CE Amplifier High Frequency Analysis August 20, 2014 1 High Frequency Analysis Models include parasitic capacitances: C gd G D rd C gs S g m vgs S Cµ B C rπ vπ rO Cπ g m vπ E E small-signal incremental model PARASITIC CAPS LIMIT GAIN AT HIGH FREQS. 1 Summary of the open-circuit time-constant method 1. Replace all coupling and bypass caps by shorts 2. Select one parasitic cap; call it CH1 3. Replace all other parasitic caps by open circuits 4. Find resistance seen by CH1 ; call it RH1 5. High frequency pole associated with CH1 is ωH1 = 6. Repeat above steps for each parasitic cap 1 1 CH1 RH1 7. Find equivalent high frequency cutoff ω H = ∑n 1 1 i=1 ωHi 2 Amplifier analysis VCC RC R1 CC2 CC1 RTH vS R2 RE CE RL At high frequencies RTH rπ RB vS Cµ B vπ RB=R1||R2 Resistance seen by Cπ Cπ C RLL=RC||RL g m vπ E Rπ = rπ || RB || RT H Resistance seen by Cµ itest vtest Is this correct? Find Rµ . Resistance seen by Cµ RB||RTH||rπ vπ Rµ g m vπ RLL=RC||RL itest vtest RB||RTH||rπ vπ Rµ g m vπ RLL=RC||RL vπ = itest (RB || RT H || rπ ) Applying KVL on the outher loop yields vtest = vπ + (itest + gm vπ )RLL = itest (RB || RT H || rπ ) +(1 + gm (RB || RT H || rπ ))itest RLL or vtest itest = RB || RT H || rπ + RLL +gm (RB || RT H || rπ )RLL Rµ = 2 Miller Theorem Miller’s theorem provides a basis for a simplified analysis of the CE configuration. Y=sC iIN iOUT vin Am Assume that Am = vout vOU T ≪ −1 vIN is independent of Y = sC. Use vOU T = Am vIN , vIN = vOU T /Am . Input: iIN = Y (vIN − vOU T ) = sC(1 − Am )vIN = sCIN vIN i.e. from the input C looks like a bigger capacitor C(1 − Am ). Output: iOU T = Y (vOU T − vIN ) 1 = sC(1 − )vOU T = sCOU T vOU T Am i.e. from the output C looks like a capacitor C(1 − 1 ) Am ≈ C. vIN vOUT Am CIN COUT To apply Miller’s Theorem, make sure that • Am is negative • Am is real, i.e. load is resistive 3 Unity Gain Frequency Device manufacturer specify the unity-gain frequency fT and Cµ . You must calculate Cπ from these values, so an appropriate relationship is needed. Due to the presence of the parasitic capacitors, the transistor’s β = ic /ib is a function of frequency. The unity-gain frequency fT is the frequency at which the transistor’s β = 1. Cµ ic ib ib Zb rπ ic vπ Cπ ic = gm vπ − vπ sCµ vπ = ib × Zb g m vπ 1 1 || sCπ sCµ 1 = 1 + sCπ + sCµ rπ rπ = 1 + srπ (Cπ + Cµ ) Zb = rπ || β(s) = ic ib gm rπ − srπ Cµ 1 + srπ (Cπ + Cµ ) β0 ≈ 1 + srπ (Cπ + Cµ ) = Midband β ≡ β0 = gm rπ β has a pole at ωβ = 1 rπ (Cπ + Cµ ) Unity-gain frequency fT f at which | β(s) |= 1 β02 = 1 + ωT2 ωβ2 √ ωT = ωβ β02 − 1 ≈ β0 ωβ Data sheet often specifies fT and Cµ ; Cπ can then be found from above equations.