EE40 Midterm 2 Spring 2006 Professor Chang Hasnain Total Time Allotted 80 minutes Total Points 100 1 20 pts Match the transfer function to the Bode plot Each transfer function matches to exactly one Bode plot Also there is no partial credit for this question a b b 1 1 1 H f H f H f 2 2 jf jf jf jf 1 1 0 5 1 100 100 100 1000 d e 1 1 H f H f 2 jf jf 1 1 100 100 Mark your answer here Magnitude Plot dB Mark your answer here Phase Plot degrees 2 35 pts The circuit schematic for a functional block known as a lead compensator is a 15 pts Let R1 10 2 ohms R2 100 2 ohms C1 100 uF and C2 100 uF Show that the transfer function of the circuit shown above is jf 1 100 H f jf 1 1000 b 12 pts In the following table write the magnitude and phase values for H f for f 100Hz f 1000Hz very low f values f 0 Hz and very high f values f infinity Hz These answers only need to be within 1 5 times the correct answer but only because of rounding errors or sketching inaccuracies that you might have Do not use the straight line approximation if it will cause your answer to be off from the exact value by more than 1 5 times f value Hz Very low f f 100 Hz f 1000 Hz Very high f 10log H w 2 ang H w c 8 pts Sketch the bode plot of this transfer function Sketch BOTH the magnitude and phase plot Make sure to label the slopes of segments the two break points of the transfer function the low frequency magnitude the nigh frequency magnitude and the highest value on the phase plot Be as accurate as you can i e do not use the straight line approximation except as a starting guide if you wish for plotting the actual transfer function 3 15 pts Find the unknown values in the circuits below For the diodes use the 0 8V On Off model If I d 0 then the diode is open or OFF If I d 0 then the diode is a 0 8V source or ON a 5 pts Find I a in the circuit below b 5 pts Find I b in the circuit below c 5 pts Let R 1 10 ohms and R 2 100 ohms Find V c in the circuit below in terms of V 1 and V 2 4 30 pts Consider the circuit shown below in which the RC time constant is very long compared to the period T of the input Vin t Use the Ideal Diode model If VD 0 then the diode is OFF and does not pass current ID 0 If ID 0 then the diode is ON and VD 0 VD is the voltage drop across the diode and ID is current through the diode VD Vout in this problem Analyze the following circuit Given Vin t Vmsin 2 T for t 0 and Vc t 0 0 a 8 pts sketch Vc t Label all key values Vc t T 2T 3T 2T 3T b 8 pts Sketch Vout t Label all key values 1 Vout t T c 8 pts Explain what is happening for different time duration d 6 pts Sketch ID t Label all key values ID t T 2T 3T
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