Rectifier circuit average value calculations

[cableguy]

I've been staring at these for about the last hour, wanted to start a thread on it to get some thoughts.

I was reworking the NCEES sample exam this afternoon, and bumped in to 115 again. I understand the integral and all that, but the dirty side of me wants something I can use more generically.

I then started looking at the Kaplan sample exam, which has several strange rectifier circuit questions.

I also looked at sources around the Internet, looking for that killer equation.

I came up with this:

Vaverage = (Vpeak / pi) * (cos a - cos d)

where a is the firing angle / start of the wave, and d is the zero crossing or end of the wave.

For example, for NCEES 115, this would be (1/pi) * (.707 + 1) = .543 (correct)

A complete half wave would be (1/pi) * (1+1) = .6366 (correct)

Now I start looking at the wonky Kaplan problems. I think they're doing them wrong.

On one problem (A34), they throw out the equation:

Vavg = (2/pi) Vpeak cos a

And on a three phase half wave rectifier problem (A36), they deus-ex-machina throw out the equation

Vavg = (3 sqrt(3)/2pi) Vpeak cos a

And I believe these formulas are incorrect.

I printed out this graphic

http://upload.wikimedia.org/wikipedia/en/6...ification_2.png

And drew vertical lines at the 30 degree marks. One of the Kaplan problems was to calculate the average voltage of a 3 phase half wave rectifier with a 120Vrms wave with a trigger that fires starting at 60 degrees and then triggers every 120 degrees after that.

I calculated 81 volts using my formula. They use the equation above and get 70.2 volts. I honestly have no idea where they got their equation.

Anyone have any insight on average values for rectifier pulses? Am I off my rocker?

Thanks!

 

[cruzy]

I've put off trying to study any kind of electronics. I gave it a shot, but seems like none of my reference material is leading to any answers. So hopefully I guess right on these, because I stopped giving any kind of effort into comprehension of electronics a few weeks back.

 

[GabeM]

Given Kaplan's reputation at this point, it would be easy to write Kaplan's equations off as errors.

Also, your equation only works if the waveform is a sine function. For example, it wouldn't work if the function was cosine.

 

[cableguy]

While the specifics of that statement are true, from the problems I looked at, none of them stated "you have a waveform of 120Vrms*cos(wt) - they were all 120Vrms*sin(wt) {or similar}.

Plus, we're talking average DC value. When you run a series of rectified pulses, a cosine wave looks exactly like a sine wave, but shifted 90 degrees, so the average DC value would be the same - as long as you accounted for the 90 degree shift. From what I've seen of these problems, none ask about the average DC value from t= absolute 0 to t=pi... They ask about the DC value of a pulse - pick a pulse, any pulse - and calculate the value. My formula above works for that.

 

[GabeM]

I see, you just have to make sure you set "0" at the beginning of a pulse for your equation to work.