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I've noticed that there is much talking about \$V_{dc}\$ in rectifiers (specifically, the half-wave rectifier) and less focus is given to \$V_{rms}\$. Why is that? I thought the RMS value was the much more important one (because it's the value of the DC signal that delivers the same power within the same time interval), but what use is the average voltage? Why do we even bother to calculate and emphasize that \$V_{dc} = \frac{V_{MAX}}{\pi}\$?

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  • \$\begingroup\$ In case the smoothing circuit uses an inductor and capacitor. \$\endgroup\$ – Andy aka Mar 14 '20 at 10:37
  • \$\begingroup\$ @Andyaka Sorry but I'm not sure I get your point.. could you please elaborate? As far as I understand, adding a capacitor will completely change the shape of the wave, so our calculation of (V_m/pi) is still useless.. \$\endgroup\$ – user401445 Mar 14 '20 at 10:55
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    \$\begingroup\$ I said using an inductor and capacitor. \$\endgroup\$ – Andy aka Mar 14 '20 at 11:21
  • \$\begingroup\$ "I've noticed that there is much talking about Vdc in rectifiers" - can you provide an example of this 'talk'? \$\endgroup\$ – Bruce Abbott Mar 16 '20 at 5:53
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Vrms is a quantity which only makes sense in the heating equivalent in a resistive load. Very few rectifier applications that I have seen have a rectifier which drives a resistive load for any heating application.

There used to be true RMS voltmeters which actually would apply the measured voltage to a resistor and would apply a DC voltage (of course using buffer amplifiers in each case) to an identical resistor which was controlled servo fashion to cause a match in the temperature rise in both resistors, and then the DC Voltage measured would be equivalent to the AC voltage (I have one of these). In this way the measured AC waveform could literally be arbitrary in shape. There are true RMS converters that do this without heaters, and add cost to a multimeter.

So I think your question is in relation to a average reading, RMS scaled readout of an AC voltage multimeter. This is a very cheap way to accomplish the RMS reading, but is only good for sinusoidal measured input, since the area under a half-sine between zero crossings is 2/π × peak and must be scaled to the .707 × peak. Any other wave shape than half wave sine output will not correspond to the 2/π.

BTW the average of a voltage is the DC voltage at the output of a lowpass filter and this is how the rectified voltage pulses are converted into a DC voltage and scaled, in the case of a sinusoid, by the ratio of 1/22 : 2/π for a cheap way to read an AC voltage as long as it is sinusoidal.

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I've noticed that there is much talking about Vdc in rectifiers (specifically, the half-wave rectifier) and less focus is given to Vrms. Why is that?

When designing a DC supply the peak and rms voltages are usually much more important. However a DC meter reads average voltage, so when measuring the rectifier output you need to know the relationship between average, rms, and peak voltage.

Average voltage is also important for calibrating an average reading AC meter (which consists of a DC meter with half wave rectifier) in the equivalent rms voltage.

As to the 'much talking' about it, I suspect it is mainly confined to basic electronics courses and multimeter usage tutorials. Few modern devices use power supplies with unfiltered half-wave rectifiers, so the need to explain why your meter is reading much lower than expected is less than it used to be.

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Power is not the only consideration when designing rectifier circuits. The goal is often to design a circuit that supplies a specific voltage to a load, and so knowing the average voltage is an important part of that design process.

If you don't believe me, try charging your beloved mobile device with a 0.1W supply....at 170V.

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