frequency response of amplifier jack ou sonoma state university
TRANSCRIPT
![Page 1: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/1.jpg)
Frequency Response of Amplifier
Jack OuSonoma State University
![Page 2: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/2.jpg)
RC Low Pass (Review)
𝑉 𝑜𝑢𝑡 (𝑆 )𝑉 𝑖𝑛 (𝑆 )
=1/(1+𝑠𝑅𝐶)
A pole: a root of the denomintor1+sRC=0→S=-RC
![Page 3: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/3.jpg)
Laplace Transform/Fourier Transform
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
(𝑠)=1/(1+𝑠𝑅𝐶)
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
( 𝑗ω)=1 /(1+ 𝑗ω 𝑅𝐶)
𝑠= 𝑗ω
)|=1/| +p|
Phase=-tan-1(/p)
p=1/(RC)
(Fourier Transform)
(Laplace Transform)
𝑗ω
-p
𝑗ω| +p|
Location of the zero in the left complexplane
𝜎
Complex s plane
![Page 4: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/4.jpg)
Rules of thumb: (applicable to a pole)Magnitude:1. 20 dB drop after the cut-off frequency2. 3dB drop at the cut-off frequencyPhase:3. -45 deg at the cut-off frequency4. 0 degree at one decade prior to the cut-frequency5. 90 degrees one decade after the cut-off frequency
![Page 5: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/5.jpg)
RC High Pass Filter (Review)
𝑉 𝑜𝑢𝑡 (𝑆 )𝑉 𝑖𝑛 (𝑆 )
=𝑠𝑅𝐶 /(1+𝑠𝑅𝐶)
A zero at DC.A pole from the denominator.1+sRC=0→S=-RC
![Page 6: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/6.jpg)
Laplace Transform/Fourier Transform
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
(𝑠)=𝑠𝑅𝐶 / (1+𝑠𝑅𝐶)
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
( 𝑗ω)= 𝑗ω𝑅𝐶 /(1+ 𝑗ω𝑅𝐶)
𝑠= 𝑗ω
)|=| |/| +p|
Phase=90-tan-1(/p)
p=1/(RC)Zero at DC.
(Fourier Transform)
(Laplace Transform)
𝑗ω
-p
𝑗ω| +p|
Location of the zero in the left complexplane
𝜎
Complex s plane
![Page 7: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/7.jpg)
Zero at the origin.Thus phase(f=0)=90 degrees.The high pass filter has a cut-off frequency of 100.
![Page 8: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/8.jpg)
RC High Pass Filter (Review)
𝑉 𝑜𝑢𝑡 (𝑆 )𝑉 𝑖𝑛 (𝑆 )
= 𝑅1𝑅1+𝑅2
1+𝑠𝑅1𝐶1+𝑠𝑅12𝐶
R12=(R1R2)/(R1+R2)A pole and a zero in the left complex plane.
![Page 9: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/9.jpg)
Laplace Transform/Fourier Transform (Low Frequency)
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
(𝑠)=𝑅1
𝑅1+𝑅21+𝑠𝑅1𝐶1+𝑠𝑅12𝐶
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
( 𝑗ω)=𝑅1
𝑅1+𝑅21+ 𝑗ω𝑅1𝐶1+ 𝑗ω𝑅12𝐶
𝑠= 𝑗ω
z=1/(RC)p=1/(R12C)
(Fourier Transform)
(Laplace Transform)
𝑗ω
-p
𝑗ω| +p|
Location of the zero in the left complexplane
𝜎
Complex s plane
| +z|
-z
At low frequencies, | +p|>| +p|.
![Page 10: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/10.jpg)
Laplace Transform/Fourier Transform (High Frequency)
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
(𝑠)=𝑅1
𝑅1+𝑅21+𝑠𝑅1𝐶1+𝑠𝑅12𝐶
𝑉 𝑜𝑢𝑡𝑉 𝑖𝑛
( 𝑗ω)=𝑅1
𝑅1+𝑅21+ 𝑗ω𝑅1𝐶1+ 𝑗ω𝑅12𝐶
𝑠= 𝑗ω
z=1/(RC)p=1/(R12C)
(Fourier Transform)
(Laplace Transform)
𝑗ω
-p
𝑗ω| +p|
Location of the zero in the left complexplane
𝜎
Complex s plane| +z|
-z
At high frequency, | +p|is almost equal to | +p|.
![Page 11: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/11.jpg)
Design
• ωz=1/R1C
• ωp=1/(R12)C
• Note that R12<R1
• If R2<<R1, ωp/ ωp=R1/R2
• Design for ωp/ ωp=1000
![Page 12: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/12.jpg)
High Frequency
![Page 13: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/13.jpg)
Examples
![Page 14: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/14.jpg)
Source Follower
![Page 15: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/15.jpg)
Device Setup
Gmoverid:
Gm=17.24 mSRS=1000 OhmsGMBS=2.8 mSCGS=62.79 fF
![Page 16: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/16.jpg)
Small Signal Parameters
Design Constraints:1. 1/(gm+gmbs)=50 Ohms2. Large R1 to minimize Q
R2=58 OhmsR1=1102 OhmsL=4.013 nH
![Page 17: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/17.jpg)
Simulation Results
![Page 18: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/18.jpg)
Current Mirror Example
![Page 19: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/19.jpg)
Gm1=201.3uSGM3=201uSCGS3=CGS4=306.9fFGDS4=3.348uSGDS2=5.119uSRload=118 KohmsCload=1 pF
Fp1=1.347 MHzFp2=52.11 MHzFz=104.2 MHz
![Page 20: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/20.jpg)
Magnitude
AvDC,matlab=27.52AvDC,sim=27.45
Fp1matlab=1.34MHzFp1sim=1.23 MHz
![Page 21: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/21.jpg)
Phase
![Page 22: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/22.jpg)
Transit Frequency
![Page 23: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/23.jpg)
Transit Frequency Calculation
![Page 24: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/24.jpg)
Understanding Transit Frequency
Since fT depends on VGS-VT, fT depndes on gm/ID.fT depends on L.
![Page 25: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/25.jpg)
Overdrive Voltage as a function of gm/ID
gm/ID=2/(VOV)
![Page 26: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/26.jpg)
Transit Frequency as function of gm/ID
![Page 27: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/27.jpg)
gm/gds as a function of gm/ID
![Page 28: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/28.jpg)
Trade-off of gm/gds and fT
15-20
fT
gm/gds
gm/ID
![Page 29: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/29.jpg)
Numerical Example
L=120n gm/gds fT(Hz)
gm/ID=5 12.05 84.32G
gm/ID=10 15.71 64.05G
gm/ID=15 17.19 43.94G
gm/ID=20 17.54 22.76G
gm/ID=25 17.05 0.42 G
VDS=0.6 V
![Page 30: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/30.jpg)
Numerical Example
gm/ID=20 gm/gds fT(Hz)
L=0.12um
17.54 22.7 G
L=0.18 um
29.88 12.6 G
L=0.25 um
37.35 7.96 G
L=1 um 46.00 714.4 M
L=2 um 47.26 190.3 MVDS=0.6 V
![Page 31: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/31.jpg)
gm/ID Principle
![Page 32: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/32.jpg)
Use to gm/ID principle to find capacitance
• gm/ID→(fT,I/W,gm/gds)
• fT=gm/cgg, cgg=cgs+cgb+cgd
• cgs/cgg is also gm/ID dependent.
![Page 33: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/33.jpg)
Example
• Assume gm/ID=20, L=120 nm, VDS=0.6V, I=100uA.
• fT=22.76 GHz• cgg=gm/fT=13.98 fF
• cgd/cgg=0.29→cgd=4.1 fF
• cgs/cgg=0.75 →Cgs=10.5 fF
![Page 34: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/34.jpg)
Noise
![Page 35: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/35.jpg)
Noise is not deterministic
The value of noise cannot be predicted at any time even if the past values are known.
![Page 36: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/36.jpg)
Average Power of a Random Signal
Observe the noise for a long time.
Periodic voltage to a loadresistance.
Unit: V2 rather than W.
It is customary to eliminate RL from PAV.
![Page 37: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/37.jpg)
Power Spectral Density
PSD shows how much Power the signal carriesat each frequency.
Sx(f1) has unit of V2/Hz.
![Page 38: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/38.jpg)
PSD of the Output Noise
![Page 39: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/39.jpg)
PSD of the Output Noise
![Page 40: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/40.jpg)
Output Noise
![Page 41: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/41.jpg)
PSD of the Input Noise
![Page 42: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/42.jpg)
Input Noise
![Page 43: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/43.jpg)
Noise Shaping
![Page 44: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/44.jpg)
Correlated and Uncorrelated Sources
(How similar two signals are.)
Pav=Pav1+Pav2
Superposition holds for only for uncorrelated sources.
![Page 45: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/45.jpg)
Uncorrelated/Correlated Sources
(Multiple conversations in progress)
(clapping)
![Page 46: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/46.jpg)
Resistor Thermal Noise
![Page 47: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/47.jpg)
Example
Vnr1sqr=2.3288 x 10-19
Vnr3sqr=7.7625 x 10-20
Vnoutsqr=3.1050 x10-19
![Page 48: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/48.jpg)
Analytical Versus Simulation
![Page 49: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/49.jpg)
as a function of length
![Page 50: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/50.jpg)
Corner Frequency (fco)
![Page 51: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/51.jpg)
fco as a function of length
![Page 52: Frequency Response of Amplifier Jack Ou Sonoma State University](https://reader036.vdocuments.us/reader036/viewer/2022062404/5519d1615503468b0c8b480e/html5/thumbnails/52.jpg)