# Insertion loss

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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 PT and the power received by the load after insertion is PR, then the insertion loss in dB is given by,

$10 \log_{10} {P_\mathrm T \over P_\mathrm R}$

## 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 (|V1|) to the signal level with the filter installed (|V2|). This ratio is described in dB by the following equation:

$\mbox{Insertion loss (dB)} = 10 \log_{10} {\left|V_1\right|^2 \over \left|V_2\right|^2} = 20 \log_{10} {\left|V_1\right| \over \left|V_2\right|}$

Note that, for most filters, |V2| will be smaller than |V1|. 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:[1][2]

$IL = -20\log_{10}\left|S_{21}\right| \,\text{dB}$

and not, as often mistakenly thought, by:

$IL = 10\log_{10}\frac{\left|S_{21}\right|^2}{1-\left|S_{11}\right|^2}\,$ dB.

Here $S_{11}$ and $S_{21}$ are two of the scattering parameters. It 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.

## References

1. ^ Pozar, David M.; Microwave Engineering, Third Edition
2. ^ Collin, Robert E.; Foundations For Microwave Engineering, Second Edition