## Power

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## Selasa, 03 April 2012

### THD

 THD Measurement and Conversion
 You have probably seen "Total Harmonic Distortion" figures, expressed in percent, applied as one measure of quality of audio gear. What does this mean, and how is it measured?

 Harmonic Voltage Power % Distortion Fundamental 4.0 volts 2 watts 2nd Harm. 0.3 volts .01125 W 0.56225 % 3rd Harm. 0.5 volts .03125 W 1.5625 % Total .0425 W 2.12475 %

"Hey, neat," you may be saying. "Only 2.12475%!" But we're not there yet; 2.12475% is another wrong answer. While this apparent THD figure is, indeed, representative of the total power of the harmonic content, we still have to convert this power to an equivalent RMS voltage in order to come up with a THD figure according to standard methodology.

So the correct answer is obtained by taking total harmonic power (0.0425 watts) and calculating the equivalent RMS voltage, given by the square root of power times output impedance, or about 0.583 volts in the example. i.e. SQRT(0.0425 watts * 8 ohms). So the THD value, as specified would actually be 100 times 0.583 volts divided by 4 volts = about 14.6% (correct answer).

To generalize this as an equation,

 THD(%) = 100 * SQRT[(P2 + P3 + P4 + ... + Pn) * Zout] / Vt

where TDH(%) is total harmonic distortion, P represents the power of each harmonic, Zout equals the load impedance, and Vt is the total RMS output voltage (containing both the fundamental and the harmonic terms).

Another way of getting the correct answer would be to take the square root of the sum of the squares of harmonic component voltages. This is because power is proportional to the square of the voltage. Let's try it. SQRT(0.32 + 0.52) = SQRT(.09 + .25) = SQRT(0.34) = 0.583. Multiply by 100 (to get percent) and divide by 4 (fundamental voltage) gives the same correct result, approx. 14.6%.

In equation form,

 THD(%) = 100 * SQRT[(V22 + V32 + V42 + ... + Vn2)] / Vt

where TDH(%) is total harmonic distortion, V represents the RMS voltage of each harmonic, and Vt is the total RMS output voltage.
Note that Zout is not present in this variant of the equation;
since P = V2/Z, the impedance terms cancel.

To understand a system with an input and an output, such as an audio amplifier, we start with an ideal system where the transfer function is linear and time-invariant. When a signal passes through a non-ideal, non-linear device, additional content is added at the harmonics of the original frequencies. THD is a measurement of the extent of that distortion.
When the input is a pure sine wave, the measurement is most commonly the ratio of the sum of the powers of all higher harmonic frequencies to the power at the first harmonic, or fundamental, frequency:
$\mbox{THD} = \frac{P_2 + P_3 + P_4 + \cdots + P_\infty}{P_1} = \frac{\displaystyle\sum_{n=2}^\infty P_n}{P_1}$
which can equivalently be written as
$\mbox{THD} = \frac{P_\mathrm{total} - P_1}{P_1}$
if there is no source of power other than the signal and its harmonics.
Measurements based on amplitudes (e.g. voltage or current) must be converted to powers to make addition of harmonics distortion meaningful. For a voltage signal, for example, the ratio of the squares of the RMS voltages is equivalent to the power ratio:
$\mbox{THD} = \frac{V_2^2 + V_3^2 + V_4^2 + \cdots + V_\infty^2}{V_1^2}$
where Vn is the RMS voltage of nth harmonic and n=1 is the fundamental frequency.
THD is also commonly defined as an amplitude ratio rather than a power ratio,[1] resulting in a definition of THD which is the square root of that given above:
$\mbox{THD} = \frac{ \sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots + V_n^2} }{V_1}$
This latter definition is 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.
As a result, THD is a non-standardized specification and the results between manufacturers are not easily comparable. Since individual harmonic amplitudes are measured, it is required that the manufacturer disclose the test signal frequency range, level and gain conditions, and number of measurements taken. It is possible to measure the full 20–20 kHz range using a sweep. For all signal processing equipment, except microphone preamplifiers, the preferred gain setting is unity. For microphone preamplifiers, standard practice is to use maximum gain.
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 relative to the fundamental as distortion attenuation.

## THD+N

THD+N means total harmonic distortion plus noise. This measurement is much more common and more comparable between devices. It is usually measured by inputting a sine wavenotch filtering the output, and comparing the ratio between the output signal with and without the sine wave:
$\mathrm{THD+N} = \frac{\displaystyle\sum_{n=2}^\infty{\text{harmonic powers}} + \text{noise power}}{\text{fundamental power}}$
A meaningful measurement must include the bandwidth of measurement. This measurement includes effects from intermodulation distortion, and so on, in addition to harmonic distortion. In Europe, it is preferable to apply a ITU-R BS.468 weighed curve, which is intended to accentuate what is most audible to the human ear, contributing to a more accurate measurement. However, as the weight of the curve adds 12 dB of gain to the critical midband, making THD+N measurements bigger, manufacturers object to its use and have widely prevented its adoption in American and Asian markets.