ee541F11HWSolutions01

ee541F11HWSolutions01 - EE 541 University of Southern...

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EE 541 University of Southern California Viterbi School of Engineering Choma Solutions, Homework #01 5 Fall Semester, 2011 U niversity of S outhern C alifornia USC Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering EE 541: Solutions, Homework #01 Fall, 2011 Due: 08/31/2011 Choma Solutions Problem #01: The model shown within the symbolic network “box” in Figure (P1) is a small signal, and therefore linear, equivalent circuit of an emitter-degenerated, common emitter amplifier. The amplifier is driven by a voltage source whose Thévenin resistance is R s , and its load termination consists of a resistance, R l in shunt with a capacitance, C l . In this problem, R s = 50 , R l = 1.2 K , R e = 120 , and C l = 300 fF . The transistor model parameters are r b = 120 , r = 3.3 K , r o = 18 K , and = 220 amps/amp . I V s R s R e r b r C l R l I r o I 2 V 2 I 1 V 1 R out R in Figure (P1) (a). Derive analytical expressions for each of the four h-parameters of the degenerated common emitter amplifier. In the network box delineated in Figure (P1), the input port current, I 1 , is identical to the branch current, I , whence the controlled current satisfies I I 1 . The hybrid h-parameters, h 11 and h 21 , are each evaluated under the condition of a short circuited output port; that is, under the condition of V 2 = 0 . With V 2 = 0 ,     o2 1 e1 2 0r I β IR I I ,   (P1-1) which leads immediately to 2 oe 2 21 1o e V=0 β rR I h 218.54 amps/amp . Ir R  (P1-2) Note that h 21 is very close to parameter because r o >> R e . Continuing with V 2 = 0 ,   1b π 1e 1 2 Vr r I I ,  (P1-3) and using (P1-2) to eliminate current I 2 in this KVL relationship,
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EE 541 University of Southern California Viterbi School of Engineering Choma Solutions, Homework #01 6 Fall Semester, 2011  2 1 11 b π oe 1 V=0 V hr r β 1rR 2 9 . 7 6K . I  (P1-4) The hybrid h-parameters, h 12 and h 22 , reflect the operating constraint, I 1 = 0 , which means that I I 1 = 0 . Accordingly, the input port voltage, V 1 , in Figure (P1) appears directly across resistance R e , while I is an open circuited branch. It follows that 1 2 22 2o e I=0 I 1 h 55.19 μ , Vr R  (P1-5) and 1 e 1 12 e R V h6 . 6 2 m V / V . R (P1-6) Parameter h 12 effectively defines the degree to which the amplifier input port is isolated from its output port. Normally, this isolation level is expressed in decibels. Thus, the I/O reverse feedback of h 12 = 6.62 mV/V is equivalent to an isolation level of –43.58 dB (20log 10 |h 12 |) . (b). Using the h-parameter expressions deduced in Part (a), derive analytical expressions for the low frequency, open loop values of voltage gain, V 2 /V s , input resistance, R in , and output resistance, R out . Using the pertinent results disclosed in Course Notes 1 , the open loop voltage gain, A vo , is 21 vo 11 s 22 l h A8 . 2 5 V / V .
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This note was uploaded on 12/22/2011 for the course EE 541 at USC.

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ee541F11HWSolutions01 - EE 541 University of Southern...

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