[Elecraft] Power measurement with a 'scope

[David A. Belsley]

> The oscilloscope accuracy is very important.
>
> Power = E^2/R. That is Power is equal to the voltage squared divided by
> the resistance.
>
> Any error in the voltage reading is squared! So if your scope is 5% off,
> the resulting calculated power will be 20% off!

Let E be true voltage, M be measured voltage, and let e be the relative 
error (such as +-.05) defined by M = E(1+e).  Let MP denote measured power 
and AP actual power.  Then

MP = M^2/R = (E(1+e))^2/R = (E^2/R)(1+e)^2 = AP(1+e)^2.

(1+e)^2 = 1 + 2e +  e^2, and for small absolute e (such as .05), this is 
approximately equal to 1+2e.  Thus, the proportionate power error is 
approximately twice that of the voltage reading.  A voltage error of 
absolute 5% would produce roughly an absolute 10% power error.

Now, it's true, if you don't know whether your 5% voltage error is high or 
low, then the resulting power measurement could be 10% low or 10% high, 
giving, in some sense, a possible 20% error spread.  But, of course, then 
the voltage measurement would, in the same sense, have been a 10% error, 
not a 5% error, and, again, the power error would be twice that of the 
voltage.

best wishes,

dave belsley, w1euy




----------------------------
David A. Belsley
Professor of Economics