Spehro Pefhany wrote:

On Sat, 08 Jan 2005 05:49:24 GMT, the renowned "Martin H. Eastburn"
wrote:


Leo Lichtman wrote:


"Vaughn" wrote: I disagree. In my experience, Watts RMS is the ONLY
meaningful measurement of the power output capability of an amplifier.
^^^^^^^^^^^^^
Vaughn, lets look at this one step at a time. RMS stands for "root mean
square." If you look at the equation for power, it is I^2 R, or E^2/R. For
DC that is very simple, but for AC, it is necessary to use an average figure
for E or I that gives the correct power. The way to get that average is to
square the instantaneous voltage or current at every instant, take an
average of the squared values, and take the square root of the
average--hence: root (meaning square root) mean (same as average) square.

The wattage rating or operating point of an amplifier is already in power
units. It is perfectly OK to talk about "average power," or "peak power,"
but RMS power suggests doing something to the numbers that has already been
done. To square, average, and take the square root again would produce a
figure that has no meaning. That's my gripe.



Why was the RMS voltage developed ? It has meaning. Very good meaning.
Martin


If you have a resistor, the average current into it is V(avg)/R. The
average *power* is (Vrms^2)/R.

You can really see the difference with pulsey waveforms. Imagine a
100V pulse at 10% duty cycle going into a 1 ohm load.


100V x----x x----x
| | | |
| | | |
| | | |
0V ----x x----------------------------x x-------

0 1ms 10ms
t-


The average current is 10A. The average voltage across the resistor is
10V (what you'd measure with a DC voltmeter). But the RMS voltage is
31.6V, so the power is 1000W, not 100W. You can see this easily
without the calculus stuff from the power when the pulse is high
(10,000W), but it's only on for 10% of the time.

Then you get into reactive loads (the cos-theta stuff really only
makes sense for sine waves)...



Best regards,
Spehro Pefhany
Now Spehro is pulling our legs again... No sin(t) or cos(t) - no time at all!
But he uses a waveform.

RMS was to match the heating ability of a battery. equal to equal.

Duty cycle and even cycle begs the cos data.

One needs to use an integral.

Yave = 1/10ms Integral from 0 to 1ms of 100 dt
Yrms = 1/10ms Integral from 0 to 1ms of 100^2 dt
For square waves.

DC is all together different.

Martin

--
Martin Eastburn, Barbara Eastburn
@ home at Lion's Lair with our computer
NRA LOH, NRA Life
NRA Second Amendment Task Force Charter Founder