EECS 210________________________PROBLEM SET #11_______________________Winter 2001

ASSIGNED: April 06, 2001. Read: Sections 15.1-15.3 of text. Replace "s" with "jw" everywhere.
DUE DATE: April 13, 2001. In Lab Book: Read the Audio Lab. No Pre-labs or Post-labs for it.
    THIS WEEK: More Bode plots and active (using op-amp) filter circuits. LAST SET.
  1. Text #14.26. Now you do for this notch filter what we did for the series RLC.
    Remember that Q=(resonant frequency)/(3 dB bandwidth of peak or dip) in (f).
  2. Text #14.28. Now apply your results from #14.26 above to design a notch filter.
  3. Text #15.3. ALSO: Sketch the Bode magnitude plot using the following element values:
    R1=10 Ohms, R2=1000 Ohms, C1=C2=10-6 F. Use Matlab only to check your answer.
  4. The Bode plot of a series RLC circuit (see Fig. 14.19) has a resonant peak at 100krad/sec with
    bandwidth 4krad/sec. If the impedance at resonance is 1000 Ohms, compute R, L, C and Q.
  5. A simple power supply (like your calculator AC adapter) uses a transformer and diodes
    to generate the rectified sine wave VI(t)=(19.7)|sin(377t)| (period=1/120 sec). This is fed
    into a RC lowpass filter with R=2 Ohms and C=0.00663 F. The output is called VO(t).
    1. Compute the Fourier series expansion of VI(t). HINT: see the inside back cover of text.
    2. Compute gain and phase of the transfer function of the RC lowpass filter. HINT: Use f.
    3. Compute the Fourier series expansion of VO(t) (provide an analytic expression). T=1/120!
    4. Using Matlab, plot VO(t) and VI(t) on same plot for 0 < t < 0.1sec. How big is the ripple?