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Encyclopedia > Total harmonic distortion

The total harmonic distortion, or THD, of a signal is a measurement of the harmonic distortion present and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental. In information theory, a signal is the sequence of states of a communications channel that encodes a message. ... The total harmonic distortion, or THD, of a signal is a measurement of the harmonic distortion present and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental. ...


Explanation

In most cases, the transfer function of a system is linear and time-invariant. When a signal passes through a non-linear device, additional content is added at the harmonics of the original frequencies. THD is a measurement of the extent of that distortion. In electrical engineering, specifically in signal processing and control theory, LTI system theory investigates the response of a linear, time-invariant system to an arbitrary input signal. ...


The measurement is most commonly the ratio of the sum of the powers of all harmonic frequencies above the fundamental frequency to the power of the fundamental: In physics, power (symbol: P) is the rate at which work is performed. ... In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. ... The fundamental tone, often referred to simply as the fundamental, is the lowest frequency in a harmonic series. ... Sine waves of various frequencies; the bottom waves have higher frequencies than those above. ...

mbox{THD} = {sum{mbox{harmonic powers}} over mbox{fundamental frequency power}} = {{P_2 + P_3 + P_4 + cdots + P_n} over P_1}

Other calculations for amplitudes, voltages, currents, and so forth are equivalent. For a voltage signal, for instance, the ratio of the squares of the RMS voltages is equivalent to the power ratio: RMS may refer to any of the following: Railway Mail Service, US mail transportation service until the mid-20th century Royal Mail Ship or Steamer, ship prefix for vessels that carry mail under contract to the British Royal Mail Royal Meteorological Society Royal Society of Miniature Painters Sculptors and Gravers...

mbox{THD} = {{V_2^2 + V_3^2 + V_4^2 + cdots + V_n^2} over V_1^2}

In this calculation, Vn means the RMS voltage of harmonic n.


Other definitions may be used. In particular, there are many authors who give the definition of THD as precisely the square root of the above given definition. This means, for example, that a THD of 0.0001% by one persons definition is equivalent to 0.1% by an others. This situation clearly makes percentage THD figures meaningless unless the author specifies the definition used. Fortunately if the THD is expressed in dB then it doesn’t matter which of the two definitions is used. For example a THD of 0.0001% as a power ratio would correspond to -60dB as would the equivalent THD of 0.1% expressed as an amplitude ratio using the alternate “square root” definition. Unfortunately, and despite the two commonly used but conflicting definitions, percentage is still the most commonly used method of expressing THD.


A measurement must also specify how it was measured. Measurements for calculating the THD are made at the output of a device under specified conditions. The THD is usually expressed in percent as distortion factor or in dB as distortion attenuation. A meaningful measurement must include the number of harmonics included (and should include other information about the test conditions). // Information processing In information processing, output is the process of transmitting information by an object (verb usage). ... A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. ... The decibel (dB) is a measure of the ratio between two quantities, and is used in a wide variety of measurements in acoustics, physics and electronics. ...


THD+N means total harmonic distortion plus noise. This measurement is much more common and more comparable between devices. This is usually measured by inputting a sine wave, notch filtering the output in question, and measuring the ratio between the output signal with and without the sine wave: In trigonometry, an ideal sine wave is a waveform whose graph is identical to the generalized sine function y = Asin[ω(x − α)] + C, where A is the amplitude, ω is the angular frequency (2π/P where P is the wavelength), α is the phase shift, and C... A notch filter, also called a band-stop filter, sometimes a narrow band-pass filter, or T-notch filter, is an electronic filter typically used when the high frequency and the low frequency are less than 1 to 2 decades apart (that is, the high frequency is less than 10...

mbox{THD+N} = {sum{mbox{harmonic powers}} + mbox{noise power} over mbox{total output power}}

A meaningful measurement must include the bandwidth of measurement. This measurement includes effects from intermodulation distortion, interference, and so on, instead of just harmonic distortion. This article or section does not cite its references or sources. ... Intermodulation distortion: Nonlinear distortion characterized by the appearance, in the output of a device, of frequencies that are linear combinations of the fundamental frequencies and all harmonics present in the input signals. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...


See also

The designer of a system for sound reproduction needs to be able to measure the systems performance in a number of areas. ... Total Harmonic Distortion (THD) Analyzers calculate the total distortion introduced by all the harmonics of the fundamental frequency wave. ...

External links


  Results from FactBites:
 
Total Harmonic Distortion (439 words)
The levels of harmonic distortion in a high quality amplifiers are sooooo far below audibility that they are basically of no concern.
When someone tells you that one amplifier is definitely going to sound better because its THD is rated at.002% vs an amp with.05%, you can be pretty sure that he doesn't know what he's talking about.
When the harmonics reach 5%, they are clearly audible.
SoundStage! Measurements - How we test amplifiers (925 words)
This section indicates the power output of the amplifier at 1% and 10% distortion levels and 8-, 4-, and 16-ohm impedances when the amplifier is driven by a 1kHz test signal.
What it tells you: Three or four measurements are displayed: 1kHz total harmonic distortion plus noise vs power output for 16-, 8-, and 4-ohm resistive loading on the 8-ohm tap for tube power amplifiers, plus SMPTE IM distortion with 8-ohm loading on the 8-ohm tap.
What it tells you: Four measurements are displayed here: Total harmonic distortion vs frequency at four power levels ranging from 1W to a value at or near the rated power of the amplifier.
  More results at FactBites »


 

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