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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 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:
P = V2
/ R
10Log10[P]
= 20Log10[V]
- 10Log10[50W]
Note, the
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
law:
V = (PR)0.5
= 0.223 V = 223000 mV
Given a resistance
of 50W and
a power of 1 mW
20Log10[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.
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dBmW/m2
= 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/m2)
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 120pW.
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 dBmV/m
for the electric field, the constant becomes 115.8
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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.
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V/m =
10{[(dBuV/m)-120]/20}
Not much
to this one; just plug away!
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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.
20Log10[120p]
= 51.5
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A/m =
10{[(dBuA/m)-120]/20}
As above,
simply plug away.
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dBW/m2
= 10Log10[V/m
- A/m]
A simple
relation to calculate decibel-Watts per square meter.
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dBmW/m2
= dBW/m2
+ 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.
10Log10[1000]
= 30
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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...
mo
= 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
+ 20Log10[4p
x 10-7]
= 2.0
dBpT = dBuV + dBpT/uV + Cable Loss
dBuV/m = dBpT + 49.5 dB
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A.H. Systems, inc.
9710 Cozycroft Ave. • Chatsworth, CA 91311
phone: (818) 998-0223 • fax: (818) 998-6892
copyright
© 1996 - 2013 A.H.Systems, inc.
All Rights Reserved.
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