アナログ・デジタル電子回路基礎

FUNDAMENTALS OF ANALOG AND DIGITAL CIRCUIT

受動素子 RLC 回路の特性

Kazu. TAKASHIO

Electron Devices !  Passive devices

!  Resistor !  Capacitor !  Inductor

!  Active devices !  Diode !  Transistor

Gain and Decibel (dB) !  Gain: a measure of the ability of a two port circuit to increase the power or amplitude of a signal from the input to the output port

!  dB: a logarithmic unit of measurement in acoustics and electronics !  for Voltage gain: 20log10X !  for Electric Power gain: 10log10X

17倍 24.6dB

22倍 26.8dB

全体で 24.6 + 26.8 = 51.4dB 17倍 x 22倍 = 374倍

15倍 23.5dB

47倍 33.4dB

全体で 111.8dB 約40万倍

31倍 29.8dB

18倍 25.1dB

dB Quick Table (20log10X) !  Rough indication !  Hardly use decimals..

倍率 dB 1 0 1.4 3 2 6 5 14 10 20 20 26 50 34 100 40 1000 60

倍率 dB 1/1000 -60 1/100 -40 1/50 -34 1/20 -26 1/10 -20 1/5 -14 1/2 -6

1/1.4 (0.7) -3 1 0

Resistor (r, R, RES) Passive two-terminal electrical component that implements electrical resistance..

!  Types !  Fixed resistor !  Potentiometer !  Trimmer

!  Materials !  Carbon film resistor !  Solid resistor !  Metal film resistor !  Metal oxide film resistor !  Wirewound resistor !  Cement resistor

Capacitor (Condenser, C) Passive two-terminal electrical component used to store energy electrostatically in an electric field.. !  Holding charge on its facing surfaces !  Reservoir temporally pooling and discharging !  Blocking DC, but passing AC (Capacitive Reactance) !  The more AC frequency is raised, the more the capacitive reactance goes down..

Inductor (Coil, L) Passive two-terminal electrical component which resists changes in electric current passing through it.. !  Passing DC, but resisting AC (Induced Reactance) !  The more AC frequency is raised, the more the induced reactance goes up..

Phase !  Phase: Position and distance between two wave signals

!  Be shifted by the presence of impedance in an electric circuit signals pass through..

x

位相が x だけずれている （x だけ進んでいる）

0 0

Impedance !  Resistance of a circuit depending of the frequency of an electric signal wave

!  Represented as a complex quantity, where the real part is the resistance and the imaginary part is the reactance..

!  Z = R + jx !  in an Inductor: jx = jωL !  in a Capacitor: jx = 1/jωC = -j/ωC !  ω = 2πf !  tanφ = x/R

インピーダンス Z

実数 r （抵抗）

虚数 j （リアクタンス）

R

x

2R +2x

コイル コンデンサ

φ ？？？

Impedance !  Inductor

!  Capacitor

コイル

コンデンサ

Simulation of a RLC Circuit !  Impedances of C1 and L1 are 1kΩ at 1kHz..

!  C1：(2π･1kHz･159nF)-1 !  L1：2π･1kHz･159mH

RLC Circuit: DC Analysis (DC Sweep) !  Simulation conditions

!  MacOS X: Right click on the schematic > Draft > SPICE directive 　> Right click in the text field > Help me edit.. > Analysis Cmd.

!  Win: Right click > Edit Simulation Cmd.

RLC Circuit: AC Analysis !  Linear small-signal frequency domain analysis

!  Output: Voltage gain and phase variation !  Analysis Cmd. (Win：Edit Simulation Cmd.) > AC Analysis !  Frequency axis: logarithmic [Octave, Decade]，linear [Linear]

RLC Circuit: AC Analysis !  Impedance

!  ZC = 1 / (2π x f x C) ... V(l): Low-pass filter !  ZL = 2π x f x L ... V(c): Hi-pass filter

RLC Circuit: Transient Analysis !  Analyzing variability over time (like an oscilloscope view)..

!  AC power source: SIN（0 1 1kHz 0 0 0） !  Stop Time：3m，Time to Start ..: 0，Max Timestep Size：3u !  Impedances of R1, C1 and L1: ZR ≒ ZC ≒ ZL（1kΩ）

RLC Circuit: Transient Analysis !  Detail analysis

!  Voltage wave at R2：V(in) - V(c) ([Add Trace] icon) !  Add new graph: Menu > Add Plot Pane !  Why the V(c) getting 0.7 V(in) rather than the half of it?

Exercise !  Simulate the resonance characteristic of the RLC circuit..

!  Step analysis: .step param Rv list 100 316 1k 1.41k 2k

Exercise !  Fix the R1 to 100Ω and use sine-signal waves..

!  Transient analysis: .trans 0 50m 0 5u !  Voltage between both ends of the L1: V(rl) - V(out)

!  Discuss why the gain was increased 20dB at R1 = 100Ω?

!  Submit to.. !  SFC-SFS

!  Deadline.. !  9th Oct. !  23:59

!  Hints.. !  Resonance

frequency