Insertion loss
# 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.

