Homework 5_soln

# Homework 5_soln - ECE 2100 Spring 2010 Homework assignment...

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ECE 2100 Spring 2010 Homework assignment 5 Solution Due April 23, 2010 Covered: Chapter 10: Amplifiers and 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. Iin=C·dV in /dt. Vout=-R F Iin = -R F C·dV in /dt = -0.1ms·dV in /dt b. Assume the input voltage is a triangular wave. What is the output waveform? Explain! Output is a square wave : a triangle wave alternates slope between positive and negative 2A/T, where A is the peak-to-peak amplitude and T is the period. Thus, the output will have an alternating sign every half cycle, with equal plus and minus amplitudes. c. Find a relationship between the frequency and peak-to-peak amplitude of the triangular wave and the peak-to-peak voltage of the output waveform. Slope = +/-2A/T, and frequency f=1/T, so the peak-to-peak amplitude of Vout will be 0.1ms·4Af (4 instead of 2 because we want the output peak-to-peak) 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. V in =0.5cos(400 π t), Vout = -0.1ms·dV in /dt=-0.02 π sin(400 π t): peak-to-peak: 0.1256V 2) Consider the transformer plus full-wave rectifier shown, driven by a 120V (peak) 60Hz voltage (that is, V 1 =120V·cos(240 π t)). Assume that the diodes can be modeled as ideal except with a turn-on voltage of 0.7V. Also assume that the transformer is ideal. a. What will the peak voltage across the capacitor be? V Cmax =V2 peak -2V TO . V2=V1/6: V2 peak = 120V/6=20V, V Cmax =18.6V 10k Vin - + Vout 0.01 μ F D1 D2 D3 D4 + V1 - I 1 + V2 - 1mF 6:1

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b. If the capacitor is loaded with a 100 resistor, sketch the waveform of Vout. What, approximately, will be the difference between the minimum and maximum voltage across the capacitor (that is, what will the ripple be?) -25 -20 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 20 25 30 time, ms Voltage V2 VC -V2 Droop rate is dV C /dt = -V C /RC = -18.6V/100ms, T=16.7ms. Can estimate ripple by assuming the capacitor voltage droops during the entire half cycle of the input (actually it droops for slightly less time than that). V Cmin ~ V Cmax - V Cmax /RC·T/2 = 18.6V(1-8.33ms/100ms) = 17V: implies a ripple of about 1.6V (it will actually be less than this: more like 1.3V) c. Sketch the current waveform sourced by the voltage source V 1 . What is the maximum and minimum current, I 1 sourced? (this is hard: its only for bonus points) -0.4 -0.2 0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 30 time, ms I1, A I 1 = I 2 /6, I 2 will only be non-zero when the diodes are on, that is, when the capacitor is recharging. Recharging happens from when V2>Vc+2V TO until V2 reaches its peak . This time starts (relative to the peak) when V2-1.4V = V Cmin or about 17V (from above): if V2=20Vcos( ω
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Homework 5_soln - ECE 2100 Spring 2010 Homework assignment...

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