Re: RMS approximation of Square/PWM signal

bill.sloman@xxxxxxxx wrote:
On Jun 23, 9:20 am, Terry Given <my_n...@xxxxxxxx> wrote:

JMini wrote:

Does anyone have a way to approximate and RMS voltage from a PWM signal.
I want to regulate the RMS voltage sent to a lightbulb, but do not have the
room for the inductor and capacitor required to carry 20+ amps of current. I
need to feedback a voltage to the PWM controller that is proportional to the
RMS voltage of the output. I don't need an EXACT RMS conversion, rather a
ratio would be fine since I can adjust the actual voltage fed back to the PWM
controller via a resistor divider. For this current design, it will be
operating at about 40kHz.

square-wave, duty cycle D = Ton/Toff


This is wrong - duty cycle is D= Ton/(Ton+Toff)


oops. I meant to write "T". thanks.

Ton/Toff is the mark to space ratio (MS) which isn't immediately
useful for this kind of calculation. Obviously, it can be greater than
one.

D= MS/(MS+1/MS)

Happily, if you define D correctly, Terry's conclusion is correct.


RMS = peak*sqrt(D)


If the pulse width modulation was very slow - slower than the thermal
time constant of the filament - the situation could be complicated by
the fact that the filament would start off with a relatively low
resistance,which would rise to normal operating levels (ticket output)
during the duration of the "on" pulse, but this is a couple of orders
of magnitude slower than 40kHz.

--
Bill Sloman, Nijmegen

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