![Page 1: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/1.jpg)
1
Frequency Response
(Part 1)
Dr. José Ernesto Rayas Sánchez
Most of the figures of this presentation were taken from the web site of the authors of the book:
A.S. Sedra and K.C. Smith, Microelectronic Circuits. New York, NY: Oxford University Press, 1998.
![Page 2: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/2.jpg)
2Dr. J.E. Rayas Sánchez
Frequency Response
! Introduction
! s-Domain Analysis
! The Amplifier Transfer Function
! Low Frequency Responses
! The FET and BJT Hybrid-πmodels
! High Frequency Responses
! Frequency Response by Computer Simulation
! Cascode Configuration
![Page 3: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/3.jpg)
3Dr. J.E. Rayas Sánchez
Introduction
! Frequency response analysis is crucial to amplifier´sperformance
! Exact frequency response analysis can be very complicated(CAD)
! The Time Constant Method will be used
![Page 4: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/4.jpg)
4Dr. J.E. Rayas Sánchez
s-Domain Analysis
Voltage gain as a transfer function of the complex frequency s = jω
)()()(
svsvsT
i
o≡
011
1
011
1)(bsbsbs
asasasasT nn
n
mm
mm
++++++++= −
−
−−
L
L
n is the order of the circuit (m < n)
For a stable circuit, all the roots of the denominator polynomial must have negative real parts
![Page 5: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/5.jpg)
5Dr. J.E. Rayas Sánchez
s-Domain Analysis (cont.)
Poles and Zeros
)())(()())(()(
21
21
n
mm PsPsPs
ZsZsZsasT−−−−−−=
L
L
Z1, ..., Zm are the transfer function zeros, or transmission zeros
P1, ..., Pm are the transfer function poles,transmission poles or natural modes
![Page 6: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/6.jpg)
6Dr. J.E. Rayas Sánchez
s-Domain Analysis (cont.)
First-Order Functions
0
01)(ω++=
sasasT
low-pass first-order network0
0)(ω+
=s
asT
0
1)(ω+
=s
sasT high-pass first-order network
![Page 7: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/7.jpg)
7Dr. J.E. Rayas Sánchez
Assignment
Read appendix F in the textbook, on Single Time Constant (STC) circuits
![Page 8: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/8.jpg)
8Dr. J.E. Rayas Sánchez
Bode Plots
(a pole or zero term)ωjaas +=+
22|| ω+=+ aas2)/(1|| aaas ω+=+
dB)/(1log20|| 2
dBa
aas ω+=+
)/(tan)( 1 aas ω−=+∠
![Page 9: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/9.jpg)
9Dr. J.E. Rayas Sánchez
Bode Plots (continue)
(a zero)
dB)/(1log20|| 2
dBa
aas ω+=+
![Page 10: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/10.jpg)
10Dr. J.E. Rayas Sánchez
Bode Plots (continue)
)/(tan)( 1 aas ω−=+∠
(a pole)
![Page 11: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/11.jpg)
11Dr. J.E. Rayas Sánchez
Bode Plots, an Example
)10/1)(10/1(10)( 52 ss
ssT++
=
![Page 12: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/12.jpg)
12Dr. J.E. Rayas Sánchez
Bode Plots, an Example (continue)
)10/1)(10/1(10)( 52 ss
ssT++
=
![Page 13: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/13.jpg)
13Dr. J.E. Rayas Sánchez
Assignment
Solve problems 7.1, 7.5 and 7.10 from the textbook
![Page 14: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/14.jpg)
14Dr. J.E. Rayas Sánchez
The Amplifier Transfer Function
![Page 15: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/15.jpg)
15Dr. J.E. Rayas Sánchez
The Amplifier Transfer Function (continue)
AM midband gain
ωL cutoff low frequency, 3-dB low frequency
ωH cutoff high frequency, 3-dB high frequency
Bandwidth (BW)
)Hz(LH ffBW −= )rad/sec(LHBW ωω −=
usually ωH >> ωL, BW ≈ ωH
Gain-Bandwith Product (GB)
GB = AM ωH
![Page 16: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/16.jpg)
16Dr. J.E. Rayas Sánchez
The Gain Function
)()()()()( sFsFA
svsvsA HLM
i
o ==
AM midband gainFL(s) low frequency response
FH(s) high frequency response
When ωH >> ω >> ωL, A(s) ≈ AM
When ω >> ωL, FL(s) ≈ 1
When ω << ωH, FH(s) ≈ 1
![Page 17: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/17.jpg)
17Dr. J.E. Rayas Sánchez
Low Frequency Response
)())(()())((
)(21
21
L
L
PnPP
ZnZZL sss
ssssF
ωωωωωω
++++++
=L
L
nL number of poles (or zeros) of FL(s)
then,,,,,if 121 LL ZnZPnPP ωωωωω KK>>
11
and)(
)( PLP
L sssF ωωω
≈+
≈ (ωP1 is a dominant pole)
If there is no dominant pole
)(2 222
21
222
21 LL ZnZZPnPPL ωωωωωωω +++−+++≈ KK
![Page 18: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/18.jpg)
18Dr. J.E. Rayas Sánchez
Low Frequency Response, Example
Calculate ωL for )25)(100()10()(++
+=ss
sssFL
1) ωP1 = 100 is a dominant pole, then ωL ≈ 100 rad/sec
rad/sec102)10(225100)2 222 =−+≈Lω
3) Using Bode plots... ωL ≈ 105 rad/sec
![Page 19: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/19.jpg)
19Dr. J.E. Rayas Sánchez
High Frequency Response
)/1()/1)(/1()/1()/1)(/1(
)(21
21
H
H
PnPP
ZnZZH sss
ssssF
ωωωωωω
++++++
=L
L
nH number of poles (or zeros) of FH(s)
then,,,,,if 121 LL ZnZPnPP ωωωωω KK<<
11
and)/1(
1)( PHP
H ssF ωω
ω≈
+≈ (ωP1 is a dominant pole)
If there is no dominant pole
)/1/1/1(2/1/1/11
222
21
222
21 HH ZnZZPnPP
H ωωωωωωω
+++−+++≈
KK
![Page 20: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/20.jpg)
20Dr. J.E. Rayas Sánchez
High Frequency Response, Example
Calculate ωH for F)104/1)(10/1(
10/1)( 44
5
×++−=
ssssH
1) ωP1 = 104 is a dominant pole, then ωH ≈ 104 rad/sec
rad/sec800,910/2)1016/(110/1/1)2 1088 =−×+≈Hω
3) Using Bode plots... ωH ≈ 9,537 rad/sec
![Page 21: Frequency Response · 2003-08-11 · 1 Frequency Response (Part 1) Dr. José Ernesto Rayas Sánchez Most of the figures of this presentation were taken from the web site of the authors](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e67acf14de32910f55c78eb/html5/thumbnails/21.jpg)
21Dr. J.E. Rayas Sánchez
Assignment
Solve problems 7.14, 7.21 and 7.27 from the textbook