## ECE 209: Circuits and Electronics Laboratory

### Laboratory 1: Introduction to the Digital Oscilloscope and Function Generator

As discussed in the course policies, all pre-laboratory assignments are individual assignments; they are NOT to be submitted by a group. You may discuss the assignment with other classmates, but the work you turn in to me should be your own and reflect your personal comprehension of the laboratory material. Do NOT split pre-lab work up among several people; each student should complete the pre-laboratory assignment in its entirety and should provide a unique submission to me at the beginning of the class.

INDIVIDUAL pre-laboratory assignment (out of 100 points): (due from each student at the beginning of class)

1. (50 points) Use Equation (2) from the second exercise of the laboratory experience to verify the RMS values of the square, sinusoidal ("sine"), triangle, and sawtooth ("ramp") waves. The expected values are shown as Vrms on each of the graphs shown in the lab book’s exercise. In particular,
• Vrms = A/sqrt(2) for a (symmetric) sine wave.
• Vrms = A for a (symmetric) square wave.
• Vrms = A/sqrt(3) for a (symmetric) triangle wave.
• Vrms = A/sqrt(3) for a (symmetric) ramp (or "sawtooth") wave.
Some hints:
• In Equation (2), the variable T is the period of the waveform.
• Remember to square the waveform. You are integrating f2(t) and not f(t).
• Remember to scale the integral by 1/T as is shown in Equation (2).
• For the sinusoidal wave, use frequency 1/T so that f(t) = A sin(2π t/T).
• Integrate the other three waveforms in pieces so that f(t) looks like a line on each piece. That way f2(t) is a simple quadratic on each piece.
• Make sure each piece has the correct slope and correct vertical intercept!
• In every case, the integral of f(t) from 0 to T should be zero! If your function has some nonzero average value, then you constructed it incorrectly.
• Remember that sqrt(A+B+C) ≠ sqrt(A) + sqrt(B) + sqrt(C).
We will discuss the physical significance of RMS signals in class.

2. (50 points) Use Equation (2) to verify Equation (3) from the third exercise of the laboratory experience. In particular, for the square, sinusoidal, triangle, and sawtooth waves, replace f(t) with f(t) + C where C is a constant offset that represents a non-zero average (i.e., "DC") component of f(t). You are verifying that the square of the new RMS value is C2 greater than the old RMS value. Some hints:
• Remember that (f(t)+C)2 = f2(t) + 2 f(t) C + C2.
• Remember to scale the integral by 1/T as is shown in Equation (2).
• Complete this exercise for each of the four waveforms.

3. BONUS (10 points): Give a strong quantitative mathematical argument (i.e., a rigorous proof) that Equation (3) holds for any integrable periodic function f(t) with period T. Some hints:
• Let f(t) = g(t) + C where C is the average value of f(t) and g(t) is a version of f(t) with zero average.
• What is the integral of g(t) over one period? (remember that g(t) is periodic and has zero average)

4. BONUS (5 points): As with laboratory reports, a pre-laboratory assignment submission generated with any flavor of TeX (e.g., LaTeX) will earn the author 5% extra credit on that assignment.

We will discuss the solutions in class. Website and original documents Copyright © 2007–2010 by Theodore P. Pavlic Licensed under a CC-BY-NC 3.0 License