ELEC 226, Spring 2012
Prof. Rich Kozick

Homework 11

Date Assigned: Thursday, April 12, 2012
Date Due: Thursday, April 19, 2012

1. Reading: In the Ulaby/Maharbiz text, please study Chapter 5, sections 1 through 7.
• In Section 5-1, we will not emphasize the material on step, ramp, and pulse functions, but you will study this in ELEC 320 in the fall.
• Section 5-2 is a review of capacitors and 5-3 is a review of inductors (most of which we discussed with transformers).
• Sections 5-4 and 5-5 contain the most important material in Chapter 5.
• When you study Section 5-6 on RC op-amp circuits, you should review Chapter 4 on operational amplifiers. You might use the integrator circuit in Figure 5-38 in Lab 6.
  
  
2. Labs: We will have Lab 6 on April 16 and 17, where you will design and implement a waveform generator that will produce square, triangle, and sine waves with variable amplitude and variable frequency. I will be available in Dana 305 on April 23 - 24 and April 30 - May 1 to help with your project.
   
   
3. Please solve the following problems in Chapter 5 and submit solutions in class on Thursday, April 19. (These problems are all straightforward and the solutions are short.)

Chapter 5: Problems 10, 14, 17, 24, 28, 31. PDF file with problem statements

Note: In Problem 28, be sure to label the inductor current directions on your circuit diagram.

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 (as discussed in class on April 17). That is, the op amp output v_out(t) switches from negative to positive voltage 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 waveforms 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.