P = V^{2}/ R

10Log_{10}[P] = 20Log_{10}[V] - 10Log_{10}[50^{Ω}]

Note, the resistance of 50 used above reflects that RF systems are matched to 50Ω. Since RF systems use decibels referenced from 1 mW, the corresponding voltage increase for every 1 mW power increase can be calculated with another form of Ohm's law:

V = (PR)^{0.5} = 0.223 V = 223000 µV

Given a resistance of 50Ω and a power of 1 mW

20Log_{10}[223000 µV] = 107 dB

The logarithmic form of Ohm's law shown above is provided to describe why the log of the corresponding voltage is multiplied by 20.

P=|E|^{2}/η

Where η is the free space characteristic impedance equal to 120p

Where AF is the antenna factor of the antenna being used, provided by the antenna manufacturer or a calibration that was performed within the last year.

Not much to this one, just plug away!

To derive the constant for the above equation, simply convert the characteristic impedance of free space to decibels, as shown below:

20Log_{10}[120p] = 51.5

As above, simply plug away.

A simple relation to calculate decibel-Watts per square meter.

The derivation for the constant in the above equation comes from the decibel equivalent of the factor of 1000 used to convert W to mW and vice versa, as shown below:

10Log_{10}[1000] = 30

In this equation, the constant 2.0 is derived as follows. The magnetic flux density, B in Teslas (T), is related to the magnetic field strength, H in A/m, by the permeability of the medium in Henrys per meter (H/m). For free space, the permeability is given as...

µ_{o} = 4p x 10^{-7} H/m

Converting from T to pT and from A/m to µA/m, and deriving the Log, the constant becomes:

240 - 120 + 20Log_{10}[4p x 10^{-7}] = 2.0

dBpT = dBuV + dBpT/uV + Cable Loss

dBuV/m = dBpT + 49.5 dB

dBuV/m = dBpT + 49.5 dB

Download our other RF Convertion formula sheets:

Typical EMC Related Formulas

Magnetic Convertion Formulas

dBm to Volts to Watts_Conversion

VSWR Calculations

Field Intensity Calculation

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