NCEES Problem 126

Guys

Please explain the solution to problem 126. What is rectangular approximation?

Pete

I don't have my book. Could you explain a little? Otherwise, I'll get back tonight if nobody else does first.

benbo said:

I don't have my book. Could you explain a little? Otherwise, I'll get back tonight if nobody else does first.

Click to expand...

Benbo

The question gives you a Zener Diode with Breakdown voltage of 5.1 and is ideal. They are asking for the average value of the output voltage. Solution is Vout= 5.1/2= 2.55 if rectangular approx is used. Is this the average value of a rectangular funcion?

If I recall correctly this circuit had an AC input, so for part of the waveform the zener was conducting, so zero voltage, and part of the waveform it was in reverse breakdown so the voltage was 5.1, so the average over the entire waveform was like you said, 5.1/2. I think the "rectangular approximation" means to assume sharp lines in the output, instead of the typical diode type waveforms - so either the voltage is 5.1 or zero. Don't worry about sloping transitional voltages or anything like that. Or something like that. I'm sure you'll get a clearer explanation, if not I'll do it when I get home.

I don't have the book, but I think I remember the problem. IIRC, they give you a plot of the output voltage. It looks like a half-wave recitified sinusoid, but the beginning of each "hump" of the sinusoid is chopped off due to the biasing voltage. The average value of the output will be 1/t * the integral of the voltage over one period (t). Rather than try to integrate that waveform, they're telling you to approximate it with a square wave of the same amplitude. The average value of a square wave is just the amplitude/2 because the wave is zero for half the period.

At least, that's how I remember it. Benbo can probably give a better explanation.

I just took a look at the book. Benbo and Mudpuppy are dead on correct. All they are doing by using the rectangular approximation is blowing off integrating the edges of the wave form. When you do that, you simplify the math considerably and still get enough resolution to correctly answer the question.

Jim

Im all for blowing off Integrating. Good explanation guys.

Would the following problem be "in-bounds" for the Power exam?

find the RMS value of a sine-wave 10V peak-to-peak, chopped at 65%

Thanks

Given the sample problem discussed in this thread, I would think a question like that would be in bounds.