# csamp - c Copyright 2010 W Marshall Leach Jr Professor...

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c ° Copyright 2010. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. The Common-Source Ampli f er Basic Circuit Fig. 1 shows the circuit diagram of a single stage common-emitter ampli f er. The object is to solve for the small-signal voltage gain, input resistance, and output resistance. Figure 1: Common-source ampli f er. DC Solution (a) Replace the capacitors with open circuits. Look out of the 3 MOSFET terminals and make Thévenin equivalent circuits as shown in Fig. 2. V GG = V + R 2 + V R 1 R 1 + R 2 R GG = R 1 k R 2 V SS = V R SS = R S V DD = V + R DD = R D (b) Write the loop equation between the V GG and the V SS nodes. V GG V SS = V GS + I S R SS = V GS + I D R SS (c) Use the equation for the drain current to solve for V GS . V GS = r I D K + V TO 1

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Figure 2: Bias circuit. (d) Solve the equations simultaneously. I D R SS + r I D K +[( V GG V SS ) V TO ]=0 (e) Let V 1 =( V GG V SS ) V TO . Solve the quadratic for I D . I D = μ 1+4 KV 1 R SS 1 2 KR SS 2 (d) Verify that V DS >V GS V TO = p I D /K for the active mode. V DS = V D V S =( V DD I D R DD ) ¡ V + I D R SS ¢ = V DD V SS I D R DD Small-Signal or AC Solutions (a) Redraw the circuit with V + = V =0 and all capacitors replaced with short circuits as shown in Fig. 3. (b) Calculate g m , r s ,and r 0 from the DC solution. g m =2 p KI D r s = 1 g m r 0 = λ 1 + V DS I D (c) Replace the circuits looking out of the gate and source with Thévenin equivalent circuits as shown in Fig. 4. v tg = v i R 1 k R 2 R i + R 1 k R 2 R tg = R 1 k R 2 v te =0 R ts = R S k R 3 2
Figure 4: Signal circuit with Thévenin gate circuit.

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## This note was uploaded on 05/26/2011 for the course ECE 3050 taught by Professor Hollis during the Summer '08 term at Georgia Tech.

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csamp - c Copyright 2010 W Marshall Leach Jr Professor...

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