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.**

- 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).

- Text #14.28. Now
*apply* your results from #14.26 above to *design* a notch filter.

- Text #15.3. ALSO: Sketch the Bode magnitude plot using the following element values:

R_{1}=10 Ohms, R_{2}=1000 Ohms, C_{1}=C_{2}=10^{-6} F.
Use Matlab *only* to check your answer.

- 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.

- A simple
*power supply* (like your calculator AC adapter) uses a transformer and diodes

to generate the *rectified sine wave* V_{I}(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 V_{O}(t).

- Compute the
*Fourier series expansion* of V_{I}(t). HINT: see the inside back cover of text.
- Compute gain and phase of the transfer function of the RC lowpass filter. HINT: Use f.
- Compute the
*Fourier series expansion* of V_{O}(t) (provide an analytic expression). T=1/120!
- Using Matlab,
*plot* V_{O}(t) and V_{I}(t) on same plot for 0 < t < 0.1sec.
How big is the *ripple*?