EE105 – Fall 2014 Microelectronic Devices and Circuits Prof. Ming C. Wu
[email protected] 511 Sutardja Dai Hall (SDH) Lecture23-Amplifier Frequency Response 1 Common-Emitter Amplifier – ωH Open-Circuit Time Constant (OCTC) Method At high frequencies, impedances of coupling and bypass capacitors are small enough to be considered short circuits. Open-circuit time constants associated with impedances of device capacitances are considered instead. 1 ωH ≅ m ∑RioCi i=1 where Rio is resistance at terminals of ith capacitor C with all other v ! R $ i R = x = r #1+ g R + L & capacitors open-circuited. µ 0 π 0 m L ix " rπ 0 % For a C-E amplifier, assuming C = 0 L 1 1 ωH ≅ = Rπ 0 = rπ 0 Rπ 0Cπ + Rµ 0Cµ rπ 0CT Lecture23-Amplifier Frequency Response 2 1 Common-Emitter Amplifier High Frequency Response - Miller Effect • First, find the simplified small -signal model of the C-E amp. • Replace coupling and bypass capacitors with short circuits • Insert the high frequency small -signal model for the transistor ! # rπ 0 = rπ "rx +(RB RI )$ Lecture23-Amplifier Frequency Response 3 Common-Emitter Amplifier – ωH High Frequency Response - Miller Effect (cont.) v R r Input gain is found as A = b = in ⋅ π i v R R r r i I + in x + π R || R || (r + r ) r = 1 2 x π ⋅ π RI + R1 || R2 || (rx + rπ ) rx + rπ Terminal gain is vc Abc = = −gm (ro || RC || R3 ) ≅ −gm RL vb Using the Miller effect, we find CeqB = Cµ (1− Abc )+Cπ (1− Abe ) the equivalent capacitance at the base as: = Cµ (1−[−gm RL ])+Cπ (1− 0) = Cµ (1+ gm RL )+Cπ Chap 17-4 Lecture23-Amplifier Frequency Response 4 2 Common-Emitter Amplifier – ωH High Frequency Response - Miller Effect (cont.) ! # • The total equivalent resistance ReqB = rπ 0 = rπ "rx +(RB RI )$ at the base is • The total capacitance and CeqC = Cµ +CL resistance at the collector are ReqC = ro RC R3 = RL • Because of interaction through 1 ω = Cµ, the two RC time constants p1 ! # rπ 0 "Cπ +Cµ (1+ gm RL )$+ RL (Cµ +CL ) interact, giving rise to a dominant pole.