Dimensionless real and positive quantities (like antenna gain *G*) and absolute values of complex-valued quantities (like absolute values of scattering parameter, i.e. |*s*_{ij}|) are often given in logarithmic scale. Logarithmic representations are advantageous if quantities vary over several orders of magnitude. Logarithmic values maintain a good resolution for both small and large values.

For power-based quantities (like antenna gain) a factor of 10 is used, whereas for voltage, current or field strength-based values (like scattering parameters) a factor of 20 is used. So, the logarithmic values are given as

A.44

where is the *common logarithm*. We do not use different symbols for linear and logarithmic representation. The pseudo-unit ‘dB’ (decibel) indicates the logarithmic scale and avoids confusing linear and logarithmic values: for example a gain of *G* = 1 in linear scale equals a gain of *G* = 0 dB in logarithmic scale. Table A.1 correlates commonly used linear and logarithmic values.

Logarithmic scale dB | Linear scale (Voltage ratio) | Linear scale (Power ratio) |

+40 | 100 | 10 000 = 10^{4} |

+30 | ≈31.6 | 1 000 = 10^{3} |

+20 | 10 | 100 = 10^{2} |

+10 | ≈3.16 | 10 = 10^{1} |

+6 | ≈2 | ≈4 |

Start Free Trial

No credit card required