Every couple of years I have to drag out the following example to
illustrate what RMS means and send it to AMPS. It think it is a good
example and goes to show that you can't just arbitrarily call average power
RMS power just because so many people do so. It is like calling all
amplifiers "linears" even if they are not linear at all but class C
amplifiers. Technical correctness is much different than political
correctness.
Just like taking the average of a number of data points. The discrete
(non-calculus) version of RMS is a definite procedure but just a little
more complicated. Below are examples of both calculating RMS voltage and
average power by using a 8 data points in a sine wave. And the applying the
RMS "proceedure" to power you will see that you get a erroneous result that
is meaningless. My example only uses 8 data points which works well for
sine waves but for arbitrary waveforms (ones that contain many frequencies)
you must use many more data points or an infinite number in some cases.
This is a non-calculus example after all.
R take square Root
of
M the Mean (average)
of
S the Squares of the values of all the points
It may look complicated as an equation or an integral expression (calculus)
but it is SIMPLE!!!!
For example...
Take one cycle of a 1 volt sine wave and divide into at least 8 equally
spaced points starting at zero degrees.
Calculate instantaneous voltage, voltage squared and power into 50 ohms
load at each point.
Do not use 360 degrees because it is the same point as 0 degrees. You may
do this for any number
of full cycles and you may want to do this on a spread sheet for each
degree (ie 360 points) or what ever.
Phase Voltage Voltage Squared Power into 50 ohms
Watts
0 0 0 0
45 .7071 .5 .01
90 1 1 .02
135 .7071 .5 .01
180 0 0 0
225 -.7071 .5 .01
270 -1 1 .02
335 -.7071 .5 .01
totals 0 4 .08
average of totals .5 .01watts Average Power
(divided by 8)
Square Root of average .7071 volts RMS
The RMS value of the signal is .7071 times the peak (1 Volt)= .7071
volts GEE look at above bold and underlined.
What is the power of this signal into a 50 ohm load?
.7071 volts squared divided by 50 ohms= .01 watts Look again above at
the average power bold.
It is all very consistent with calculations using RMS voltage or
Current and resistance and power.
Now what happens when we take RMS of the Power??
Phase Voltage Voltage Squared Power into 50 ohms Power
Squared
Watts
0 0 0 0
0
45 .7071 .5 .01
.0001
90 1 1 .02
.0004
135 .7071 .5 .01
.0001
180 0 0 0
0
225 -.7071 .5 .01
.0001
270 -1 1 .02
.0004
335 -.7071 .5 .01
.0001
totals 0 4 .08
.0012
average of totals .5 .01 Average
power .0015
Square Root of
average .7071 0.01225
RMS power ?????
OK above is your RMS power for what ever good it is....
And it does not relate to any of the other numbers you may use such as
voltage, current. resistance or power. But does give you 22.5% bigger
number in this example.
73
Bill wa4lav
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