

RF Related Conversions
TYPICAL CONVERSION FORMULAS (234Kb)
dBmW = dBmV
 107
The constant
in the above equation is derived as follows. Power
is related to voltage according to Ohm's law.
The Log_{10}
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 = V^{2
}/ R
10Log_{10}[P]
= 20Log_{10}[V]
 10Log_{10}[50^{W}]
Note, the
resistance of 50 used above reflects that RF systems
are matched to 50^{W}.
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 mV
Given a resistance
of 50W and
a power of 1 mW
20Log_{10}[223000
mV]
= 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.

dBmW/m^{2}
= dBmV/m
 115.8
The
constant in this equation is derived following similar
logic. First, consider the poynting vector which
relates the power density (W/m^{2})
to the electric field strength (V/m) by the following
equation.
P=E^{2}/h
Where h
is
the free space characteristic impedance equal to 120p^{W}.
Transforming this equation to decibels and using the
appropriate conversion factor to convert dBW/m^{2}
to dBmW/m^{2}
for power density and dBV/m to dBmV/m
for the electric field, the constant becomes 115.8

dBmV/m
= dBmV
+ AF
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.

V/m =
10^{{[(dBuV/m)120]/20}}
Not much
to this one; just plug away!

dBmA/m
= dBmV/m
 51.5
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

A/m =
10^{{[(dBuA/m)120]/20}}
As above,
simply plug away.

dBW/m^{2}
= 10Log_{10}[V/m
 A/m]
A simple
relation to calculate decibelWatts per square meter.

dBmW/m^{2}
= dBW/m^{2}
+ 30
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

dBpT =
dBmA/m
+ 2.0
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...
m_{o}
= 4p
x 10^{7}
H/m
Converting
from T to pT and from A/m to mA/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








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