Download Decibels Made Simple

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