Measuring voltage controlled by an SCR

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mull982

Senior Member
We do a similar process to get the RMS voltage, but we have to square the voltage first (RMS stands for root-mean-squared). So we have the integral of sin^2 (x) from 0 to pi/4 and from 3pi/4 to pi. We then get the average of that (divide by 2 pi again), and finally we take the square root to get our answer.

Steve

I know that to find RMS voltage from peak voltage we use Vp /sqrt(2). When finding RMS from a function though it looks like we square the function?
 

Besoeker

Senior Member
Location
UK
So with this can we assume that when chopping first and last quarter of pos half cycle then RMS voltage will be aprox 1/4 of full waveform? And have we then confirmed that this 1/4 voltage will produce 1/16th power lin load? I'm still a bit confused.
The 0.213 calculated is 0.213 of the peak voltage or about 0.301 times the full cycle rms.
Power for a resistive load is just over 9% of what it would be if the full voltage was applied over the whole cycle.
 

steve66

Senior Member
Location
Illinois
Occupation
Engineer
I know that to find RMS voltage from peak voltage we use Vp /sqrt(2). When finding RMS from a function though it looks like we square the function?

Yes, to find the RMS:

1. Square the function
2. Then find the mean or average. We do this by taking the integral of the function over one cycle, and then dividing by the period of the cycle.
3. Take the square root of the average.

For a normal sine wave, we can use the same process to prove that the RMS value is the Vp/sqrt (2). We should be able to use the equation Besoeker posted {1- (sin 2x)/2} between the limits of 0 and 2*pi, and divide by the period of 2*pi to get 1/sqrt (2).

i must admit, I can't quite get the math to work our right the first time through it.

Steve
 

Smart $

Esteemed Member
Location
Ohio
...

i must admit, I can't quite get the math to work our right the first time through it.
Yeh, my calculus is too rusty to even attempt it ;)

An alternative non-calculus method is to use what I call the "statistical analysis method"...

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Fairly easy to do in Excel. Link. I used 1000 data samples over the period of one cycle. Once opened, scroll or jump to bottom for calculation. If you want to check/calculate SCR waveforms, simply enter 0's in the DATA column for the angles when the SCR is not triggered.

PS: Link is to file uploaded to Windows Live's SkyDrive. In the past, they have been known to change URL's to files. If in the future the above link doesn't work and you want to download it, PM me to that effect.
 
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Besoeker

Senior Member
Location
UK
Yeh, my calculus is too rusty to even attempt it ;)

An alternative non-calculus method is to use what I call the "statistical analysis method"...
I agree.
The waveforms I posted earlier were from a *.xls spreadsheet.
I also used that as a means of checking the values I got by integration.
 

rattus

Senior Member
Formula:

Formula:

This is the formula for a single active interval:

Vrms/Vpk = sqrt[x2/4pi - sin(2*x2)/8pi - x1/4pi + sin(2*x1)/8pi]

where x2 and x1 are the upper and lower limits of integration.

Example:

Let x1 and x2 be 0 and 2pi respectively, then

Vrms/Vpk = 1/sqrt(2) = 0.707

For multiple active intervals, the results of the integrations are summed before the square root is taken.

This formula is easily done in a spreadsheet.
 
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