# Output voltage of a rectifier

Is the output DC voltage of any rectifier (Halfwave, Fullwave or bridge) simply equal to $$\\sqrt{2}\$$ times Phase to neutral AC input voltage? Or does every rectifier circuit have its own formula to calculate DC output voltage?

• actually, the output of a rectifier is not a DC voltage – jsotola Sep 27 '18 at 7:59
• I agree with @jsotola comment but more precise: the output voltage can be a DC voltage assuming there's a smoothing capacitor and you do not load the DC output. Then assuming the rectifier diodes have zero voltage drop (that will never be the case) then the DC output voltage will be $\sqrt{2}$ the AC input voltage. Phase/neutral is irrelevant. Also before even thinking about formulas, concentrate on how a circuit works. Would I hire an EE who knows every formula: No. Would I hire an EE who understands circuits? Yes. – Bimpelrekkie Sep 27 '18 at 8:15

Ignoring diode losses. If you measure the output voltage of a rectifier as the Root Mean Square (RMS) voltage you are getting a reading which reflects the amount of power that the source can deliver as compared to the equivalent DC voltage.

The RMS output of a full wave rectifier is the same as the RMS the original waveform. The squared bit removes the effect of half of the original waveform being negative giving the same answer.

The RMS output of the halfwave rectifier is half the value of the original waveform. The mean bit of RMS means you are taking the mean over a full cycle and you only have half of the original waveform there.

Things change if, as normal, you put a capacitor across the output of the rectifier then you get DC. In this case the capacitor charges to √2 times the input voltage, this is the peak of the input.

If you take a load current from this arrangement you get a pulsating DC voltage. The pulsations value depends on the frequency the size of the capacitor and the current. This is well documented in other questions. See this question.

Rectifier circuits include halfwave, fullwave, voltage doubler, and voltage multiplier types. A simple diode rectifier is a halfwave type, and usually has significant forward voltage and temperature dependence, and will have different output current into different loads (in particular, a capacitor load will cause higher forward-voltage losses and holds the AC peak voltage).

There is no single formula for all rectifier/load combinations, but there are lots of approximate ones that can be useful.

Most universal-input power supplies have voltage-doubler rectification of 120VAC and bridge rectification of higher voltages. Many have phase-correcting modifications of the input AC waveform. Simple formulas aren't accurate in such cases.