log10GE

log10GE refers to the base-10 logarithm of the electric field gain, often encountered in signal processing and antenna theory. The electric field gain, denoted by GE, is a dimensionless quantity that represents the ratio of the electric field strength produced by an antenna in a specific direction to the electric field strength that would be produced by a reference antenna (typically an isotropic radiator) at the same distance, for the same input power. Taking the base-10 logarithm of this gain is a common practice because antenna gains often span a very large range of values. Using a logarithmic scale allows for a more manageable representation of these values, making it easier to compare different antennas or analyze signal propagation characteristics.

The unit commonly associated with log10GE is the decibel (dB). Specifically, when referring to electric field gain, the logarithmic value is often expressed as 20 log10(GE). This factor of 20 arises from the relationship between power and amplitude. Power is proportional to the square of the amplitude (or electric field strength). Therefore, when converting a power ratio to a decibel scale, one uses 10 log10(Power Ratio), and since the electric field gain is a ratio of amplitudes, the power gain is the square of the electric field gain. Thus, 10 log10(GE^2) = 20 log10(GE). This value, 20 log10(GE), provides a linear representation of the antenna's directivity and efficiency relative to a reference.