title: Insertion loss
text: # Insertion loss
  
  In telecommunications, insertion loss is the loss of signal power resulting from the insertion of a device in a transmission line or optical fiber and is usually expressed in decibels (dB).
  
  If the power transmitted to the load before insertion is $P_T$ and the power received by the load after insertion is $P_R,$ then the insertion loss in decibels is given by,
  
      $IL(\mathrm {dB} )=10\log _{10}{P_{\mathrm {T} } \over P_{\mathrm {R} }}$
  
  ## Electronic filters
  
  Insertion loss is a figure of merit for an electronic filter and this data is generally specified with a filter. Insertion loss is defined as a ratio of the signal level in a test configuration without the filter installed ($\left\vert V_{1}\right\vert$) to the signal level with the filter installed ($\left\vert V_{2}\right\vert$). This ratio is described in decibels by the following equation:
  
      ${\mbox{Insertion loss (dB)}}=10\log _{10}{\frac {\left\vert V_{1}\right\vert ^{2}}{\left\vert V_{2}\right\vert ^{2}}}=20\log _{10}{\frac {\left\vert V_{1}\right\vert }{\left\vert V_{2}\right\vert }}$
  
  For passive filters, $\left\vert V_{2}\right\vert$ will be smaller than $\left\vert V_{1}\right\vert$. In this case, the insertion loss is positive and measures how much smaller the signal is after adding the filter.
  
  ## Link with scattering parameters
  
  In case the two measurement ports use the same reference impedance, the insertion loss ($IL$) is defined as:
  
      $IL=-20\log _{10}\left|S_{21}\right|\,{\text{dB}}$.
  
  Here $S_{21}$ is one of the scattering parameters. Insertion loss is the extra loss produced by the introduction of the DUT between the 2 reference planes of the measurement. The extra loss can be introduced by intrinsic loss in the DUT and/or mismatch. In case of extra loss the insertion loss is defined to be positive.
  
  