Report

Frequency Response of Amplifier Jack Ou Sonoma State University RC Low Pass (Review) = 1/(1 + ) A pole: a root of the denomintor 1+sRC=0→S=-RC Laplace Transform/Fourier Transform ω (Laplace Transform) () = 1/(1 + ) Complex s plane | ω+p| = ω (Fourier Transform) (ω) = 1/(1 + ω) ω -p p=1/(RC) |(ω)|=1/| ω+p| Phase((ω))=-tan-1(ω/p) Location of the zero in the left complex plane 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 RC High Pass Filter (Review) = /(1 + ) A zero at DC. A pole from the denominator. 1+sRC=0→S=-RC Laplace Transform/Fourier Transform ω (Laplace Transform) () = /(1 + ) Complex s plane | ω+p| = ω (Fourier Transform) (ω) = ω/(1 + ω) p=1/(RC) Zero at DC. |(ω)|=| ω|/| ω+p| Phase((ω))=90-tan-1(ω/p) ω -p Location of the zero in the left complex plane Zero at the origin. Thus phase(f=0)=90 degrees. The high pass filter has a cut-off frequency of 100. RC High Pass Filter (Review) 1 1 + 1 = 1 + 2 1 + 12 R12=(R1R2)/(R1+R2) A pole and a zero in the left complex plane. Laplace Transform/Fourier Transform (Low Frequency) ω (Laplace Transform) 1 1 + 1 () = 1 + 2 1 + 12 Complex s plane | ω+p| ω | ω+z| = ω (Fourier Transform) 1 1 + ω1 (ω) = 1 + 2 1 + ω12 z=1/(RC) p=1/(R12C) -p -z Location of the zero in the left complex plane At low frequencies, | ω+p|>| ω+p|. Laplace Transform/Fourier Transform (High Frequency) ω (Laplace Transform) 1 1 + 1 () = 1 + 2 1 + 12 Complex s plane | ω+z| ω | ω+p| = ω (Fourier Transform) 1 1 + ω1 (ω) = 1 + 2 1 + ω12 z=1/(RC) p=1/(R12C) -p -z Location of the zero in the left complex plane At high frequency, | ω+p|is almost equal to | ω+p|. Design • • • • • ωz=1/R1C ωp=1/(R12)C Note that R12<R1 If R2<<R1, ωp/ ωp=R1/R2 Design for ωp/ ωp=1000 High Frequency Examples Source Follower Device Setup Gmoverid: Gm=17.24 mS RS=1000 Ohms GMBS=2.8 mS CGS=62.79 fF 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 Simulation Results Current Mirror Example 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 Magnitude AvDC,matlab=27.52 AvDC,sim=27.45 Fp1matlab=1.34MHz Fp1sim=1.23 MHz Phase Transit Frequency Transit Frequency Calculation Understanding Transit Frequency Since fT depends on VGS-VT, fT depndes on gm/ID. fT depends on L. Overdrive Voltage as a function of gm/ID gm/ID=2/(VOV) Transit Frequency as function of gm/ID gm/gds as a function of gm/ID Trade-off of gm/gds and fT fT gm/gds gm/ID 15-20 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 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 M VDS=0.6 V gm/ID Principle 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. 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 Noise Noise is not deterministic The value of noise cannot be predicted at any time even if the past values are known. Average Power of a Random Signal Periodic voltage to a load resistance. Observe the noise for a long time. It is customary to eliminate RL from PAV. Unit: V2 rather than W. Power Spectral Density Sx(f1) has unit of V2/Hz. PSD shows how much Power the signal carries at each frequency. PSD of the Output Noise PSD of the Output Noise Output Noise PSD of the Input Noise Input Noise Noise Shaping Correlated and Uncorrelated Sources Pav=Pav1+Pav2 Superposition holds for only for uncorrelated sources. (How similar two signals are.) Uncorrelated/Correlated Sources (Multiple conversations in progress) (clapping) Resistor Thermal Noise Example Vnr1sqr=2.3288 x 10-19 Vnr3sqr=7.7625 x 10-20 Vnoutsqr=3.1050 x10-19 Analytical Versus Simulation as a function of length Corner Frequency (fco) fco as a function of length