Now you are oversimplifying.  Sometimes the use of RMS values for measurements will be more appropriate, depending on what you are doing.

But as I've said, and as Verpies and Poynt99 have also confirmed, the proper way to do _power_ calculations, if you have the data as you do from a DSO, is to do the instantaneous multiplication of the actual per-sample values of voltage and current, which generates an instantaneous power waveform, then take the _average_  (not RMS) value of that IP waveform. This procedure works for all waveforms, whether complex or not, all load types, and all power factors. All the phase shift and other complications are taken care of by the sample-by-sample calculations performed in the scope, typically at hundreds of thousands of samples per second or more, so the errors caused by this "numerical methods integration" are very small.

Yes, I realise. Possibly a good idea to check with both equations anyway. Its not hard. Just a case of gathering the data which one will be doing anyway.

As one equation partially verifies the other.

   Chris Sykes
       hyiq.org

For Giggles:

The 1KHz Signal is from a High Side Mosfet Driver. The 1K Resistor is measured to be 1K.

Mean Calculation: Red Channel

V / R = I = 5 / 1000 = 0.005 Amperes

I² * R = P = (0.005² * 1000) * 0.5 (Duty Cycle) = (0.000025 * 1000) * 0.5 (Duty Cycle) = 0.0125 Watts

RMS Calculation: Yellow Channel

V² / R = P = 3.458² / 1000 = 11.957764 / 1000 = 0.011957764 Watts

Now I must have something wrong here? We see: 0.000542236 Watts difference!

   Chris Sykes
       hyiq.org

I am still seeing a possible problem if the resistance changes in time, or am I seeing something that is not there?

In all of the Equations we use, Ohm's Law, if R changes during the operation of the circuit, then the Power through the Circuit Element in question will change.

Eliminating the problem, like TK has pointed out, can only be done with a Current Sensing Resistor with absolute minimal Inductance and using this Voltage Drop, Across the Non Inductive Current Sensing Resistor, CSR.

   Chris Sykes
       hyiq.org

Actually the Ohm's Law relationships are definitions of each term in terms of the others. So, since the current depends on the resistance (if voltage is constant) then even though the resistance isn't explicitly included in the particular formula you may be using, it is still there hidden in the other variable values. So P=VxI does have the resistance in there, because I = V/R.

Here's where it becomes important to understand how the scope calculates "Average" or mean values. It is adding up values from very short timeslices and then dividing by the number of slices. So even if the resistance (or voltage, or current) may vary during the "on" time of a pulse, the sampling system will catch it, as long as it isn't varying too fast. But at 1 gigasamples per second..... well, you can see that even very small, very fast changes will be caught by the system and will give the true average. This is actually a problem sometimes, since the scope may be including noise or random glitches in the average. Hence, the scopes will have "Bandwidth limiting" that can be selected which will cut down on the presence of this kind of noise in the input samples to the averaging function.

On my Rigol, the 20 MHz bandwidth limiting is indicated by a "B" symbol in the Channel V/Div display at the bottom of the screen.

Yes, this is the way I see it also, one can be interchanged to work out the other. Each are complimentary.

Ok I see what you mean, the over all Mean Sampling is fast and accurate enough to see any circuit changes most of the time. I must admit, I was not think clearly when posting the last post and really did not need to post it, so I am sorry for the Interlude there.

I think still, the oscilloscope is the most awesome machine we Humans have ever built. We would be lost without them!

   Chris Sykes
       hyiq.org

So as you can see the cursors in the CH1 test are showing 12.30 V for the peak values. Multiplying the Peak by the square root of the 19.44 percent Duty Cycle gives
12.30 x sqrt(.1944) = 5.42 V_rms, and the scope is reporting 5.40 V_rms. Not too bad, an error of less than 1 percent.

In the second test with the CH2 readings... the cursors are giving me a value of 128.0 mA for the peak values. Multiplying this by the square root of the Duty Cycle gives 0.1280 x sqrt(.1944) = 0.0564 or 56.4 mA _rms, and the scope is reporting 63.1 mA _rms. WTF? This is a large error. And for the Mean value, the 0.1280 x .1944 = 24.9 mA, whereas the scope says 30.8 mA. Again, a large error. WTF? Is this due to an inaccurate channel, or bad calibration, bad cursor positioning, or what? Perhaps the channel is just not accurate at very sensitive settings?

In the third test with the Math readings, the cursors give me 1.540 W for the peak value, and factoring in the duty cycle gives 1.540 x 0.1944 = 299.4 mW as the average. And the scope is reporting 305 mW as the average. Again not too bad, about 2 percent error.

These three shots are using the same sample set, I have stopped the scope and am just moving cursors around between the screensaves.

The poor result on CH2 has made me start the Self-Calibrate routine; maybe it will get better, or maybe not.

TK - A nice example of how we can see some inaccurate measurements on the Oscilloscope. Thanks for sharing this.

What's the Channel like at higher voltage levels? Does this error margin come down some?

   Chris Sykes
       hyiq.org