A.H. Systems Model PAM-0118 Pre-Amplifier
TYPICAL CONVERSION FORMULAS
dBmW = dB
µ
V
–
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
Ω
]
Note, the resistance of 50 used above reflects that RF systems are matched to 50
Ω
. 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
µ
V
Given a resistance of 50
Ω
and a power of 1 mW
20Log
10
[223000
µ
V] = 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
= dB
µ
V/m
–
115.8
The constant in this equation is derived following similar logic. First, consider the pointing vector
which relates the power density (W/m
2
) to the electric field strength (V/m) by the following equation.
P=|E|
2
/
η
Where
η
is the free space characteristic impedance equal to 120
π
Ω
. 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 dB
µ
V/m for the electric field, the constant becomes 115.8.
dB
µ
V/m = dB
µ
V + 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!
dB
µ
A/m = dB
µ
V/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
[120
π
] = 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 decibel-Watts 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.
A.H. Systems inc. – April 2009
REV B
10
