Useful formulas for RF related conversions

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Typical EMC Related Formulas

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The constant in the above equation is derived as follows.  Power is related to voltage according to Ohm's law.  The Log₁₀ function is used for relative (dB) scales, so applying the logarithmic function to Ohm's law, simplifying, and scaling by ten (for significant figures) yields:


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:

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

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

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The constant in this equation is derived following similar logic. First, consider the poynting vector which relates the power density (W/m²)to the electric field strength (V/m) by the following equation:

Where η is the free space characteristic impedance equal to 120p^Ω Transforming this equation to decibels and using the appropriate conversion factor to convert dBW/m² to dBmW/m² for power density and dBV/m to dBµV/m for the electric field, the constant becomes 115.8

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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.

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Not much to this one, just plug away!

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

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As above, simply plug away.

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

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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:

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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...

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

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View our other RF Conversion formula sheets:
Antenna Factor and Gain Calculations
dBm to Volts to Watts conversion
Magnetic field conversions
Field Intensity Calculation
Antenna Beamwidth Coverage Calculations
Frequency and Wavelength Calculator
VSWR Calculations