The Decibel - dB

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.

PowerAmplifier

Power in Power out

Decibel - Power Gain

Pi Po

Amplifier

Ap

dBP

PA

i

op 10log10

The power gain (Ap) of an amplifier is the logarithmic ratio between input power (Pi ) and output power (Po )

Decibel - Power Gain

Po 200mWAmplifier

Ap

Pi 100mW

dBA

P

PA

p

i

oP

3100

200log10

2100

200

10

A 3dB gain is a doubling of power.

Decibel - Attenuation

Po 1mWAmplifier

Ap

Pi 100mW

dBAp 2010.0

001.0log10 10

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.

A reduction of one hundred times is expressed as -20dB

Power Gain - Activity

Input OutputPowerAmplifier

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.

Multi-stage Power Gain

1st Stage(Pre-Amp)

Ap1=10Pi

2nd Stage(Power-Amp)

Ap2=100Po

System Gain (Ap) is the sum of the individual stage gains.

Ap = Ap1 + Ap2 = 10 + 100 = 110dB

Multi-stage Power Gain - Activity

1st Stage(Pre-Amp)

Ap1

Pi

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.

Decibel - Amplitude Gain

dBV

VA

i

ov 10log20

Input Vi Vo OutputSignal

AmplifierAv

It is also common to express the ratio of voltage or current in decibels

The output resistance (Ro ) must be equal to the input resistance (Ri ), ie the condition for maximum power transfer.

Ri Ro

Decibel - Amplitude Gain

Vi 20mV Vo 200mVSignalAmplifier

dBA

V

V

v

i

o

2020

200log20

1020

200

10

A voltage gain of ten times is equal to +20dB

Amplitude Gain - Activity

Input OutputSignal

AmplifierAv

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.

Gain and Loss 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

To get a ‘feel’ for power gain and loss expressed in dB the following shows the corresponding ratios,

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.