[Vintage-Audio] Re: Vintage-Audio]V40#9 - RMS

[Phil Barnes-Roberts WA6DZS]

vintage-audio-request at mailman.qth.net opined  on 11/15/2007 01:03 AM:
...
> Subject: [Vintage-Audio] how to calculate RMS power
> From: rick <rick at mnbrewers.com>
> Date: Wed, 14 Nov 2007 15:34:21 -0600
> To: vintage-audio at mailman.qth.net
> 
> Since I just calculated RMS power on a homebrewed guitar amp, this is 
> fresh in my mind.  I'll let smarter people than me to answer Duane's 
> questions.
> 
> measure the peak to peak voltage at max output before clipping
> divide by two to measure peak voltage - since it half is above and half 
> is below
> multiple by the square root of 2 to get RMS
> Vrms squared divided by the speaker load equals watts RMS
> 
> example is my amp (single ended 6v6gt) measured 14.8 volts peak to peak 
> with an 8 ohm speaker.
> 
> 14.8/2 = 7.4
> 7.4 * 0.7 = 5.2 volts rms
> 5.2*5.2/8 = 3.4 watts rms
> 
Very Close, Rick--

Your calculation comes out correct, but it actually is (according to the 
Handbook; made me look, to be sure):

Vrms = Vpk/sqrt(2) (rather than Vpk*sqrt(2)); but since sqrt(2) is 
1.414, "sqrt(2)/2" is "sqrt(2)/(sqrt(2)^2)" or .707, so "*.707" comes 
out the same.

It's the old pre-algebra trick; divide (or multiply) both top and bottom 
of the fraction by the same (sqrt(2) here) value to flip the divide to a 
multiply...

And of course, it all only applies to a sine wave, not necessarily to a 
complex waveform like real music or even speech.  Back to integrals for 
that, but it's plenty close enough for rough design.

And like Duane, I recall reading that brouhaha in PopTronics about IHF 
vs. Peak, which finally settled out to using RMS.  And how much Total 
Harmonic Distortion at that level.  Sheesh.  My tin ear (now too many 
flight lines and rifle ranges, and thousands of phone patches) never cared.

Just like the phony specs-manship more recently, of dBi vs. dBd on 
antenna ads, which kept those out of QST ads until recently.  The 
imaginary 'isotropic' (spherical pattern) radiator is 2.1dB down from a 
real dipole (donut pattern in free-space).  If you could find one of 
either...

-- 
'---O=o=O---'
73, Phil Barnes-Roberts WA6DZS < Mailto:pbarnrob at acm dot org >
"When you are trying to get a handle on a big decision, try looking
at it like this; 'What kind of world do I want to live in?'"
  --Ann Bodenhamer Martin, author of /Calico/ /Families/