Dimensionless real and positive quantities (like antenna gain G) and absolute values of complex-valued quantities (like absolute values of scattering parameter, i.e. |sij|) 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
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 = 104|
|+30||≈31.6||1 000 = 103|
|+20||10||100 = 102|
|+10||≈3.16||10 = 101|