ehm6307-bİlgİsayar desteklİ devre analİzİ

EHM6307-BİLGİSAYAR DESTEKLİ DEVRE ANALİZİ

2020-2021 GÜZ DÖNEMİ

ELEKTRONİK DOKTORA PROGRAMI

UZAKTAN EĞİTİM DERS NOTLARI

20 Ekim 2020

Doç. Dr. Umut Engin AYTEN

DEVRE DENKLEMLERİ

İdeal Elemanlar:

+

_

v i

Two-terminal

+

_

v1

i1

Two-port

i1

+

_

v2

i2

i2

DEVRE DENKLEMLERİÇok Kapılı Elemanlar:

DEVRE DENKLEMLERİ

DEVRE DENKLEMLERİ

İdeal Elemanlar:

Ideal elements

Element Branch Eqn

Resistor v = R·i

Capacitor i = C·dv/dt

Inductor v = L·di/dt

Voltage Source v = vs, i = ?

Current Source i = is, v = ?

VCVS vs = AV · vc, i = ?

VCCS is = GT · vc, v = ?

CCVS vs = RT · ic, i = ?

CCCS is = AI · ic, v = ?

DEVRE DENKLEMLERİ

0

1 2

R1G2v3

R3

R4Is5

0

0

11100

00111

5

4

3

2

1

i

i

i

i

i

A i = 0

Kirchhoff’s Current Law (KCL)

N equations

DEVRE DENKLEMLERİ

0

1 2

R1G2v3

R3

R4Is5

0

0

0

0

0

10

10

11

01

01

2

1

5

4

3

2

1

e

e

v

v

v

v

v

v - AT e = 0 B equations

DEVRE DENKLEMLERİ

0

1 2

R1G2v3

R3

R4Is5

55

4

3

2

1

5

4

3

2

1

4

3

2

1

0

0

0

0

00000

01

000

001

00

0000

00001

sii

i

i

i

i

v

v

v

v

v

R

R

G

R

Kvv + i = is B equations

DEVRE DENKLEMLERİ

1 2 3 j B

12

i

N

branches

nodes (+1, -1, 0)

{

Aij = +1 if node i is terminal + of branch j-1 if node i is terminal - of branch j0 if node i is not connected to branch j

DEVRE DENKLEMLERİ

Sparse Table Analysis (STA)Brayton, Gustavson, Hachtel

Modified Nodal Analysis (MNA)McCalla, Nagel, Roher, Ruehli, Ho

DEVRE DENKLEMLERİ

1. Write KCL: Ai=0 (N eqns)

2. Write KVL: v -ATe=0 (B eqns)

3. Write BCE: Kii + Kvv=S (B eqns)

BCE (Branch Constitutive Equations)

Se

v

i

KK

AI

A

vi

T 0

0

0

0

00N+2B eqnsN+2B unknowns

N = # nodesB = # branchesSparse Tableau

Sparse Table Analysis (STA)

DEVRE DENKLEMLERİ

Avantajları:

• Herhangi bir devreye uygulanabilir.

• Giriş verisinden (Spice .cir dosyası) denklemler doğrudan elde edilebilir.

• Matris seyrek yapıda.

ProblemZaman ve bellek verimliliği için gelişmiş programlama

teknikleri ve veri yapıları gereklidir.

Sparse Table Analysis (STA)

DEVRE DENKLEMLERİR3

0

1 2

R1

G2v3

R4Is5

1. KCL: Ai=0

2. BCE: Kvv + i = is i = is - Kvv A Kvv = A is

3. KVL: v = ATe A KvATe = A is

Yne = ins

52

1

433

3

2

3

2

10

111

111

sie

e

RRR

RG

RG

R

Nodal Analysis (NA)

Nodal Matrix

Spice input format: Rk N+ N- Rkvalue

kk

kk

RR

RR

11

11

N+ N-

N+

N-

N+

N-

iRk

sNN

k

others

sNN

k

others

ieeR

i

ieeR

i

1

1KCL at node N+

KCL at node N-

Direnç referans düğümüne bağlı ise ne olur?

….Sadece köşegenekatkıda bulunur.

DEVRE DENKLEMLERİResistor “Stamp”

DEVRE DENKLEMLERİ

Spice input format: Gk N+ N- NC+ NC- Gkvalue

kk

kk

GG

GG

NC+ NC-

N+

N-

N+

N-

Gkvc

NC+

NC-

+

vc

-

sNCNCkothers

sNCNCkothers

ieeGi

ieeGi KCL at node N+

KCL at node N-

VCCS “Stamp”

DEVRE DENKLEMLERİ

Spice input format: Ik N+ N- Ikvalue

k

k

I

I

N+ N-

N+

N-

N+

N-

Ik

Current source “Stamp”

DEVRE DENKLEMLERİ

How do we deal with independent voltage sources?

ikl

k l+ -

Ekl

klkl

l

k

Ei

e

e

011

1

1k

l

Modified Nodal Analysis (MNA)

• ikl cannot be explicitly expressed in terms of node voltages it has to be added as unknown (new column)

• ek and el are not independent variables anymore a constraint has to be added (new row)

DEVRE DENKLEMLERİ

ik

N+ N-+ -

Ek

Spice input format: ESk N+ N- Ekvalue

kE

0

00 0 1

0 0 -1

1 -1 0

N+

N-

Branch k

N+ N- ik RHS

Voltage Source “Stamp”

DEVRE DENKLEMLERİ

How do we deal with independent voltage sources?

Augmented nodal matrix

MSi

e

C

BYn

0

Some branch currents

MSi

e

DC

BYn

In general:


DEVRE DENKLEMLERİ

CCCS and CCVS “Stamp”

DEVRE DENKLEMLERİ

Step 1: Write KCLi1 + i2 + i3 = 0 (1)-i3 + i4 - i5 - i6 = 0 (2)i6 + i8 = 0 (3)i7 – i8 = 0 (4)

0

1 2

G2v3

R4Is5R1

ES6

- +

R8

3

E7v3

- +4


DEVRE DENKLEMLERİ

Step 2: Use branch equations to eliminate as many branch currents as possible1/R1·v1 + G2 ·v3 + 1/R3·v3 = 0 (1)- 1/R3·v3 + 1/R4·v4 - i6 = is5 (2)i6 + 1/R8·v8 = 0 (3)i7 – 1/R8·v8 = 0 (4)

Step 3: Write down unused branch equationsv6 = ES6 (b6)v7 – E7·v3 = 0 (b7)

0

1 2

G2v3R4

Is5R1

ES6

- +

R8

3

E7v3

- +4


DEVRE DENKLEMLERİ

Step 4: Use KVL to eliminate branch voltages from previous equations1/R1·e1 + G2·(e1-e2) + 1/R3·(e1-e2) = 0 (1)- 1/R3·(e1-e2) + 1/R4·e2 - i6 = is5 (2)i6 + 1/R8·(e3-e4) = 0 (3)i7 – 1/R8·(e3-e4) = 0 (4)(e3-e2) = ES6 (b6)e4 – E7·(e1-e2) = 0 (b7)

0

1 2

G2v3

R4Is5R1

ES6

- +

R8

3

E7v3

- +4


DEVRE DENKLEMLERİ

0

6

0

0

0

001077

000110

1011

00

0111

00

0100111

0000111

5

7

6

4

3

2

1

88

88

433

3

2

3

2

1

ES

i

i

i

e

e

e

e

EE

RR

RR

RRR

RG

RG

R

s

MSi

e

C

BYn

0

0

1 2

G2v3

R4Is5R1

ES6

- +

R8

3

E7v3

- +4


DEVRE DENKLEMLERİ

Avantajları

• MNA yöntemi herhangi bir devreye uygulanabilir.

• Giriş verisinden (Spice .cir dosyası) denklemler doğrudan elde edilebilir.

• MNA yöntemi ile elde edilen matris Yn matrisine yakındır.

Sınırlamalar

• Bazen anaköşegende sıfırlar olur ve temel minörler tekil olabilir.


DEVRE DENKLEMLERİ

I51Adc

R2

1k

R3

1k

0

V4

10Vdc R1

1k R1 1 0 1kR2 1 2 1kR3 2 0 1kV4 1 0 DC 10VI5 2 0 DC 1A

𝐺1 + 𝐺2 −𝐺2 1−𝐺2 𝐺2 + 𝐺3 01 0 0

𝑣𝑑1𝑣𝑑2𝑣𝑑3

=0110

kk

kk

RR

RR

11

11

N+ N-

N+

N-

N+

N-

iRk

k

k

I

I

N+ N-

N+

N-

N+

N-

Ik

ik

N+ N-+ -

Ek

kE

0

00 0 1

0 0 -1

1 -1 0

N+

N-

Branch k

N+ N- ik RHS

DEVRE DENKLEMLERİ

SPICE historyProf. Pederson with “a cast of thousands”• 1969-70: Prof. Roher and a class project

• CANCER: Computer Analysis of Nonlinear Circuits, Excluding Radiation

• 1970-72: Prof. Roher and Nagel• Develop CANCER into a truly public-domain, general-purpose circuit simulator

• 1972: SPICE I released as public domain• SPICE: Simulation Program with Integrated Circuit Emphasis

• 1975: Cohen following Nagel research• SPICE 2A released as public domain

• 1976 SPICE 2D New MOS Models

• 1979 SPICE 2E Device Levels (R. Newton appears)

• 1980 SPICE 2G Pivoting (ASV appears)

Circuit Simulation

Simulator:Solve dx/dt=f(x) numerically

Input and setup Circuit

Output

Types of analysis:

– DC Analysis

– DC Transfer curves

– Transient Analysis

– AC Analysis, Noise, Distorsion, Sensitivity

Program Structure (a closer look)

Numerical Techniques:

– Formulation of circuit equations

– Solution of linear equations

– Solution of nonlinear equations

– Solution of ordinary differential equations

Input and setup Models

Output

Formulation of Circuit Equations

Circuit withB branches

N nodes

Simulator

Set ofequations

Set ofunknowns

Referanslar

1. Vedat Tavşanoğlu, ‘Devre Teorisi Ders Notları’, 2005.

2. Prof. Alberto Sangiovanni-Vincentelli, Instructor: Alessandra Nardi ‘Computer-Aided Verification of Electronic Circuits and Systems’, 2002.

ehm6307-bİlgİsayar desteklİ devre analİzİ

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