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# [SOLVED]Understanding of Total Harmonics Distortion and it's importance

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#### Onedust

##### Junior Member level 2
Good day, everyone.

I have a question regarding understanding of the Total Harmonic Distortion (THD) and why is it a good merit for signal distortion measurement.

With the FOURIER Transform (let’s talk only about DFT) we can decompose any signal into sinusoids of different frequencies, phases and amplitudes. That means that any signal can be composed from the sum of these sinusoids.

Now, if we send a signal through an amplifier we would like to get the same signal on the output, but with the amplified amplitude. So if we check the spectrum before and after we can see, how good the amplifier is and if the signal was not only amplified, but also changed.

THD gives us a relationship between the power (amplitude) of the fundamental frequency, i.e sinusoid with the highest amplitude in the spectrum and the sum of powers of all harmonic components of the signal. This way we can send a pure sine wave through an amplifier and see if it was changed and what harmonic components (this is why it is total harmonic distortion) have changed the signal.

But what about other frequency components? The signal is not made of only harmonic frequencies. Why do we only check harmonic frequencies? I am sure I missed something fundamental.

Regards,

Den

#### Onedust

##### Junior Member level 2
" i.e sinusoid with the highest amplitude in the spectrum" - I mean the lowest frequency, not the highest amplitude. Don't know why did I write the highest amplitude.... well in most cases it's so, that fundamental frequency has the highest amplitude, but it's not what qualifies the fundamental frequency. In fact it can even have zero amplitude.

#### barry

What 'other frequencies' are you speaking about? Are you talking about noise? If so, that's why there is also a specification for THD+noise. The specification for THD is based on a measurement of a sine wave input. YOUR signal may not be "made of only harmonic frequencies", but the way THD is determined is with a single sine wave. If you look at the specification for an amplifier, the THD is specified at a particular amplitude and frequency.

Onedust

### Onedust

Points: 2

#### KlausST

##### Super Moderator
Staff member
Hi,

Imagine a pure sine.
In the FFT results you see one peak.

Now try to distort this sine in a way that the next (distorted) sinewave looks the same as the one before.
So the distortion also repeats with the same interval time than the pure sine.
Then you will find out that this is only possible with integer multiples of the fundamental sine.
(Maybe you can try this with excel)

This means that every other frequency is not distortion. It is considered to be noise.

Noise is independent of signal, distortion depends on signal.

Klaus

Onedust

### Onedust

Points: 2

#### Warpspeed

The basic premise is that you feed in a pure sine wave test signal that contains only one fundamental frequency, with no additional harmonics (or noise).

You then measure the output amplitude, which becomes your 100% reference.

If the fundamental is then removed by means of a very deep and effective notch filter, all that remains are all the harmonic distortion products (plus noise).
The sum total amplitude of all the residual distortion products can then be quoted as a percentage distortion, or as a distortion decibel ratio.

Its a pretty easy to measure, repeatable and reliable indication of overall distortion.

Onedust

### Onedust

Points: 2

#### Onedust

##### Junior Member level 2
@Barry, @KlausST and @ Warpspeed,

Well my main concern was that of the meaning of distortion. A signal can be influenced by a cross-talk and its frequency spectrum will contain other than harmonic frequencies. Should in that case these frequencies (not harmonic) be just seen as noise?

To conclude:

THD is a merit to determine how the “Device Under Test” changes a pure sine wave, which was given at the input, on the output side?

Regards,

Den

#### D.A.(Tony)Stewart

With more than one sine source you get intermod dist. or IMD so THD is the sum of HD and IMD.

choose mag/phase button then log view then select sine and draw some distortion in either time or frequency domiain with mouse.

You can even listen to it and change frequency or change waveforms.

Onedust

### Onedust

Points: 2

#### Onedust

##### Junior Member level 2
@SunnySkyguy,

thank you. A very nice application. Very nicely visualizes the influence of different harmonics on the signal.

#### D.A.(Tony)Stewart

I refer to it often for "show n tell"

Like... clear input then click a dot at full scale to make a narrow repeating pulse the width of the pulse is exactly where the null frequency lies.

Or how to measure asymmetry in a square wave without a scope.

Answer: Measure the 2nd harmonic and use a lookup table between -dB and asymmetry. ( for when 49/51% is not good enough in data recovery)

e.g. BPF and precision peak detector with 60 dB range.

#### Warpspeed

A signal can be influenced by a cross-talk and its frequency spectrum will contain other than harmonic frequencies. Should in that case these frequencies (not harmonic) be just seen as noise?
Yes, because they consist of something other being added quite independently of the original signal. Mains induced ripple and hum is a classic example.

Remove the signal, and the noise and crosstalk will still be there, so crosstalk is really just another form of noise.

On the other hand, distortion products are invariably harmonically related to the original signal.

#### D.A.(Tony)Stewart

I agree. Testing THD with a single 1kHz signal does not tell the true performance not include noise floor.

Sometimes people use THD and others graph THD vs output level for 2 sine inputs. Others use THD & N
Noise ought to include spurious and thermal noise.

The method specs depends highly on the application. For example RF COMM radios, it is done differently.

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