How power analyzer works for high input frequencies

Hi everybody!

As DSP is not really my field I have a question that bothers me and I
think
someone here has enough experience to at least nudge me in the right
direction.

In my field I frequently use power analyzer to measure RMS (square
root
of sum of squares) values of voltage and current. Basically I measure
power of a signal. From power analyzer specs I know it has sampling
frequency around 20kHz. Somehow it can measure accurately also the
signals which are higher than the sampling frequency. Thinking (and
reading) about this has led me to few interesting facts.

I know that higher frequency signals 'translate' into the frequency
band
between 0Hz and sampling frequency, so as long as there is no analog
anti-aliasing filter the frequency 'translation' is actually a good
thing when
measuring power of a signal.
(thanks to http://www.wescottdesign.com/articles/Sampling/sampling.html)

This method can give accurate results for most of the signals within
the
device bandwidth (lets fix it at ten times the sampling frequency). It
only
fails it the input signal has almost the same frequency as a multiple
of half
the sampling frequency (m*10kHz in our case). Additional research led
me to believe that the width of the frequency window (around m*10kHz)
where the method fails is dependent on width of the sampling window
from
which we calculate RMS value. The longer the window, the narrower the
frequency interval around multiple of half sampling frequency where we
get inaccurate results.

The question I really want to ask is: How does the power analyzer
overcome this effect, because even if I feed him input signals around
its
sampling frequency it gives me correct results?

Come to think of it one possible solution is to sample the signal
three
times. Each time with different sampling frequency (e.g. 19kHz, 20kHz,
21kHz) with long enough window in order for frequency window where the
result is inaccurate be narrover than 500Hz, and do the majority vote
on
the three results.

But is you have a "twisted" input signal consisting of a 20001Hz and
38002Hz components you would need 5 different sampling frequencies.
Therefore you get stuck in a loop where you need to select appropriate
sampling frequencies based on a spectral composition of measured
signal,
which is unknown, or you set bounds on the input signal you which
makes
the device unreliable (useless).

Does anybody have any experience with this kind of scheme?

Is there a better scheme?

Thanks for all the thoughts you put in my "problem"

Regards, Mitja

Korenje wrote:

> In my field I frequently use power analyzer to measure RMS

> From power analyzer specs I know it has sampling
> frequency around 20kHz.

> The question I really want to ask is: How does the power analyzer
> overcome this effect, because even if I feed him input signals around
> its
> sampling frequency it gives me correct results?
> 
> Come to think of it one possible solution is to sample the signal
> three times.

Since you are only interested in RMS value, all you need for that is 
enough of data points for averaging (if the signal is stationary within 
  the period of measurement). Sample rate doesn't matter. For the 
accuracy of 1%, you will need ~10k points. There could be pathological 
cases when there is an integer relation between the sample rate and the 
signal frequency. In order to avoid such cases, you can sample at random 
intervals.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Feb 15, 4:14=A0pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> Korenje wrote:
> > In my field I frequently use power analyzer to measure RMS
> > From power analyzer specs I know it has sampling
> > frequency around 20kHz.
> > The question I really want to ask is: How does the power analyzer
> > overcome this effect, because even if I feed him input signals around
> > its
> > sampling frequency it gives me correct results?
>
> > Come to think of it one possible solution is to sample the signal
> > three times.
>
> Since you are only interested in RMS value, all you need for that is
> enough of data points for averaging (if the signal is stationary within
> =A0 the period of measurement). Sample rate doesn't matter. For the
> accuracy of 1%, you will need ~10k points. There could be pathological
> cases when there is an integer relation between the sample rate and the
> signal frequency. In order to avoid such cases, you can sample at random
> intervals.
>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultanthttp://www.abvolt.com

Whoa, it works! Thank you very much Vladimir!

I have ran some simulations that confirm the average error
drops below 1% when number of samples gets above ~3k (number depends
on how
much do you randomize sampling frequency). If you would be so kind and
point
me to some literature where the relation between error and number of
samples
is explained (I suspect it is 1/sqrt(number of samples), though I am
not
sure) and random sampling is explained I would be even more grateful.

Mitja

Korenje wrote:

> On Feb 15, 4:14 pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> 
>>Korenje wrote:
>>
>>>In my field I frequently use power analyzer to measure RMS
>>>From power analyzer specs I know it has sampling
>>>frequency around 20kHz.
>>>The question I really want to ask is: How does the power analyzer
>>>overcome this effect, because even if I feed him input signals around
>>>its
>>>sampling frequency it gives me correct results?
>>
>>>Come to think of it one possible solution is to sample the signal
>>>three times.
>>
>>Since you are only interested in RMS value, all you need for that is
>>enough of data points for averaging (if the signal is stationary within
>>  the period of measurement). Sample rate doesn't matter. For the
>>accuracy of 1%, you will need ~10k points. There could be pathological
>>cases when there is an integer relation between the sample rate and the
>>signal frequency. In order to avoid such cases, you can sample at random
>>intervals.
>>
> 
> Whoa, it works! Thank you very much Vladimir!

You bet.


> I have ran some simulations that confirm the average error
> drops below 1% when number of samples gets above ~3k (number depends
> on how
> much do you randomize sampling frequency). If you would be so kind and
> point
> me to some literature where the relation between error and number of
> samples
> is explained (I suspect it is 1/sqrt(number of samples), though I am
> not
> sure) and random sampling is explained I would be even more grateful.

This is very basic; any textbook on probability and statistics has that.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com