The decibel (dB) is a logarithmic unit used to express the ratio of two power levels or amplitudes. It is commonly used to measure sound levels and power in electronic systems. A decibel represents one tenth of a bel and can express power gain or attenuation. Power gain is calculated as 10 times the log of the ratio between output and input power. A 3dB gain doubles the power. Attenuation is expressed as a negative value and represents a reduction in power. Gain can also be expressed for voltage or current using 20 times the log of the output to input ratio. Multiple stage amplifiers have a total gain equal to the sum of the individual stage gains.

1. The Decibel - dB
Power in
Power
Amplifier
Power out
The decibel (dB) is a logarithmic unit of measurement
that expresses the magnitude of power or amplitude
relative to a specified reference level and is commonly
used in the measurement of sound or power when
investigating electronic systems.
A decibel is one tenth of a bel, a seldom-used unit.

2. Decibel - Power Gain
Amplifier
Pi
Po
Ap
The power gain (Ap) of an amplifier is the logarithmic
ratio between input power (Pi ) and output power (Po )
Ap = 10 log10
Po
Pi
dB

3. Decibel - Power Gain
Pi 100mW
Amplifier
Ap
Po 200mW
Po 200
AP =
=
=2
Pi 100
200
Ap = 10 log10
= 3dB
100
A 3dB gain is a doubling of power.

4. Decibel - Attenuation
Pi 100mW
Amplifier
Ap
Po 1mW
It is also possible to express a reduction of power in
decibels – this is known as attenuation and the result
takes a negative sign indicating a reduction.
0.001
Ap = 10 log10
= −20dB
0.10
A reduction of one hundred times is expressed as -20dB

5. Power Gain - Activity
Input
Power
Amplifier
Output
A power amplifier is required to drive a 100 watt speaker
system from a 5 watt signal source. Determine the gain
of the amplifier in dB.
It is required to double the output power to 200 watts,
determine the new gain of the amplifier assuming the
source signal is the same.
Comment on your results.

6. Multi-stage Power Gain
Pi
1st Stage
(Pre-Amp)
Ap1=10
2nd Stage
(Power-Amp)
Ap2=100
Po
System Gain (Ap) is the sum of the individual stage
gains.
Ap = Ap1 + Ap2 = 10 + 100 = 110dB

7. Multi-stage Power Gain - Activity
Pi
1st Stage
(Pre-Amp)
Ap1
2nd Stage
(Power-Amp)
Ap2
Po
A hi-fi system is made up of a pre-amplifier and a power
amplifier. To drive a 400W speaker system the power amplifier
requires 2W.
Determine the system power gain in dB if the pre-amp draws
20mW (0.02W) from a signal source when operating at full power.
Investigate the system in two stages
a) as a single system and b) as two separate systems in cascade.
Comment on your results.

8. Decibel - Amplitude Gain
Input
Vi
Ri
Signal
Amplifier
Av
Ro Vo
Output
It is also common to express the ratio of
voltage or current in decibels
Vo
Av = 20 log10
Vi
dB
The output resistance (Ro ) must be equal to the input resistance (Ri ),
ie the condition for maximum power transfer.

9. Decibel - Amplitude Gain
Vi 20mV
Signal
Amplifier
Vo 200mV
Vo 200
=
= 10
Vi
20
Av = 20 log10
200
= 20dB
20
A voltage gain of ten times is equal to +20dB

10. Amplitude Gain - Activity
Input
Signal
Amplifier
Av
Output
A signal amplifier provides a 12 volt output when a 2 volt
signal is applied to its input. Determine the gain of the
amplifier in dB.
If the gain control is adjusted to provide a 24 volt signal
at the output for the same input signal, determine the
new gain of the amplifier.
Comment on your results.

11. Gain and Loss Ratios
To get a ‘feel’ for power gain and loss expressed in dB the
following shows the corresponding ratios,
A gain of 10,000 = 40dB
1000 = 30dB
100 = 20dB
10 = 10dB
1 = 0dB
A loss (attenuation) of 0.5 = -3dB
0.1 = -10dB
0.01 = -20dB
0.001 = -30dB
0.0001 = -40dB

12. dB Ratios
dBm is an abbreviation for the power ratio in decibels (dB)
of the measured power referenced to one milliwatt (mW). It is used
in radio, microwave and fibre optic networks as a convenient
measure of absolute.
dBW is referenced to one watt (1000 mW) and is an absolute unit,
used when measuring absolute power.
In audio dBm is typically referenced relative to a 600 ohm
impedance, while in radio frequency work dBm is typically
referenced relative to a 50 ohm impedance.