop

Mesh A loop that does not contain any other loops in it



bull A circuit containing three nodes and five branches

bull Node 1 is redrawn to look like two nodes it is still one nodes

P18


bull sum of all currents entering a node is zero

bull sum of currents entering node is equal to sum of currents leaving node

KCL

KCL MathematicallyKCL Mathematicallyi1(t)

i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110

bull Find currents through each light bulb

IB = 1W120V = 83mA

bull Apply KCL to the top node

IS - 50IB = 0

bull Solve for IS IS = 50 IB = 417mA

KCL-Christmas LightsKCL-Christmas Lights


KCL

P111 We can make supernodes by aggregting node

0

0

7542

461

iiii

iii

3 Leaving

2 Leaving

076521 iiiii3 amp 2 Adding


KCL

Current dividerCurrent divider

N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12


In case of parallel 1 21 2

1 1 1 V=

I IG G G

R R R R G

sum of voltages around any loop in a circuit is zero

KVL

bull A voltage encountered + to - is positivebull A voltage encountered - to + is negative

KVL Mathematically 0)(1

n

jj tv 0

1

n

jjV


KVL is a conservation of energy principle

KVL

A positive charge gains electrical energy as it moves to a point with higher voltage and releases electrical energy if it moves to a point with lower voltage

AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV

If the charge comes back to the same Initial point the net energy gain Must be zero

0)( CABCAB VVVq


KVL

P113 Determine the voltages Vae and Vec


10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL

Voltage dividerVoltage divider

R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV

Important voltage Divider equations

NV

R

RV n

kk

kk

1


KVLVoltage dividerVoltage divider

kR 151

Volume control

P114 Example Vs = 9V R1 = 90kΩ R2 = 30kΩ


Slide 1

Slide 2

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References bull W H Hayt Jr J E Kemmerly and S M Durbin Engineering

Circuit Analysis McGraw-Hill 2005 ISBN 978-7-121-01667-7
















9 Midterm




17 Review




12 Basic Quantities






Amplifiers



Power Supplies



Speakertransmitter





Solution








































red green blue




=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 81













9 Midterm




17 Review




12 Basic Quantities






Amplifiers



Power Supplies



Speakertransmitter





Solution








































red green blue




=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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12 Basic Quantities






Amplifiers



Power Supplies



Speakertransmitter





Solution








































red green blue




=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 81


Amplifiers



Power Supplies



Speakertransmitter





Solution








































red green blue




=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 81





Solution








































red green blue




=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 77

Slide 78

Slide 79

Slide 80

Slide 81






































red green blue




=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 81




=

10

1 10

10

cossin

sincoscossin

)sin(

kkmkm

k kkkmkkm

kkkm

tkCtkBA

tkAtkAA

tkAA

0 0

0

0

1

2sin

2cos

T

T

km

T

km

A f t dtT

B f t k tdtT

B f t k tdtT


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 80

Slide 81


21

01)(

t


2 3 t

1

)12sin(12

14]5sin

5

13sin

3

1[sin

4)(

l

tll

ttttf

For the example 2 2

0 0 0

1 1 11 1 0


2 2

0 0

00

1 1cos 1 cos 1 cos

2 2 cos sin 0


k td t k tk

2 2

0 0

00 40

1 1sin 1 sin 1 sin

2 2 2 sin cos 1 cos

km

k


k td t k t kk k

k is even

k is odd




基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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基波

3次谐波





1st series (k = 1)

3rd series (k = 3)




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 81




freq5kHz



freq610kHz

ModulatorModulator

Signal

SourceModulator

Power

Amplifier

Antenna




Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 41

Slide 42

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Slide 46

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Slide 52

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Slide 59

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Slide 69

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81



Input Signal

Output Signal








AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81







AntennaAntenna



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

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Slide 51

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Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81



RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

Audio

Amplifier

Antenna

Speaker






0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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0 frequency



AntennaAntenna








0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 80

Slide 81







0 frequency

Undesired Signals

Desired Signal



0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 3

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Slide 5

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Slide 9

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Slide 27

Slide 28

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Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

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Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

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Slide 61

Slide 62

Slide 63

Slide 64

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Slide 66

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Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81


0 frequency

Undesired Signals

Desired Signal

455 kHz





0 frequency

Desired Signal

455 kHz





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 81





Output Signal

Input Signal















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81















RFAmplifier

IFMixer

IFAmplifier

EnvelopeDetector

AudioAmplifier

Antenna

Speaker

Power Supply



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 59

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Slide 61

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Slide 64

Slide 65

Slide 66

Slide 67

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81



Half-waveRectifier

Low-passFilter



+

-R C

+

-VoutVin

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 80

Slide 81

12 Basic Quantities



ndash 10-9 nano (n)

ndash 10-6 micro ()


ndash 103 kilo (k)

ndash 106 mega (M)

ndash 109 giga (G)

ndash 1012 tera (T)



bull Current (I)


bull Voltage (V)

ndash in Volts (V)

bull Energy (W)

ndash in Joules (J)

bull Power (P)

ndash in Watts (W)

I t q

VI

R

IR V

W qV Pt V I t

P VI

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 80

Slide 81

CurrentCurrent




t

dxxitq )()(

Unit mAA 3101 AmA 3101 (1 A = 1 Cs)

12 Basic Quantities


i(t) i(t)

t t



CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 81

CurrentCurrent


2 A -2 A


Ans Ans II11 = -1 mA = -1 mA II2 2 = +1 = +1

mAmA

12 Basic Quantities







baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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baab VVV

b

a

b

aab ldE

q

ldF

q

WV



+

ndash

ndash

+

2 V -2 V

12 Basic Quantities






a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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a

b


b

a

V6aV V4bV Vab =



12 Basic Quantities

Example


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 81


ab

cacute

c d

dacute

2211

21

221121222

2

21112

1111

111

1b1bb

0

)(

)(

0

rRrR

EEI

rRrRIEEIrEVIrVV

EVV

RrRIEIRVV

rRIEIrVV

IREVEV

IRVIRVVVV

V

dda

dd

cd

cc

bc

aab

a

12 Basic Quantities

Example

I


K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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K Open

K Close

Va=)V(521

)V(18

a

a

V

V

12 Basic Quantities

Example

I

I

I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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I

11 2

a

Ev E R

R R

12 Basic Quantities

ExampleExample

I

1 21 1

1 2a

E Ev E R

R R

1 2 3 1 2 3 2 1 3 3 1 2

1 2 3 1 2 3 2 3 1 2 1 3

a a a aa



PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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PowerPower



P = Wt )()()()()( titVdt

dqtVdttdwtp abab




+

ndash

v(t)



12 Basic Quantities

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 81

PowerPower

Example

12 Basic Quantities

2A+

ndash


+

ndash

5V

2A


Note +

ndash

+5V

+

ndash

-5V

2A

-2A

Power absorbed

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

PowerPower



Rtv )(2)(2 tvG

Gti )(2

12 Basic Quantities

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

PowerPower

1

2

3 4

5

I1 I2 I3+

-

-

-

-

-

+

+

+

+-

+

+

-

+-


12 Basic Quantities

A21 I A12 IA13 I

V35 V

V41 V

V82 V V43 V

V74 V

3

16

7

4

8

535

212

734

323

111

WVIP

WVIP

WVIP

WVIP

WVIP



I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 81


I=0 V=E P=0E

R0


E

R0

R ＝ 0 0R

EI 00 IREV

02RIPE

12 Basic Quantities

RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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RR

EI

o

0IREIRV

02RIEIVI


E

R0 R

I

0PPP E

12 Basic Quantities















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 78

Slide 79

Slide 80

Slide 81















ResistorsResistors


S


v-i relationship

v

i




R1 R2 R3


R1 R2 R3

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 79

Slide 80

Slide 81

Capacitors







1F=106F 1F=106PF


Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 79

Slide 80

Slide 81

Capacitors


v-i relationship

dt

dqti =)(

dt

dvC

t

dxxiC

tv )(1

)(

i(t)+

-

v(t)

Therestofthe

circuit

dt

dvcvivp 2

2





series

parallel


vC(t+) = vC(t-)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

v(t)5V

1s 2s(1)

00

0

1

0

2

1

1

0

1

0

1

0 0 0

11 1 0 5 1 0 5

021

2 1 5 5 2 1 5 002

0 1s

11 0 5 1 5

021s 2s

11 5 10 5 2 0

02

t

tv t i t dt v t

Ct v

v dt

v dt

t

v t dt t v

t

v t dt t v

For (1)

Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Capacitors

t

i(t)1A

-1A 1s

2s

i(t)

+

-

v(t)02F

P17


t

w (t)

25J

1s 2s(2)

0 0

0

2 20

20

1

2

1 If 0

2Now 0 0 1 5 2 0

1 01 25 25

2 01 0 0

t t

t t

t

t

dvw t Pdt C v dt

dt

C vdv C v t v t

v t w t C v t

v v v

w

w

For (2)

For (1) (2)

dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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dt

tdiLtv

)()(

t

dxxvL

ti )(1

)(

Inductors



-

v(t)L




dt

diLiivP )(

2


022

000 2)( titi

LidiLdt

dt

diiLPdttw

ti

tv

t

t

t

t

iL(t+) = iL(t-)


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 81


+VS

RS ＝ 0

v

i

VS

Ideal

sS

sS

IRVV

IRV

practical



I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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I

v

iIS

RS infin＝

Ideal

SS

SS

RVII

RVI

practical


n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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n

kSkS VV

1


n

kSkS RR

1


n

kSkS II

1

SnSSS

SnSSS

RRRR

RRRR

1111

21

21



+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 74

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Slide 78

Slide 79

Slide 80

Slide 81


+_

_

+

Sv Svv


+_ Sriv Si





_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Slide 81



_

+

SvSgvi

Si Sii



Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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Independent source

dependent source










ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 79

Slide 80

Slide 81




ndash Resistors


Review















P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81













P18




KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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KCL


i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(

n

jjI

1

0




KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

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Slide 54

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Slide 69

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Slide 71

Slide 72

Slide 73

Slide 74

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Slide 77

Slide 78

Slide 79

Slide 80

Slide 81



KCL

P19

DCBA iiii


In

Out

0A B C O

I

I

i i i i

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

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Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

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Slide 49

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Slide 51

Slide 52

Slide 53

Slide 54

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Slide 56

Slide 57

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Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

KCL

+

-120V

50 1W Bulbs

Is

P110


IB = 1W120V = 83mA


IS - 50IB = 0




KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

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Slide 27

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Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

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Slide 66

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Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

KCL


0

0

7542

461

iiii

iii

3 Leaving

2 Leaving



KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

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Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

KCL


N VG1

G2

I+

-

I1I2

IGG

GG

G

IVGI

21

1111

IGG

GVGI

21

222

I

G

GI

n

kk

kk

1

121

21

111

11

RRR

RRI

RRI

R

VI

I

RR

RI

21

12



1 1 1 V=

I IG G G

R R R R G


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81


KVL



n

jj tv 0

1

n

jjV



KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81


KVL


AV

BBV)( AB VVqW

q

abV

a bq

abqVW LOSES

cdV

c dq

cdqVW GAINS

AV

BBV

q

CV

ABV

BC

V

CAV


0)( CABCAB VVVq


KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

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Slide 60

Slide 61

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KVL



10 24 0aeV

16 12 4 6 0aeV

4 + 6 + Vec = 0

KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



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KVL


R1

R2

-

V1

+

+

-

V2

+

-

V

21

111 RR

RVIRV

21

222 RR

RVIRV


NV

R

RV n

kk

kk

1



kR 151

Volume control



Slide 1

Slide 2

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kR 151

Volume control



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circuits and analog electronics 电路与模拟电子技术

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