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Frequency Response of Amplifier Jack Ou Sonoma State University

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RC Low Pass (Review) A pole: a root of the denomintor 1+sRC=0S=-RC

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Laplace Transform/Fourier Transform p=1/(RC) (Fourier Transform) (Laplace Transform) -p Location of the zero in the left complex plane Complex s plane

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Rules of thumb: (applicable to a pole) Magnitude: 1.20 dB drop after the cut-off frequency 2.3dB drop at the cut-off frequency Phase: 1.-45 deg at the cut-off frequency 2.0 degree at one decade prior to the cut-frequency 3.90 degrees one decade after the cut-off frequency

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RC High Pass Filter (Review) A zero at DC. A pole from the denominator. 1+sRC=0S=-RC

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Laplace Transform/Fourier Transform p=1/(RC) Zero at DC. (Fourier Transform) (Laplace Transform) -p Location of the zero in the left complex plane Complex s plane

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Zero at the origin. Thus phase(f=0)=90 degrees. The high pass filter has a cut-off frequency of 100.

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RC High Pass Filter (Review) R 12 =(R 1 R 2 )/(R 1 +R 2 ) A pole and a zero in the left complex plane.

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Laplace Transform/Fourier Transform (Low Frequency) z=1/(RC) p=1/(R 12 C) (Fourier Transform) (Laplace Transform) -p Location of the zero in the left complex plane Complex s plane -z

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Laplace Transform/Fourier Transform (High Frequency) z=1/(RC) p=1/(R 12 C) (Fourier Transform) (Laplace Transform) -p Location of the zero in the left complex plane Complex s plane -z

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Design ω z =1/R 1 C ω p =1/(R 12 )C Note that R 12

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High Frequency

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Examples

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Source Follower

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Device Setup Gmoverid: Gm=17.24 mS RS=1000 Ohms GMBS=2.8 mS CGS=62.79 fF

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Small Signal Parameters Design Constraints: 1.1/(gm+gmbs)=50 Ohms 2.Large R1 to minimize Q R2=58 Ohms R1=1102 Ohms L=4.013 nH

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Simulation Results

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Current Mirror Example

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Gm1=201.3uS GM3=201uS CGS3=CGS4=306.9fF GDS4=3.348uS GDS2=5.119uS Rload=118 Kohms Cload=1 pF Fp1=1.347 MHz Fp2=52.11 MHz Fz=104.2 MHz

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Magnitude Av DC,matlab =27.52 Av DC,sim =27.45 Fp1 matlab =1.34MHz Fp1 sim =1.23 MHz

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Phase

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Transit Frequency

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Transit Frequency Calculation

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Understanding Transit Frequency Since f T depends on V GS -V T, f T depndes on g m /I D. f T depends on L.

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Overdrive Voltage as a function of g m /I D g m /I D =2/(V OV )

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Transit Frequency as function of g m /I D

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gm/gds as a function of g m /I D

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Trade-off of g m /g ds and f T 15-20 fTfT g m /g ds g m /I D

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Numerical Example L=120ng m /g ds f T (Hz) g m /I D =512.0584.32G g m /I D =1015.7164.05G g m /I D =1517.1943.94G g m /I D =2017.5422.76G g m /I D =2517.050.42 G VDS=0.6 V

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Numerical Example g m /I D =20g m /g ds f T (Hz) L=0.12um17.5422.7 G L=0.18 um29.8812.6 G L=0.25 um37.357.96 G L=1 um46.00714.4 M L=2 um47.26190.3 M VDS=0.6 V

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g m /I D Principle

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Use to gm/ID principle to find capacitance g m /I D (f T,I/W,g m /g ds ) f T =g m /c gg, c gg =c gs +c gb +c gd c gs /c gg is also g m /I D dependent.

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Example Assume gm/ID=20, L=120 nm, VDS=0.6V, I=100uA. fT=22.76 GHz c gg =g m /f T =13.98 fF c gd /c gg =0.29c gd =4.1 fF c gs /c gg =0.75 C gs =10.5 fF

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Noise

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Noise is not deterministic The value of noise cannot be predicted at any time even if the past values are known.

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Average Power of a Random Signal Observe the noise for a long time. Periodic voltage to a load resistance. Unit: V 2 rather than W. It is customary to eliminate RL from P AV.

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Power Spectral Density PSD shows how much Power the signal carries at each frequency. S x (f 1 ) has unit of V 2 /Hz.

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PSD of the Output Noise

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Output Noise

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PSD of the Input Noise

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Input Noise

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Noise Shaping

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Correlated and Uncorrelated Sources (How similar two signals are.) P av =P av1 +P av2 Superposition holds for only for uncorrelated sources.

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Uncorrelated/Correlated Sources (Multiple conversations in progress) (clapping)

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Resistor Thermal Noise

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Example Vnr1sqr=2.3288 x 10 -19 Vnr3sqr=7.7625 x 10- 20 Vnoutsqr=3.1050 x10 -19

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Analytical Versus Simulation

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Corner Frequency (f co )

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f co as a function of length

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Filters By combining resistor, capacitor, inductor in special ways we can design circuits that are capable of passing certain frequency while rejecting.

Filters By combining resistor, capacitor, inductor in special ways we can design circuits that are capable of passing certain frequency while rejecting.

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