ee541F10HWSolutions01-02

ee541F10HWSolutions01-02 - U niversity of S outhern C...

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U niversity of S outhern C alifornia USC Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering EE 541: Solutions, Homework #01-#02 Fall, 2010 Due: 09/09/2010 Choma Solutions Problem #01: The model shown within the symbolic network “box” in Fig- ure (P1) is a linearized 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 termi- nation consists of a resistance, R l in shunt with a capacitance, C l . In this problem, R s = 50 Ω , R l = 1.2 K , R e = 120 , and C l = 300 fF . The transistor model parameters are r b = 90 , r π = 2.8 K , r o = 25 K , and β = 120 amps/amp . β I + V s R s R e r b r π 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 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 119.42 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 (P1-1) to eliminate current I 2 in this KVL relationship, 2 1 11 b π 1 V hr r β 1 r R 17.34 K . 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
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EE 541 University of Southern California Viterbi School of Engineering Choma Solutions, Homework #01-#02 8 Fall Semester, 2010 R e , while β I is an open circuited branch. It follows that 1 2 22 2o e I=0 I1 h 39.81 μ , Vr R === + (P1-5) and 1 e 1 12 e R V h 4.78 mV/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 = 4.78 mV/V is equivalent to an isolation level of –46.41 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 A hR h1 R =− = ++ 7 . 8 6 V / V . (P1-7) The open loop input resistance, R ino , is simply ino 11 Rh 1 7 . 3 4 K , == (P1-8) while the open loop output resistance, R outo , is outo 22 1 R 25.12 K . h (P1-9) (c). Using the h-parameter expressions deduced in Part (a), derive an analytical expression for the low frequency loop gain of the amplifier. Discuss the influence that the emitter degen- eration resistance, R e , has on this loop gain.
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ee541F10HWSolutions01-02 - U niversity of S outhern C...

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