Is your meter true RMS capable? Many are only
accurate for sinewaves, and tend to be frequency
limited to boot.
Let's say your pulse peak is Vp, the on time is Ton,
the off time is Voff. The total energy delivered
to a purely reistive load R during one cycle is then:
E = (Vp^2/R)*Ton
and the average power over the cycle is:
P = E/(Ton + Toff)
= (Vp^2/R)*Ton/(Ton + Toff)
For DC voltage the power is V^2/R. The RMS voltage for
your pulse would give an equivalent average power, so
we can equate:
Vrms = Vp*sqrt(Ton/(Ton + Toff))
In your case that would work out to about 8.2V
Would help if the OP would furnish information on the meter.
As has been established the OPs meter is a Fluke 87 and is "true RMS"
But Fluke states the bandwidth is 20kHz.
The OP states he is measuring a pulse with a frequency of 64kHz. And a
pulse has frequency components far higher than 64kHz.
RMS and DC voltages are not the same for time-varying signals.
RMS = Root mean square. Calculate the mean (time-average) value of
the amplitude-squared waveform over one period and find the square
root of the result. Here's a start:
+-----+ <-- 14*146
--+ +--------+ <-- 0
0 5.4 15.6
A DC voltmeter should report the average voltage measured over one
period. Same wave as above, except peak amplitude is 14, so:
Vavg = (14 * 5.4)/15.6 = 4.84.
If you want 5.6 "vdc", you must adjust the duty cycle, peak voltage,
For any waveform, the RMS voltage is the square root of the mean square
voltage. In concept, you take the voltage as a function of time, square
that, integrate it over one cycle of the waveform, divide by the period
of one cycle, and then take the square root.
In the case where the waveform in question is a square wave whose
voltage is 0 for part of the period and Vp for the rest of the period,
evaluating the above is particularly simple. You ought to work it out
for yourself to see just how simple, but the answer is
Vp * sqrt(Ton / (Ton + Toff))
So the true RMS voltage is 8.24 V.
If it is a true RMS reading meter, then either your meter or your scope
is out of calibration. On the other hand, most meters do *not* read RMS
voltage, they read either peak voltage or average voltage, and then
scale that by a correction factor so they read RMS voltage *for a
sine wave*. Their reading isn't valid for non-sine waveforms.
Do you really want 5.6 V RMS output? If so, you need to adjust Ton and
Toff, or possibly Vp.
email@example.com (Dave Martindale) wrote in
Hmmm what does a Fluke 87 measure in? I must have lost certain brain
cells and begining to confuse myself.
The peak of (US) AC outlets is 170v peak. The value the Fluke measures
is 120 or (0.707) * 170.
So I should be measuring the RMS of the pulse.
That's correct. Although integrating a sin^2 function is somewhat more
difficult than integrating a square wave (I recommend looking it up in a
table of integrals, or (these days) checking online), it turns out that
the integral of sin^(t) over one cycle is t/2, or the mean square of a
sine function with peak 1 is 0.5. That means the RMS voltage of a sine
wave is 1/sqrt(2) times the peak.
Interestingly, that's *also* true for a square wave with a low voltage
of 0 V, high voltage of 1 V and a 50% duty cycle. So RMS is 1/sqrt(2)
times peak for this waveform too. But the *average* voltage is not the
same - the mean absolute value for the sine wave is 108V, while the
square wave's mean value will be 85. So an average-reading meter that
measures 108 V and "converts" it to 120 V for display will be fooled by
the 85 V mean of the square wave and display a bogus voltage, not 120
This is getting somewhat off topic, but I saw a particularly elegant
explanation on the Web about why the integral of sin^2(t) over one
cycle is t/2:
* Because of Pythagoras, and the definition of sin and cos,
sin^2(x) + cos^2(x) = 1, for any x
* So, the integral of (sin^2(t) + cos^2(t)) dt is just t
* So the definite integral of this sum over any interval 2*pi in length
is just 2*pi.
* But cos(x) is really the same function as sin(x) with a phase shift.
The same is true of cos^2 and sin^2. If you integrate over one
period of the waveform, the integral is always the same no matter what
start and end points you pick.
* So the sin^2 and cos^2 terms contribute equally to the integral (as
long as you integrate over one period), and each one is half the
* So the integral of sin^2(t) dt over a 2*pi period is just 1*pi, and
the mean value of the amplitude is 1/2.
Are you saying that the Fluke 87 reads 5.6 VDC on *this* waveform?
The Fluke displays the correct RMS voltage when measuring a 60 Hz sine
wave with 170 V peak. But virtually *any* meter will do that, even if
it's average-reading, doesn't work above 100 Hz, and is accurately
calibrated on only the 200 V scale.
Now, the Fluke probably is accurately calibrated on all scales, and it
is a RMS-reading meter. But as someone else pointed out, it can only
read the RMS voltage of a waveform accurately under limited conditions:
the peak-to-average ratio of the waveform has to be within some maximum,
and all the significant harmonics of the waveform have to be within the
meter's measuring bandwidth. The *fundamental* of your waveform is 64
kHz, and the meter bandwidth is only 20 kHz, so you shouldn't expect it
to provide an accurate measurement of even a sine wave at that
It looks like you need something with a bandwidth of 1 MHz or so to
accurately measure the RMS voltage of this waveform. For example,
digital storage scopes can capture the waveform, and some of them have
built-in functions that display the RMS voltage measured over one cycle
of a waveform.
firstname.lastname@example.org (Dave Martindale) wrote in writes:
OK, this is more interesting. Yes, the meter reads 5.6V DC on the
waveform I provided details for.
It's a pulse width modulator driving a FET.
I'm trying to learn how one would associate this with say a motor.
Possibly I don't care about voltage and only the feedback of the motor's
speed. I assume if I have a motor with a 5-volt max, I can have it spin
at half speed at 2.5v - ignoring any thoughts about starving the motor
for a moment.
So my inital curiosity is what type of pulse width I would provide to
supply a DC voltage of 2.5v
This is where my questions came from - pure curiosity, however, it
appears I'm getting in-depth (and partially confusing) answers.
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