# Average DC voltage and RMS voltage, Question

Joined Sep 12, 2014
12
Hi,

I can not seem to figure out the difference between the Average DC value of a half wave rectifier and the RMS value.

To me; when I calculate the RMS of a signal I am finding out what size battery would give me the same load power output.

If this is the case, how is the average DC value of the sinusoid any different?

#### alfacliff

Joined Dec 13, 2013
2,458
a sine wave has no average dc value, it goes equally negative and positive, the average voltage is zero.

Joined Sep 12, 2014
12
a sine wave has no average dc value, it goes equally negative and positive, the average voltage is zero.
Thanks but in the case I am talking about it is not a true sine wave it is half wave rectified

#### alfacliff

Joined Dec 13, 2013
2,458
then it will charge up the filter to the peak value max, or less depending on load.

Joined Sep 12, 2014
12
then it will charge up the filter to the peak value max, or less depending on load.
Sorry just so we are on the same page here I will detail the problem I am having a little better, What I have is:

A series circuit consisting of an AC voltage source (Vin), a ideal diode and a load resistance (VL).

When Vin is positive the diode is in forward biased and VL = Vin.
When Vin is negative the diode is in reverse bias and VL = 0V.

Now I cant seem to figure out the difference between getting the Average DC voltage and the RMS voltage.

#### MrChips

Joined Oct 2, 2009
24,408
At some point we have to write a sticky note for RMS.

What is RMS, or root mean square value?

The RMS value of any signal is the constant DC voltage that would deliver the same power as the given signal.

How does one determine or calculate the RMS voltage?

RMS stands for root-mean-square.

(1) To find the power we compute the square of the voltage.

(2) Compute the sum (or take the integral) of the voltage squared over a certain length of time. If the waveform of the signal is periodic, we need to sum (or integrate) over an integer number of cycles.

(3) Compute the mean or average by dividing by the number of samples (or by the time-duration of the integration).

(4) Compute the square-root of the average.

That is why it is called root-mean-square.

#### alfacliff

Joined Dec 13, 2013
2,458
the average dc is the same as the rms value.

#### MrChips

Joined Oct 2, 2009
24,408
The average value of a sinewave symmetrical about 0V is zero.

The RMS value is non-zero because we compute the RMS value from the square of the voltage which removes the negative sign.

Joined Sep 12, 2014
12
Here is my circuit and my solution (See attached)

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Joined Sep 12, 2014
12
At some point we have to write a sticky note for RMS.

What is RMS, or root mean square value?

The RMS value of any signal is the constant DC voltage that would deliver the same power as the given signal.

How does one determine or calculate the RMS voltage?

RMS stands for root-mean-square.

(1) To find the power we compute the square of the voltage.

(2) Compute the sum (or take the integral) of the voltage squared over a certain length of time. If the waveform of the signal is periodic, we need to sum (or integrate) over an integer number of cycles.

(3) Compute the mean or average by dividing by the number of samples (or by the time-duration of the integration).

(4) Compute the square-root of the average.

That is why it is called root-mean-square.
Thanks for that informative post, I now understand what RMS is.

But I am stumped as to what the average DC value is?

If we wanted to know the power dissipation in some resistor we would use RMS, why would we not use VDC average?

#### crutschow

Joined Mar 14, 2008
27,902
the average dc is the same as the rms value.
No. The average value of a rectified, unfiltered sinewave is not the same as it's RMS value. The average (DC value) of a full-wave rectified sinewave is about 0.637 of the peak value and the RMS is about 0.707. The average is just that, the average voltage value of the waveform integrated over its period. The RMS value is the heating value of the waveform averaged over its period. They differ because the average value does not include the V^2 term that you use in calculating RMS.