lect. 10: pole, zero, bode plot (razavi 11.1) frequency...
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Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot (Razavi 11.1)
Frequency response is an important element of circuit/system characteristics
What determines frequency responses of MOS amplifiers?
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
- How do we express frequency-domain characteristics of circuits?
Transfer functions in s-domain (Laplace Transform)
( )H s
1( )1
H jj RC
We are often interested in the sinusoidal steady-state response s j
( )( )
out
in
V sV s
1 /1 /
sCsC R
11 sRC
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
- How do magnitude and phase of H (j) change as frequency changes?
1( )1
H jj RC
2
1( )1 ( )
H jRC
Magnitude:
1( ) tanH j RC
Phase: ( ) vs logH j
1RC
1020 log ( ) (dB) vs logH j
1RC
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
Bode Plots
Named after Hendrik Bode (1905 – 1982), an American engineer who specialized in control theory
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
In general, linear systems (electronic circuits included) are characterized by multiple poles and zeros
1 20
1 2
1 1( )
1 1
z z
p p
s s
H s As s
Frequency response can be determined by pole, zero identification and 'addition' of each pole and zero response in log scale
Bode plot?
Zeros:
Poles:
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
H(s) = s
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
H(s) = 1/s
x
1/
-90o
( )H j
( )H j
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
( ) 1z
sH s
<< z: Does not change much with
>> z : Proportionally increase with ,
( ) 1z
sH s
Magnitude
Phase
<< z : 0
>> z : 90 deg
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
1( )1
p
H s s
<< p: Does not change much with
>> p : Proportionally decrease with ,
Magnitude
Phase
<< p : 0
>> p : - 90 deg
1( )1
p
H s s
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
1 2
1 2
( ) , 1 1( )( )S F
S F
sH s R C R Cs s
R C R C
1 2
1 1log ( ) log log log1 1( ) ( )S F
H s ss s
R C R C
1 2
1 1( ) 1 1( ) ( )S F
H s ss s
R C R C
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
- Bode Plot for MOS circuit (Ignoring MOS frequency response, = 0)
Electronic Circuits 2 (17/1) W.-Y. Choi
Lect. 10: Pole, Zero, Bode Plot
- Homework: Determine magnitude and phase Bode plots for small-signal voltage gain (Vout/Vin). Ignore the frequency response of M1. Assume = 0, the input pole frequency is lower than the output pole and zero frequencies, and all pole zero frequencies are well separated.