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High voltage input question?

Transformers, peak voltage, and Vrms?

  • This is about a transformer and we are supposed to find the number of turns for the second coil. I already solved the question using the ratio equation which relates the voltages and wire turns for the primary and secondary coils using the Vrms voltage given: V2/V1=N1/N2 My question is: Would it also be correct to input the Vp (peak voltage) into the ratio equation instead of Vrms(1/sqrt2 of the peak voltage)? I noticed they give the same result, does it have to do with using the voltages at a different phase shift of the sinusoidal voltage input? When do we have to convert Vp into Vrms or vice versa?

  • Answer:

    Yes, in theory you can use the peak voltage as long as you remember that it's not RMS the next time you look at your work :) - bottom line: for a sinusoidal voltage, they are two ways of talking about the same thing, differing by a constant factor of √2. In practice, if your waveform is not a sinusoid, for example a square wave, you must allow for the high-frequency response of the transformer. In such a case, the peak and RMS values are not so simply related and the relationship varies with the frequency. For an introductory course, you're OK, but make sure that your teacher/prof knows that you know what you're doing. Q: When do you have to convert Vp into Vrms or vice versa? A: When it's clear that you need one or the other. For example, if you are writing the voltage as a function of time, you use Vp: V(t) = Vp sin(ωt + Φ) But if you are calculating the power dissipated in a resistive load, you use Vrms: P = (Vrms)²/R In transformer design you use both at different stages of the process.

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For a sine wave you should get the same result either way. Vp in, Vp out. Vrms in, Vrms out. People deal in rms voltages more than peak voltages, so the equation is written that way. The relationship between Vp and Vrms is different for non-sinusoidal waveforms, and with these (since they have high-frequency harmonics) you may also have to take into account the frequency response of the transformer (as you also would with a high enough frequency of sine wave). A clean square wave has measurable harmonics at least up through ten times the fundamental frequency. Frequency rolloff will show up as rounding of the corners.

David Beierl

The ratio is the same for Vp and Vrms since Vrms = Vp/sqrt(2) for sinusoidal waves. This is also true for other waveshapes since Vrms = kVp, where k is just dependent on the waveshape! Vrms is used because the average power use in a resistive load is Vrms^2/R allowing us to use the same familiar power relations in AC as in DC theory It is perfectly possible to construct all the relevant equations using Vp but not usually done!

Oliver

The equation you gave is correct for either peak or RMS voltages. For the transformer turn ratio there is no need to convert from one to the other.

Rick

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