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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.
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:
-
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:
-
In this calculation, Vn means the RMS
voltage of harmonic n.
Other definitions may be used. Many authors define THD as an
amplitude ratio rather than a power ratio. This results in a
definition of THD which is the square root of that given above.
For example in terms of voltages the definition would be:
-
This latter definition is the one commonly used in audio
distortion (percentage THD) specifications. 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. Fortunately if the THD is expressed in dB then both
definitions are equivalent. Note however that this is not the
case if the THD is expressed as a percentage.
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).
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:
-
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.
See also
-
Audio system measurements
-
THD analyzer
External links
-
Explanation of THD measurements
-
Rane audio's definition of both THD and THD+N
-
Conversion: Distortion attenuation in dB to distortion
factor THD in %
Category:
Electronics terms