Richard,

I understand the historical difficulties of making accurate RMS
measurements, however I didn't know the original post only solicited ways to
make the measurement with "current generation of commercial surplus
equipment ". My intention was to point out some measurement nuances that
might not be obvious at first glance.

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.


Joe
W3JDR


"Richard Clark" wrote in message
...
On Fri, 14 Oct 2005 20:28:17 GMT, "W3JDR" wrote:

Richard,
What you said is largely accurate, however at low S/N ratios, or where the
distortion becomes comparable to the signal level, the reading of the
composite signal (signal+noise+distortion) with anything other than an RMS
meter could produce erroneous results.

Hi Joe,

In the practical world of SINAD (having tuned a number of GE and
Motorolas), one is not very interested in how poor your set is, but
rather meeting a service standard (that 12 dB which is as arbitrary as
any).

I doubt if many of the current generation of commercial surplus
equipment comes with a stock tester employing what would have been an
expensive converter chip to insure RMS measurements. I come by that
assessment by noting those I used employed standard meter movements.
The first RMS meters I calibrated in the mid 70s came from Fluke (just
up the highway), and the components of that circuit were scrubbed of
all identification numbers or cast in epoxy. Such was the cachet of
being hi-priced, and having others try to break into the market with
knock-offs.

My Radio Shack multimeter makes that claim (ca 1995) and if memory
serves, that Micronta's "True RMS" was barely capable of poor voice
grade bandwidth. This was 20 years after Fluke, costing about as much
(economic inflation), and not performing as well (technical
deflation).

73's
Richard Clark, KB7QHC

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

I understand the historical difficulties of making accurate RMS
measurements, however I didn't know the original post only solicited ways to
make the measurement with "current generation of commercial surplus
equipment ".

Hi Joe,

That was interjected by me, knowing the market of the past several
years being flooded after trunk systems began replacing older service.

My intention was to point out some measurement nuances that
might not be obvious at first glance.

Useful information, that.

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.

Yes, the miracle of Moore's law. 20 years ago I was with HP, here, to
help them introduce their 100KHz real-time dual channel audio spectrum
analyzer. That was a tremendous effort with a million lines of Pascal
code and 5 years in the making when most HP instrumentation hit the
market in 18 months from inception.

I got to know the range of FFTs under some of the most brilliant minds
on the topic. One, Nick Pendergrass, went on to teach at an eastern
university.

Today, it is an underclass topic, probably occupying no more than 6
weeks of instruction coupled to other interests. Still and all, I see
considerable errors of omission in the discussion. Such errors often
make the difference in delivering a serviceable performance compared
to that which is 100 times better (actually a million times, but few
could get their imagination around a number that big so I understate
it).

73's
Richard Clark, KB7QHC

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
--