Homework 5 - ECE 2100 Homework 5 Due April 14, 2011...

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ECE 2100 Homework 5 Due April 14, 2011 Professor Alyosha Molnar Subjects: Complex power, complex conjugate power matching, transformers, op-amp circuits, non-ideal op-amps. 1) Prelab: Consider the following differentiating Op Amp circuit. a. Derive a relationship between the input voltage and the output voltage. Assume the Op Amp is ideal. b. Assume the input voltage is a triangular wave (shown below). What is the output waveform? Explain! c. Find a relationship between the frequency, f and peak-to-peak amplitude, Vpp , of the triangular wave and the peak-to-peak voltage of the output waveform. Hint: based on frequency and peak-to-peak voltage, what is the slope of the triangle wave d. Predict the output voltage peak-to-peak value if the input is driven by a 1 volt peak-to-peak, 200 Hz sine wave. 2) Prelab: consider the inverting amplifier shown. a. Assume the op-amp is ideal (Zin = , Zout = 0) but with finite gain Av. Write equations for the amplifier gain, input and output impedance as a function of A. As A gets very large, what do these converge to? 10k Vin - + Vout 0.1 μ F
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b. Now include finite input and output impedances (assume Rin = Rout = 1k ) and rewrite equations for gain, input and output impedance as a function of A. As A gets very large, what do these converge to? 3) Book problem 9.14 4) Book problem 9.16
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5) Book problem 9.42 6) Book problem 9.49 7) Book problem 9.59
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8) In applications where large amounts of electrical power are used (such as factories with large electric motors) it is common to use “3-phase” AC power, where three 60Hz sinewaves are supplied, phase split by 120º. This has a variety of benefits, such as making for simple AC motors. We will explore another benefit here. Assume power is supplied to an inductive load as shown, either using standard two phase or three phase AC power. In each case frequency is 60Hz (so what is ω ?), and all resistors and inductors are equal in value: R=10 , L=0.1H. a. For the two phase case, what is the current (as a function of time, in the form Acos( ϖ t) + Bsin( ϖ t)) through V1 and V2, each as a function of time? (hint, use super position to find currents due to each and then sum)
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Homework 5 - ECE 2100 Homework 5 Due April 14, 2011...

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