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Small Signal Circuit for a Common Source Amplifier

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Small Signal Circuit for a Common Source Amplifier 3. Fundamental amplifier configurations & Elementary R forms Sedra & Smith Sec. 5.6 (S&S 5th Ed: Sec. 4.7) ECE 102, Fall 2012, F. Najmabadi Voltage Amplifier Model Input Resistance: Ri = vi/ii Voltage gain: Av = vo/vi with load Open-loop gain: Avo = vo/vi with no load Output resistance: Ro (resistance seen between output terminals with vi= 0 ) v R i = i vsig Ri + Rsig vo RL = Av = Avo ⋅ vi RL + Ro vo Ri RL = ⋅ Avo ⋅ vsig Ri + Rsig RL + Ro F. Najmabadi, ECE102, Fall 2012 (2/23) Fundamental MOS Amplifier Configurations We are considering only signal circuit here! There are only FOUR single-transistor MOS Amplifier Configuration F. Najmabadi, ECE102, Fall 2012 (3/23) Possible MOS amplifier configurations Common-Source Common-Gate Common-Drain Same as Common Gate Common-Source with Rs (vi does not change) Not Useful F. Najmabadi, ECE102, Fall 2012 (4/23) PMOS configurations are the same as NMOS Common-Source Common-Gate Common-Drain Since PMOS has the same signal model, configurations and results are exactly the same F. Najmabadi, ECE102, Fall 2012 (5/23) Textbook includes RD in its analysis Small Signal Circuit for a Common Source Amplifier Textbook: Textbook is inconsistent. It includes RD for common source and common gate but does not include RS in common drain. Note RD is parallel to RL. Lecture: To avoid confusion, I am using only one resistor, R’L, which is the equivalent of all resistors in the drain circuit (e.g., for the above circuit, R’L = R L || RD ) F. Najmabadi, ECE102, Fall 2012 (6/23) Common Source Configuration (Gain) Signal Circuit: vo = −gmvgs (ro || RL′ ) vo Av = = −gm (ro || RL′ ) vi Avo = −gmro Small Signal Circuit Relevant circuit for with MOS SSM Gain calculation F. Najmabadi, ECE102, Fall 2012 (7/23) By KCL Common Source Configuration (Ri) Small Signal Circuit with MOS SSM Relevant circuit for Ri calculation ii = 0 vi Ri = = ∞ ii F. Najmabadi, ECE102, Fall 2012 (8/23) Common Source Configuration (Ro) Small Signal Circuit with MOS SSM Relevant circuit for Ro calculation (set vi = 0) Current source becomes open circuit Ro = ro F. Najmabadi, ECE102, Fall 2012 (9/23) Common Source with Source Resistor Signal Circuit: Small Signal Circuit with MOS SSM Input Resistance vi ii = 0 ⇒ Ri = = ∞ ii F. Najmabadi, ECE102, Fall 2012 (10/23) Common Source with Source Resistor (Gain*) Relevant circuit for Gain calculation Node voltage method: v = v − v v g r R′ gs i S A = o = − m o L − v + + + ′ Node vS vS vo vi ro (1 gmro )R S RL vS + − gm (vi − vS ) = 0 RS ro gm RL′ − Av ≈ − Node vo vo vS + + ′ vo + + gm (vi − vS ) = 0 1 gm R S RL / ro RL′ ro Avo = −gmro F. Najmabadi, ECE102, Fall 2012 (11/23) * Text book ignore ro Common Source with Source Resistor (Ro*) set vi = 0 Attach vx and compute ix Ro = vx /ix Node voltage method: vgs = −vS − Node vS vS vx vS + − gm (−vS ) = 0 RS ro v v S = x 1 ix 1 RS ro + (1+ gmro )RS ≡ = Ro vx ro + (1+ gmro )RS vS vx ix = = RS ro + (1+ gmro )RS Ro = ro + (1+ gmro )RS F. Najmabadi, ECE102, Fall 2012 (12/23) * Text book ignore ro Common Gate Configuration Signal Circuit: Small Signal Circuit with MOS SSM F. Najmabadi, ECE102, Fall 2012 (13/23) Common Gate Configuration (Gain*) Node voltage method: v = −v gs i v 1+ g r v v − v A = o = m o (r || R′ ) o + o i + g (−v ) = 0 v o L Node vo m i vi ro RL′ ro ′ v 1+ g r Av ≈ gm (ro || RL ) o = m o v ′ i ro || RL ro Avo ≈ gmro F. Najmabadi, ECE102, Fall 2012 (14/23) Common Gate Configuration (Ri and Ro*) Input Resistance KVL: vi = (ii +gmvgs )ro + ii RL′ vi (1+ gmro ) = ii (ro + RL′ ) vi ro + RL′ Ri = = ii 1+ gmro 1 RL′ Ri ≈ + gm gmro Output Resistance (set vi = 0) Current source becomes open circuit Ro = ro F. Najmabadi, ECE102, Fall 2012 (15/23) * Text book ignore ro Common Drain Configuration (Source Follower) Gain Node voltage method: vgs = vi − vo v v o + o − − = Node vo gm (vi vo ) 0 RL′ ro vo gmvi = + gmvo ro || RL′ gm (ro || RL′ ) Av = 1+ gm (ro || RL′ ) gmro Avo = ≈1 1+ gmro F. Najmabadi, ECE102, Fall 2012 (16/23) Common Drain Configuration (Source Follower) Input Resistance ii = 0 vi Ri = = ∞ ii Output Resistance (set vi = 0) vx vx vx ix = − gmvgs = + ro ro 1/ gm 1 1 Ro = || ro ≈ gm gm F. Najmabadi, ECE102, Fall 2012 (17/23) MOS Fundamental Amplifier Configurations (PMOS circuits are identical) Common Source Common Gate = − ′ Av gm (ro || RL ) Av = gm (ro || RL′ ) Common Source with RS Common Drain/Source Follower g R′ ′ A = − m L gm (ro || RL ) v Av = 1+ g R +R′ / r m S L o 1+ gm (ro || RL′ ) F. Najmabadi, ECE102, Fall 2012 (18/23) Elementary R Forms F. Najmabadi, ECE102, Fall 2012 (19/23) A Transistor can be configured to act as a resistor for small signals! Ex: Output resistance of a CS Amplifier ro Notation: Set vi = 0, current source becomes open circuit ro is the small-signal resistance Ro = ro between the point and ground If we connect any two terminals of a MOS, we get a two-terminal device. o For Small Signals, this two terminal device can be replaced with its Thevenin equivalent circuit. o As there is NO independent sources present, the Thevenin equivalent circuit is reduced to a resistor. F. Najmabadi, ECE102, Fall 2012 (20/23) A Transistor can be configured to act as a resistor for small signals! But, MOS should be in saturation for small signal model to work! o Connection between MOS terminals are, therefore, made through ground for signals. o In fact, one or two MOS terminals have to be connected to bias power supply to ensure that MOS is in saturation (there is an exception, see next page) Real Circuit Signal Circuit A) B) No Signal circuit MOS is NOT in saturation F. Najmabadi, ECE102, Fall 2012 (21/23) MOS Elementary R Forms (PMOS circuits are identical) ro (1+gm R) + R ∞ ≈ ro (1+gm R) r +R 1 R o ≈ + 1+ gmro gm gmro Output resistance Input resistance Input resistance of CS Amp with Rs of CG Amp of CS Amp ro Diode-connected 1 1 || ro ≈ Transistor gm gm Always in saturation! Above configurations are for Small Signal. Typically one or both grounds are connected to bias voltage sources to ensure that MOS is in saturation! F. Najmabadi, ECE102, Fall 2012 (22/23) Gain, input, and output resistances of MOS amplifiers can be found using fundamental amplifiers configurations and elementary R forms F. Najmabadi, ECE102, Fall 2012 (23/23) .
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