On Sat, 15 Oct 2005 00:40:34 GMT, "W3JDR" wrote:


Recently, it has become quite easy to do true RMS measurement at audio
frequencies using DSP techniques. In fact at audio you can even do an
accurate RMS measurement in DSP using a PIC microcontroller to sample the
signal and perform the calculations.

I mentioned in an earlier post that I had done some comparisons of
true RMS response based SINAD measurements and average responding
meters.

I have just rerun the test.

I have a receiver with 2400Hz wide IF , fed with SSG and connected to
a HP334A Distorion Analyser. I have adjusted the SSG for 12dB
indicated SINAD on the HP334A.

The HP334A's meter is boldly labelled RMS, but it is an average
responding meter scaled for RMS with a sine wave.

I measured the output from the HP334A using a no-name true RMS
voltmeter that covers the audio frequencies involved (trap there...
some dont make it past power frequencies), and measured SINAD of
11.3dB.

I connected the HP334A output to a PC running FSM and measured the
following figures for Vtotal and Vfiltered

total filtered
V Average 2708 679
V RMS 2753 763
V Peak 4287 2302

(The three detectors in FSM are all calibrated to read the same on a
sine wave.)

The FSM measurements indicate a SINAD of 11.1dB RMS responding and
12dB average responding.

Overall, the two / three methods are reasonably consistent indicating
around 12dB SINAD using an average response meter, and around 11.2 dB
using RMS responding meters.

That suggests to me that using an average responding instrument may
overestimate the SINAD by a little less than a dB. However, given the
statistical variance of the noise, I would not be fretting about it,
especially on an FM rx where it might only need a smaller change in
C/N for that SINAD change.

I connected the rx to a Motorola R1013A which indicated 12dB SINAD (it
is most unlikely to have an RMS responding ALC and meter).

Owen
--

On Mon, 17 Oct 2005 00:05:18 GMT, Owen Duffy wrote:

This is seriously bad, replying to one's own post... but.

It occurs to me a quick test to reveal whether a SINAD meter is RMS
responding or average responding is to test it with a 1KHz square
wave. I am not suggesting this as a cal procedure, just a test that is
more sensitive to the meter response than noise testing.

IIRC, the Taylor series coefficients for a square wave a all even
harmonics are 0, the others are 4/pi/n.

So, theoretically:
- an ideal average responding meter should read (1-2/pi)% which is
36.3% or 8.8dB on an perfect square wave;
- an ideal RMS responding meter should read
(1-(2^-0.5*4/PI())^2)^0.5*100% which is 43.5% or 7.23dB.

Does the maths make sense?

I observe that my R1013A indicates 9dB on a good square wave, and the
HP334A around 35% (9.1dB)... so another indication that they are
average responding. I expect the readings a little low because neither
instrument has infinite bandwidth.

Owen
--

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.

Owen
--

Hello Owen,

Seems both average-responding and trms meters use rectifiers, so a
square wave input with perfect symmetry should result in BOTH meters
reading the same: an amount equal to the peak square wave voltage. Am I
confused on this?

Chuck

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.

Owen
--

Nope. See my previous post.


A square wave has an average equal to the RMS equal to the peak. It's just
like DC.

The "older types" RESPOND to average of a SINE (63% of peak) but display the
value for the RMS (71% of peak), so they have a 1.11 correction factor to
get from average to RMS.

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


"chuck" wrote in message
ink.net...
Hello Owen,

Seems both average-responding and trms meters use rectifiers, so a
square wave input with perfect symmetry should result in BOTH meters
reading the same: an amount equal to the peak square wave voltage. Am I
confused on this?

Chuck

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.

Owen
--

You're correct, of course, Steve. I was thinking the average-responding
meter was calibrated to display average levels, but it is not: it is
calibrated to give the rms value of a true sine wave with that average
value. So the only way to measure the average value of a non-sinusoidal
ac signal is to use an average-responding meter and correct the
displayed reading as you have noted. Not relevant to the SINAD
discussion but interesting.

Thanks for the clarification.

Chuck

Steve Nosko wrote:
Nope. See my previous post.


A square wave has an average equal to the RMS equal to the peak. It's just
like DC.

The "older types" RESPOND to average of a SINE (63% of peak) but display the
value for the RMS (71% of peak), so they have a 1.11 correction factor to
get from average to RMS.

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


"chuck" wrote in message
ink.net...

Hello Owen,

Seems both average-responding and trms meters use rectifiers, so a
square wave input with perfect symmetry should result in BOTH meters
reading the same: an amount equal to the peak square wave voltage. Am I
confused on this?

Chuck

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.

Owen
--

On Mon, 17 Oct 2005 16:39:25 GMT, chuck wrote:

Hello Owen,

Seems both average-responding and trms meters use rectifiers, so a
square wave input with perfect symmetry should result in BOTH meters
reading the same: an amount equal to the peak square wave voltage. Am I
confused on this?

Leaving aside the rectifier point which is arguable:

If we accept that the RMS responding instrument reads correctly on all
types of waveforms, the issue is with the average responding
instrument.

The average responding instrument is (usually) calibrated for the form
factor of a sine wave, and its scaling in RMS is only valid for
waveforms with the same form factor.

There are two cases to consider, the square wave, and the square wave
with the fundamental removed. The form factor of both are different to
the form factor of a sine wave, and more importantly to each other, so
the average responding meter does not provide an accurate ratio of the
(true) power of each wave.

Does that make sense?

Owen
--

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
--

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
--

On Tue, 18 Oct 2005 10:37:15 -0500, "Steve Nosko"
wrote:

Owen,


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.


Some discussion arose about the extent of errors when using an aveage
responding meter to measure SINAD (compared to a true RMS meter).

My experimental evidence is that when measuring SINAD on a 2.4KHz wide
receiver at SINAD=12dB, the error is less than 1dB. Of course, it will
be less for higher SINAD ratios, and worse for lower ones.

I offered that a simple test of whether a SINAD meter was average
responding or true RMS responding, was to measure the SINAD of a good
square wave. The average responding meter will indicate about 9.3dB
whereas an RMS responding meter will indicate around 7.3dB.

I think we both understood that.


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.

As I stated above, and you stated, the comparison will depend on the
extent to which the sine wave dominates the total signal, and so will
depend on the SINAD being measured. I suggest that it will also depend
on the noise bandwidth.

Repeating, my experimental evidence is that when measuring SINAD on a
2.4KHz wide receiver at SINAD=12dB, the error is less than 1dB.

At the end of the day, it doesn't matter that much for normal
applications if the SINAD meter is average responding, they appear to
overestimate the SINAD, but by a very small amount.


Therefo

GOTO [[ my statement in brackets above ]]


You are trying to send Wes in a loop.

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

Dangerous territory, this could become an international incident when
you bring pronunciation into scope. There, and you all (mostly)
thought I didn't know how to spell... all those esses where they
should be zeds, no thats zees isn't it.

Owen
--