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# Discussion Groups | Comp.DSP | What is "percentage distortion"?

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# What is "percentage distortion"? - Jerry Avins - 2012-10-25 14:43:00

```Starting about 1950, when I first got serious about audio, I have
periodically run into arguments about how to decide what "10% harmonic
distortion" means. Some were both subtle and bitter. For example, if a
signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
1^2). If the 300 Hz component represents a distortion product, is the
THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
to be so many dB down. At audio, we sometimes measure the signal with a
voltmeter (peak? RMS? average?) with and without the fundamental notched
out, then report the ratio. What does that number mean?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
```
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# Re: What is "percentage distortion"? - 2012-10-25 17:01:00

```I

On Thursday, October 25, 2012 2:42:11 PM UTC-4, Jerry Avins wrote:
> Starting about 1950, when I first got serious about audio, I have
>
> periodically run into arguments about how to decide what "10% harmonic
>
> distortion" means. Some were both subtle and bitter. For example, if a
>
> signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
>
> Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
>
> 1^2). If the 300 Hz component represents a distortion product, is the
>
> THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
>
> to be so many dB down. At audio, we sometimes measure the signal with a
>
> voltmeter (peak? RMS? average?) with and without the fundamental notched
>
> out, then report the ratio. What does that number mean?
>
>
>
> Jerry
>
> --
>
> Engineering is the art of making what you want from things you can get.
>
>

I assume it is something like (power of (measured signal - reference signal))/ (power of
reference signal).

I guess it gets tricky in practice since simple notching out may not completely separate the
distortion from the reference.

I seem to recall the standby THD measurement was do something like put 1000HZ into the system
and then measure the powers of the 1000Hz out of the system and the power of the distortion (all
other frequencies) and find their ratio.

my \$0.02 worth

Clay

```
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# Re: What is "percentage distortion"? - glen herrmannsfeldt - 2012-10-25 17:07:00

```Jerry Avins <j...@ieee.org> wrote:
> Starting about 1950, when I first got serious about audio, I have
> periodically run into arguments about how to decide what "10% harmonic
> distortion" means.

Interesting question. Most of us just read it on the spec. sheets,
then decide to buy the one with the lower number. (Well, maybe.)

> Some were both subtle and bitter. For example, if a
> signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
> Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
> 1^2). If the 300 Hz component represents a distortion product, is the
> THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
> to be so many dB down. At audio, we sometimes measure the signal with a
> voltmeter (peak? RMS? average?) with and without the fundamental notched
> out, then report the ratio. What does that number mean?

I suspect it is written into the FTC rules somewhere, along with
the rule against an amplifier (or receiver) model number being
twice its rated (RMS, according to the FTC definition) power.

Now, if it is small enough, like 0.2%, then the difference doesn't
matter much. I hope there are no home amplifiers with 10% THD,
but maybe car stereo.

-- glen
```
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# Re: What is "percentage distortion"? - Vladimir Vassilevsky - 2012-10-25 17:18:00

```"Jerry Avins" <j...@ieee.org> wrote in message
> Starting about 1950, when I first got serious about audio, I have
> periodically run into arguments about how to decide what "10% harmonic
> distortion" means. Some were both subtle and bitter. For example, if a
> signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
> Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
> 1^2). If the 300 Hz component represents a distortion product, is the THD
> 10% or 0.5%? At RF, we always use power, and transmitted spurs need to be
> so many dB down. At audio, we sometimes measure the signal with a
> voltmeter (peak? RMS? average?) with and without the fundamental notched
> out, then report the ratio. What does that number mean?

http://www.analog.com/static/imported-files/tutorials/MT-053.pdf

```
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# Re: What is "percentage distortion"? - rickman - 2012-10-25 20:35:00

```On 10/25/2012 2:43 PM, Jerry Avins wrote:
> Starting about 1950, when I first got serious about audio, I have
> periodically run into arguments about how to decide what "10% harmonic
> distortion" means. Some were both subtle and bitter. For example, if a
> signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
> Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
> 1^2). If the 300 Hz component represents a distortion product, is the
> THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
> to be so many dB down. At audio, we sometimes measure the signal with a
> voltmeter (peak? RMS? average?) with and without the fundamental notched
> out, then report the ratio. What does that number mean?
>
> Jerry

I don't think you are doing the math right.  RMS is the root of the mean
of the square of an AC waveform considering all of the instantaneous
voltages over time, not the RMS of individual frequency components.

If the 100 Hz signal is (10^2)/R Watts and the 300 Hz signal is (1^2)/R
Watts then the 300 Hz signal is 1/100th the power of the 100 Hz signal
and you have 1% distortion.  If they want the distortion as a voltage
ratio, then it would be 10%.

This is why I like dB.  The convention is that no matter what you
measure to get the number, it is converted to a power ratio.

I think I understand the problem.  The signal is 10 Vrms, the distortion
is 1 Vrms.  You then calculate the Vrms of the combined signal based on
the power calculation.  The mistake is subtracting the 10 Vrms signal
from the combined signal Vrms to get the distortion voltage.  But you
HAVE the distortion voltage, 1 Vrms.

Rick
```
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# Re: What is - steveu - 2012-10-25 20:52:00

```Hi Jerry,

>Starting about 1950, when I first got serious about audio, I have
>periodically run into arguments about how to decide what "10% harmonic
>distortion" means. Some were both subtle and bitter. For example, if a
>signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
>Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
>1^2). If the 300 Hz component represents a distortion product, is the
>THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
>to be so many dB down. At audio, we sometimes measure the signal with a
>voltmeter (peak? RMS? average?) with and without the fundamental notched
>out, then report the ratio. What does that number mean?

Its pointless trying to think this through, as you will realise there are
several perfectly reasonable ways to express a distortion figure. You need
to look up the IEC and IEEE specifications which include distortion
measurements. One of those bodies expresses THD as effectively a percentage
of power, and the other expresses it as effectively a percentage of
amplitude. They both, however, define exactly what they mean by THD.

Steve
```
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# Re: What is "percentage distortion"? - Les Cargill - 2012-10-25 21:27:00

```Jerry Avins wrote:
> Starting about 1950, when I first got serious about audio, I have
> periodically run into arguments about how to decide what "10% harmonic
> distortion" means. Some were both subtle and bitter. For example, if a
> signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
> Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
> 1^2). If the 300 Hz component represents a distortion product, is the
> THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
> to be so many dB down. At audio, we sometimes measure the signal with a
> voltmeter (peak? RMS? average?) with and without the fundamental notched
> out, then report the ratio. What does that number mean?
>
> Jerry

Both, unfortunately:

http://en.wikipedia.org/wiki/Total_harmonic_distortion

"It is unfortunate that these two conflicting definitions of THD (one as
a power ratio and the other as an amplitude ratio) are both in common
usage."

Chances are, the measurements were done with voltage using an RMS
voltmeter. So I'd say any published spec is likely to be an amplitude
measurement.

--
Les Cargill
```
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# Re: What is "percentage distortion"? - Les Cargill - 2012-10-25 21:35:00

```rickman wrote:
> On 10/25/2012 2:43 PM, Jerry Avins wrote:
>> Starting about 1950, when I first got serious about audio, I have
>> periodically run into arguments about how to decide what "10% harmonic
>> distortion" means. Some were both subtle and bitter. For example, if a
>> signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
>> Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
>> 1^2). If the 300 Hz component represents a distortion product, is the
>> THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
>> to be so many dB down. At audio, we sometimes measure the signal with a
>> voltmeter (peak? RMS? average?) with and without the fundamental notched
>> out, then report the ratio. What does that number mean?
>>
>> Jerry
>
> I don't think you are doing the math right.  RMS is the root of the mean
> of the square of an AC waveform considering all of the instantaneous
> voltages over time, not the RMS of individual frequency components.
>

The method for measuring THD is to measure once
with the fundamental, then without the fundamental
( using a notch filter ).

> If the 100 Hz signal is (10^2)/R Watts and the 300 Hz signal is (1^2)/R
> Watts then the 300 Hz signal is 1/100th the power of the 100 Hz signal
> and you have 1% distortion.  If they want the distortion as a voltage
> ratio, then it would be 10%.
>

Yep. I think that's actually true.

> This is why I like dB.  The convention is that no matter what you
> measure to get the number, it is converted to a power ratio.
>

Nope. dBV vs dBu have a similar dimensional problem. :) Same signal,
two different dB regimes. Technically, it's *all* dBV unless
the circuit is 600 ohm.

> I think I understand the problem.  The signal is 10 Vrms, the distortion
> is 1 Vrms.  You then calculate the Vrms of the combined signal based on
> the power calculation.  The mistake is subtracting the 10 Vrms signal
> from the combined signal Vrms to get the distortion voltage.  But you
> HAVE the distortion voltage, 1 Vrms.
>

In that case, 10% ( or -20dBV - gain dB ) is the THD figure.

> Rick

--
Les Cargill
```
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# Re: What is "percentage distortion"? - Jerry Avins - 2012-10-25 23:59:00

```On 10/25/2012 5:07 PM, glen herrmannsfeldt wrote:
> Jerry Avins <j...@ieee.org> wrote:
>> Starting about 1950, when I first got serious about audio, I have
>> periodically run into arguments about how to decide what "10% harmonic
>> distortion" means.
>
> Interesting question. Most of us just read it on the spec. sheets,
> then decide to buy the one with the lower number. (Well, maybe.)
>
>> Some were both subtle and bitter. For example, if a
>> signal has only two components, say 10 volts at 100 Hz and 1 volt at 300
>> Hz, what is the total voltage? Many would agree that it is sqrt(10^2 +
>> 1^2). If the 300 Hz component represents a distortion product, is the
>> THD 10% or 0.5%? At RF, we always use power, and transmitted spurs need
>> to be so many dB down. At audio, we sometimes measure the signal with a
>> voltmeter (peak? RMS? average?) with and without the fundamental notched
>> out, then report the ratio. What does that number mean?
>
> I suspect it is written into the FTC rules somewhere, along with
> the rule against an amplifier (or receiver) model number being
> twice its rated (RMS, according to the FTC definition) power.
>
> Now, if it is small enough, like 0.2%, then the difference doesn't
> matter much. I hope there are no home amplifiers with 10% THD,
> but maybe car stereo.

I built myself an Ultralinear Williamson amplifier in 1952 using a pair
of 6L6 output tubes. It was rated 12 watts at some vanishingly small
distortion. I carried it to work one day in order to try it at a
friend's house on mt way home, and when I got to the Port Authority
Terminal -- half the size then than it is now -- I found people running
around with megaphones because the 50W PA amplifier had crapped out. The
guy at the information kiosk was a sort of buddy, and I swapped my
amplifier for the terminal's, with a big red tag declaring me it's
rightful owner. I'm sure it ran at least 10% distortion that day, but is
sounded no worse than what it had replaced. It sounded great when I used
it as the plate modulator of a 50W transmitter, but a little clipping is
tolerable there. (It's up in my attic, but I imagine the lytics are shot.)

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
```
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# Re: What is "percentage distortion"? - Jerry Avins - 2012-10-26 00:06:00

```On 10/25/2012 9:27 PM, Les Cargill wrote:

...

> Chances are, the measurements were done with voltage using an RMS
> voltmeter. So I'd say any published spec is likely to be an amplitude
> measurement.

Wouldn't the marketers like to see power ratio? The numbers are much lower!

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
```
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