title: Distortionmeter
text: # Distortionmeter
  
  A distortionmeter (or more precisely distortion factor meter) is an electronic measuring instrument which displays the amount of distortion added to the original signal by an electronic circuit.
  
  ## Harmonic distortion
  
  Harmonic distortion is equivalent to adding harmonics to a signal. When a purely sinusoidal signal is in this way, a series of harmonics is superimposed on the original signal, and can be detected with suitable equipment.
  
  If the input is
  
      ${f_{i}}=a_{1}\cdot sin(\omega t)$
  
  The normalized output is
  
      ${f_{o}}=a_{1}\cdot sin(\omega t)+a_{2}\cdot sin(2\omega t)+a_{3}\cdot sin(3\omega t)+..$
  
  The value of Total Harmonics Distortion (THD) is defined as the ratio of the harmonics to the fundamental; i.e.,
  
      $THD={\frac {\sqrt {{a_{2}}^{2}+{a_{3}}^{2}+..}}{a_{1}}}$
  
  This ratio can be given in dB or in percentage.
  
  ## The instrument
  
  A distortionmeter is actually a levelmeter with two switchable parallel circuits at the input. The first circuit measures the total signal at the output of a system. (For low distortion levels this will be almost equal to fundamental). That value is adjusted to read 100% or, equivalently, to 0 dB. The second circuit is a high pass filter which removes (as much as practical) the fundamental frequency. This can be a notch filter, one which passes all but the fundamental, with negligible attenuation at other frequencies (including whatever harmonics might be present). Alternatively, if the distortion products are at higher frequencies, a highpass filter can be used if its cutoff rate is sufficiently steep to not affect the expected distortion products. The output of the filter is measured as a percentage of the fundamental, and the reported value will be the distortion value.
  
  