6.012 Recitation 22: CS Amplifier Frequency Response

Recitation 22 CS Amplifier Frequency Response 6.012 Spring 2009 Recitation 22: CS Amplifier Frequency Response Yesterday, we discussed the frequency response of a CE Amplifier, using the following methods. Vout • Full analysis (using model Analysis to derive ) Vs • Miller approximation • Open circuit time constant technique Today we will look at the frequency response of CS Amplifier using 2-3. Small signal equivalent circuit model Low frequency voltage gain (ignoring the two capacitors) Vout = −gm Rout where Rout = γo ||γoc ||RL Vs Vout   = Vs , Vout = −gm Rout Vgs =⇒ = −gm Rout ) Vs Av,LF = (∵ Vgs 1 Recitation 22 CS Amplifier Frequency Response 6.012 Spring 2009 Miller Approximation  CM = Cgd (1 − AvCgd ) = Cgd (1 + gm Rout ) Cgd is in the position between input and output  Vout = −gm Vgs · Rout Zc Vgs = · Vs , where Zc = impedance of 2 capacitors (Cgs & Cin ) in parallel Zc + Rs 1 Zc = jw(Cgs + CM ) 1/jw(Cgs + CM ) 1 = Vgs = Vs · Vs 1/jw(Cgs + CM ) + Rs 1 + Rs (jw(Cgs + CM ))  gm Rout · Vgs 1 Vout  ∴ = − = −gm Rout Vs 1 + jwRs (Cgs + CM ) Vs 1 1 w3dB = =  )) Rs (Cgs + CM ) Rs (Cgs + Cgd (1 + gm Rout To compare with CE Amplifier, w3dB =  (C Rin π 1  )) + Cμ (1 + gm Rout Open Circuit Time Constant Analysis Assumptions 1. No zeros (or zeros can be ignored) 2. One dominant pole ( τ11  1 1 τ2 , τ3 ···) Procedures 1. Open circuit all capacitors 2  = Rs ||γπ Rin Recitation 22 CS Amplifier Frequency Response 6.012 Spring 2009 2. Turn off all independent sources, find Thevenin resistance for each capacitor 3. Sum up the RTH · Ci =⇒ b1 =  i Ci RTHi , w3dB  1 b1 RTH1 = Rs Vgs Vt + Vgs , it = gm Vgs +  Rs Rout Vt + (−Rs · it ) = gm (−Rs · it ) +  Rout  = (−gm Rout · Rs − Rs ) · it + Vt it = − =⇒ it  it · Rout   + Rs (1 + gm Rout )) Vt = it (Rout Vt   RTH2 = = Rout + Rs (1 + gm Rout ) it =⇒ b1 = Cgs · RTH1 + Cgd · RTH2 w3dB   + Rs (+gm Rout )) = Cgs · Rs + Cgd · (Rout 1 1  =  )) + R b1 Rs (Cgs + Cgd (1 + gm Rout out · Cgd This is actually also the result if we do full analysis 3 Recitation 22 CS Amplifier Frequency Response 6.012 Spring 2009 Miller + OCT RTH = Rs  =⇒ b1 = (Cgs + CM ) · RTH = Rs (Cgs + CM ) = Rs (Cgs + Cgd (1 + gm Rout )) 1 w3dB =  )) same as the Miller approximation analysis, but a lot easier Rs (Cgs + Cgd (1 + gm Rout The comparison of wT (or fT ) & w3dB fT = w3dB = 1 gm 2π Cgs + Cgd 1  )) + R C Rs (Cgs + Cgd (1 + gm Rout out gd  , &A fT is intrinsic to the device, while with w3dB we have the effect of Rs , Rout v,LF . Do not need more gain than really needed. 4