Decibels Made Simple
by
Bob Young
The Bel was originally named
after Alexander Graham Bell.
Originally used to measure
audio levels in phone circuits.
Logarithmic progression.
Non-linear scale.
1 Bel: gain factor of 10
2 Bels: gain factor of 100
3 Bels: gain factor of 1000
etc.
This scale was too large to
use.
1/10th of a Bel – a deciBel –
became the standard.
The 10’s Approximation
(for gain)
10 dB = x 10
20 dB = x 100
30 dB = x 1,000
40 dB = x 10,000
50 dB = x 100,000
1
(x10 )
2
(x10 )
(x103)
(x104)
(x105)
The 10’s Approximation
(for loss)
-10 dB = / 10
-20 dB = / 100
-30 dB = / 1,000
-40 dB = / 10,000
-50 dB = / 100,000
(x10-1)
(x10-2)
(x10-3)
-4
(x10 )
-5
(x10 )
The 3’s Approximation
(for gain)
3 dB = x 2
6 dB = x 2 x 2
9 dB = x 2 x 2 x 2
(x21)
2
(x2 )
(x23)
The 3’s Approximation
(for loss)
-3 dB = / 2
-6 dB = / 2 / 2
-9 dB = / 2 / 2 / 2
-1
(x2 )
(x2-2)
(x2-3)
The Gain/Loss Formula
dB = 10Log10(Pout/Pin)
Converting dB
to Gain Factor
GF =10(dB/10)
(Uses the 10x function on calculator)
Example
If an amplifier has an input of
50 watts and an output of 100
watts, what is the gain in dB?
3 dB
Units of Measure
dBm
• 0 dBm = 1 milliwatt
• 0 dBm = 1 mw
• 0 dBm = 0.001w
Another kind of dBm
• "Zero level is the reference level
obtained with a 1000 Hz signal and
1 milliwatt of power in a line or
circuit of 600 ohms resistance (a
600-ohm line). The corresponding
voltage level is 0.773 volts. This
level is sometimes called 0 dBm."
dBw
• 0 dBw = 1 watt
• 0 dBw = 1 w
dBk
• 0 dBk = 1 kilowatt
• 0 dBk = 1,000 watts
• 0 dBk = 1kw
Units of Field Intensity
dBu
• 0 dBu = 1 microvolt/meter
• 0 dBu = 1 mV/m
dBmV
• 0 dBmV = 1mV into a 50 ohm
load.
dBd
• 0 dBd is equivalent to the
standard radiation pattern of
a half-wave dipole antenna.
dBi
• 0 dBi is equivalent to the
radiation pattern of an
isotropic radiator
A half-wave dipole antenna
has a gain of 2.14 dB when
compared to an isotropic
radiator.
Practice Problems