Owen,

[[[ while I suspect the difference is so small that it makes little
difference in the receiver sensitivity number arrived at, I proceed
anyway. ]]


From your last two posts, it appears you/we have vastly different
interpretations of what the question was. You talk about removing the
fundamental from the square wave and this puzzles me. I do not believe the
intent was to measure SINAD using a square wave modulation. Therefore
removing its fundamental and measuring its RMS does not fit the situation.


My understanding of the issue was measuring SINAD with the older
"Average-measuring-, RMS-reading" type (call it the "AVG-Type") of meter vs,
a "true RMS" reading meter.

While I did talk about measuring a square wave with the "AVG_Type" meter,
that was a digression only ment to show (what I think is) the difference for
the previously proposed reference measurement. Namely try simply measuring
a square wave for comparing the two meter readings, not SINAD measurements.
I did this to show a calculation of how the two meters would read knowing
the average and RMS values of _some_ waveform. I was thinking that I could
do this for the two SINAD waveforms, but as you see here, I gave up...

Back to SINAD.
Therefore, the issue I was addressing was the following:
(for the normal SINAD technique, 1 kHz sine wave tone):
A- Assume the RMS meter gives the "correct" reading.
B- What does the "AVG_Type" show on the display/scale?

So, B has two parts.

1- What does the "AVG-Type" read for the un-notched signal, and
2- What does the "AVG-Type" show for the notched signal.

1- As a first approximation, lets say the un notched reading is dominated by
the sine wave. With this assumption, they both read the same. To refine
this estimate, I am unable to assess, easily, the effect of the noise on
either measurement except that the True RMS mwter will give an indication of
the total tone and noise power (actually Erms^2). As a first approximation,
we could say that the "AVG-Type" reads the average of the sine plus the
average of the noise voltages...and my estimation powers peter-out right
there.
2- What does the "AVG_Type" read on the noise (notched signal)... yep, peter
once again.

Therefo

GOTO [[ my statement in brackets above ]]



Then there's the pronunciation. Some say "sin' add" and some say "sign'
add". We said SIN add.

Nice exercise, time for me to move on to other things.

73, Steve, K,9.D;C'I


"Owen Duffy" wrote in message
...
On Mon, 17 Oct 2005 05:09:06 GMT, Owen Duffy wrote:

On Mon, 17 Oct 2005 03:09:11 GMT, Owen Duffy wrote:


So, theoretically:
- an ideal average responding meter should read (1-2/pi)% which is
36.3% or 8.8dB on an perfect square wave;

I think this is close to the right answer, but for the wrong reason. I
think it needs to be evaluated iteratively, and I get an answer closer
to 34.3% or 9.3dB.

An analytical approach to solution of the problem.

A unit height square wave has a fundamental component of amplitude
4/pi.

To find the area under the filtered curve, I think we are looking for
the integral from 0 to pi/2 of absolute(1-4/pi*sin(theta))). I will
divide the integral at theta=asin(pi/4) to deal with the absolute
function since the problem function is positive from 0 to asin(pi/4)
and negative from asin(pi/4) to pi/2.

Here is some Perl to evaluate the ratio:

#find the zero crossing point
$theta=asin($pi/4);
#find the area under the curve
$area=$theta-4/$pi*(-cos($theta)+cos(0)); #first part
$area+=4/$pi*(-cos($pi/2)+cos($theta))-($pi/2-$theta); #second part
#divide by area under unit square wave
$ratio=$area/($pi/2);
print "Average response ratio is $ratio \n";

And the answer is 0.3430678471... or 9.3dB. It is about 9.4dB if you
only consider the harmonics up to 50KHz.

One of you mathematical whizzes might know a better way to put this!

Owen
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