ELEC 226, Spring 2010
Prof. Rich Kozick

Homework 10

Date Assigned: Thursday, April 15, 2010
Date Due: Thursday, April 22, 2010 in class at 8:30 AM

1. Reading: Continue to study Chapter 7, Sections 7.1–7.4. Also, please read Sections 7.5–7.7, which are useful for the oscillator and integrator circuits that we are using in lab.
   
   
2. The reports for Lab 6 (one report per group) are due by 4 PM on Thursday, April 22. Your report may be submitted on paper or electronically as an email attachment.
   
   
3. Please solve the following problems in Chapter 7: 7.34 and 7.55.
   
   
4. The following circuit is a slightly more general version of the clock circuit from Lab 5, where R_a and R_b may be unequal. Assume that the op amp is powered so that -10 V <= v_out(t) <= +10 V, and let T denote the period of the waveform produced by the oscillator circuit.

• Find the formulas for the capacitor voltage, v_c(t), during the time intervals 0 <= t <= T/2 and T/2 <= t <= T. Assume that the circuit is in "steady-state" at time t=0, i.e., the circuit has been oscillating for a long time before t=0. Also assume that the capacitor voltage has its minimum (most negative) value at t=0.
  Your formulas will be a function of all of the resistor and capacitor values in the circuit (R, C, R_a, R_b).
• Use your results for v_c(t) to find a formula for the period, T, as a function of the resistor and capacitor values in the circuit.
• Sketch v_out(t) and v_c(t) versus time, and indicate the effects of the circuit parameters on the amplitudes and period in your plot.
• How should R_a and R_b be chosen so that v_c(t) is close to a triangle wave? Please explain based on your formulas for v_c(t).
  
  

Thank you.