RF Related Conversions
TYPICAL CONVERSION FORMULAS (234Kb)
dBmW = dBmV
in the above equation is derived as follows. Power
is related to voltage according to Ohm's law.
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:
P = V2
resistance of 50 used above reflects that RF systems
are matched to 50W.
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
V = (PR)0.5
= 0.223 V = 223000 mV
Given a resistance
of 50W and
a power of 1 mW
= 107 dB
form of Ohm's law shown above is provided to describe
why the log of the corresponding voltage is multiplied
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
the free space characteristic impedance equal to 120pW.
Transforming this equation to decibels and using the
appropriate conversion factor to convert dBW/m2
for power density and dBV/m to dBmV/m
for the electric field, the constant becomes 115.8
is the antenna factor of the antenna being used, provided
by the antenna manufacturer or a calibration that was
performed within the last year.
to this one; just plug away!
the constant for the above equation, simply convert
the characteristic impedance of free space to decibels,
as shown below.
simply plug away.
relation to calculate decibel-Watts per square meter.
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.
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...
from T to pT and from A/m to mA/m,
and deriving the Log, the constant becomes:
240 - 120
dBpT = dBuV + dBpT/uV + Cable Loss
dBuV/m = dBpT + 49.5 dB
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