Total Harmonic Distortion

The term English Total Harmonic Distortion , abbreviated THD and roughly translates to total harmonic distortion , as part of the signal analysis is an indication to the size of the shares resulting from non-linear distortion of a signal to quantify. There are various stipulations that relate either to the ratio of a power variable or to field variables such as the time course of an electrical voltage in the form of an amplitude ratio.

Performance ratio

The THD is defined as the ratio of the summed power P _{h of} all harmonics to the power of the fundamental P ₁ . A square wave signal with 50 kHz, for example, contains a sinusoidal fundamental oscillation with 50 kHz and harmonics with 3, 5, 7, 9 etc. times the fundamental frequency, which can be shown in the context of the Fourier analysis .

The information can be given in% of the ratio of the two services, i.e.

${\displaystyle \mathrm {THD} _{\%}={\frac {P_{\mathrm {h} }}{P_{1}}}\cdot 100}$

or as a ratio of the powers in dB, that is

${\displaystyle \mathrm {THD} _{\mathrm {dB} }=10\cdot \log _{10}\left({\frac {P_{\mathrm {h} }}{P_{1}}}\right)}$

Field variables such as voltages and currents are included in the reference as a square. For a voltage signal, the ratio of the rms value - voltages is equivalent to the energy ratio:

${\displaystyle \mathrm {THD} ={\frac {{U_{2}}^{2}+{U_{3}}^{2}+{U_{4}}^{2}+\cdots +{U_{n}}^{2}}{U_{1}^{2}}}\,}$

In this calculation, U _{n means} the rms value voltage U _{eff of} the harmonic n .

It is also common to specify the THD + N , where N is noise ( English noise ) is.

Here, the sum of the interference powers is P _sturgeon = interference power of the harmonics P _h plus noise power of the noise P _noise with the performance of the overall signal P _ges compared.

${\displaystyle P_{\mathrm {ratio} }={\frac {P_{\mathrm {st{\ddot {o}}r} }}{P_{\mathrm {ges} }}}={\frac {P_{\mathrm {h} }+P_{\mathrm {rausch} }}{P_{\mathrm {ges} }}}}$

Here, too, the information can be given in% or in dB, i.e.

${\displaystyle \mathrm {THD+N} _{\%}={\frac {P_{\mathrm {st{\ddot {o}}r} }}{P_{\mathrm {ges} }}}\cdot 100}$

or

${\displaystyle \mathrm {THD+N} _{\mathrm {dB} }=10\cdot \log _{10}\left({\frac {P_{\mathrm {st{\ddot {o}}r} }}{P_{\mathrm {ges} }}}\right)}$

Amplitude ratios

Alternatively, in audio engineering , among other things , the amplitude ratios instead of the power ratios are put in relation and referred to as THD. This leads to the following definition which deviates from the above definition:

${\displaystyle \mathrm {THD} _{\mathrm {\%audio} }={\frac {\sqrt {{U_{2}}^{2}+{U_{3}}^{2}+{U_{4}}^{2}+\cdots +{U_{n}}^{2}}}{U_{1}}}\,}$

The THD is also determined for electrical power supply networks. Electrical devices with non-linear characteristics such as loads with semiconductor elements ( switched-mode power supply , inverter , dimmer with phase control , etc.) do not cause a sinusoidal current in the power supply network, which corresponds to distortion reactive power. This can also be viewed as the emission of harmonics which, due to the network impedances, distort the network voltage, which can lead to disturbances in the consumers and increase the losses in the energy supply network. A low THD of the mains voltage therefore corresponds to good voltage quality in the mains. In Europe, the interference level defined in the EN-61000 standard applies.

In power engineering, the THD of the voltage is defined according to the IEEE standard 1459-2010 as

${\displaystyle \mathrm {THD} _{\mathrm {U} }={\frac {\sqrt {{U}^{2}-{U_{1}}^{2}}}{U_{1}}}\,}$

with U the effective value of the voltage and U ₁ to the effective value of the fundamental.

The same applies to electricity:

${\displaystyle \mathrm {THD} _{\mathrm {i} }={\frac {\sqrt {{I}^{2}-{I_{1}}^{2}}}{I_{1}}}\,}$.

The distortion factor is similarly defined as an amplitude ratio, but uses the rms value of the entire signal as a reference and not just the rms value of the fundamental. At a voltage U , the distortion factor k is defined as:

${\displaystyle k=\mathrm {THD} _{\mathrm {R} }={\frac {\sqrt {U^{2}-U_{1}^{2}}}{U}}={\frac {\mathrm {THD} _{\mathrm {U} }}{\sqrt {1+\mathrm {THD} _{\mathrm {U} }^{2}}}}}$

In English-language specialist literature, the distortion factor is referred to as THD _R , for English THD root mean square .

literature

• Jürgen Schlabbach: Electric power supply . VDE-Verlag, 1995, ISBN 3-8007-1999-1 .
• DIN-EN 61000-2-4 / VDE 0839 part 2-4: Electromagnetic compatibility (EMC) . May 2005.
• Walt Kester: Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so You Don't Get Lost in the Noise Floor . Analog Devices, company publication , 2005 ( analog.com [PDF; 93 kB ] MT-003).

Web links

• Conversion: Total Harmonic Distortion in% and distortion attenuation in dB and back
• THD distortion as the sound effect of "artistic" distortion. (PDF; 255 kB)

Individual evidence

1. ↑ G. Randy Slone: The audiophile's project source book . McGraw-Hill, 2001, ISBN 0-07-137929-0 , pp. 10 .
2. ^ IEEE: IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions . 2010.
3. ↑ Doron Shmilovitz: On the definition of Total Harmonic Distortion and Its Effect on Measurement interpretation . tape 20 , no. 1 . IEEE Transactions on Power Delivery, January 1, 2005, doi : 10.1109 / TPWRD.2004.839744 ( eng.tau.ac.il [PDF]).