midterm1_w2011_solns

# midterm1_w2011_solns - CW {5 ECE 100 Midterm Examination...

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Unformatted text preview: CW {5 ECE 100 Midterm Examination Winter 2011 This examination is closed book, you may not use any reference materials or any calculator. Be sure to show your work carefully. No credit will be given for unsupported answers. 1. Consider the parallel combination of an inductor and a capacitor. (a) Find the impedance Z1,(s) for this paraliel combination. (b) Find the resonant frequency 000 and shew that IZP(wD)l—>00. (c) Show how to design a passive RLC band-pass filter that makes use of the parallel resonance. Draw the circuit and explain your design. (d) Write the transfer function H(s) as a rational function. 2. You are asked to design a low-pass ﬁlter to meet the specs shown to the right. What order transfer function will you need if you decide to use a maximally-flat (Butterworth) approximation? The pass-band corner is —3dB at 1 Khz and the stop-band corner is —50dB at 10 Khz. 3. You need an audio circuit to boost the frequencies above 1 Khz. After some thouglﬁrou decide to use the circuit sketched to the right. You plan to use an opamp with RIN >> 1M9 and ROUT < 1009 . Its gain is A(s) : G is, where G = 2 313106. The first design step is to get the correct “ideal” transfer function. (a) Find the ideal transfer function H(s) = VOUT(s)/Vm(s) in terms of R E, and C. assuming that lAl 400. (b) Draw the Bode plot for 1H(oJ)|. (c) Find the C that will start the boost at a comer frequency of 1 Khz. The next design step is to make sure that the real circuit is stable. I (d) Write the loop gain T(s) as a rational function of s. (e) Plot the magnitude and phase of T(UJ) on a Bode Plot. (f) Find the phase margin and explain its significance. The ﬁnal design step is to modify the circuit to improve its stability. r a (g) Show how to “compensate” this circuit to make it useful in practice. CD (3“ “HQ: A: M R‘%23 [Zr- sL/ r + 321.6 z b S L f‘ at L/ H s L/e +g2Lc ...
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midterm1_w2011_solns - CW {5 ECE 100 Midterm Examination...

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