.. _antenna_gains:

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Using Antenna Gains
===================

It is common practice to specify the magnitude of signal in terms of a gain. For the most part gains are only used in :ref:`radcube` when applying the responses of the antenna/electronics. This is fairly opaque to the user. However, it is worthwhile to discuss gains here.

Gains are unit-less quantities (though they are given the pseudo-units of decibels, dB, in the same way that radians are unit-less) that describe the logarithm of a ratio. They come in two forms, power, :math:`G_\text{P}`, and amplitude/linear, :math:`G_\text{A}`.

  :math:`G_\text{P} = 10 \log_{10}\left( \frac{P}{P_\text{ref}} \right)`

  :math:`G_\text{A} = 20 \log_{10}\left( \frac{A}{A_\text{ref}} \right)`

Generally speaking, they are only useful if one knows the reference quantity, :math:`P_\text{ref}` or :math:`A_\text{ref}`. For example, in the case of an antenna's gain, which is a function of the arrival direction of the EM wave and its frequency, it is common practice to give the reference as an ideal, isotropic antenna.

  :math:`G_\text{ant}(f,\theta,\phi) = 10 \log_{10}\left( \frac{P}{P_\text{iso}} \right)`

Other times, an exact reference is implicitly chosen. For example, the units of dBm have a reference power of 1 milliWatt.

  :math:`\text{dBm}(P) = 10 \log_{10}\left( \frac{P}{1\text{mW}} \right)`

Likewise, the units dBm/Hz includes a reference of 1\,mW\,Hz.

Intuitively, gains are simply a scaled version of a log-plot with some reference offset.