Chapter 1
(part 2)
Gain, Attenuation, Decibels
EKT343 –Principle of Communication
1
Engineering
Gain, Attenuation,
and Decibels
• Most circuits in electronic communication are
used to manipulate signals to produce a
desired result.
• All signal processing circuits involve:
– Gain
– Attenuation
Gain, Attenuation,
and Decibels
Gain
– Gain means amplification. It is the ratio of a circuit’s output to its
input.
output Vout
AV = =
input Vin
Figure 2-1: An amplifier has gain.
Gain, Attenuation,
and Decibels
• Most amplifiers are also power amplifiers, so the same
procedure can be used to calculate power gain AP where Pin is
the power input and Pout is the power output.
Power gain (Ap) = Pout / Pin
• Example:
The power output of an amplifier is 6 watts (W). The power gain
is 80. What is the input power?
Ap = Pout / Pin therefore Pin = Pout / Ap
Pin = 6 / 80 = 0.075 W = 75 mW
Gain, Attenuation,
and Decibels
• An amplifier is cascaded when two or more
stages are connected together.
• The overall gain is the product of the individual
circuit gains.
• Example:
Three cascaded amplifiers have power gains of 5, 2, and 17.
The input power is 40 mW. What is the output power?
Ap = A1 × A2 × A3 = 5 × 2 × 17 = 170
Ap = Pout / Pin therefore Pout = ApPin
Pout = 170 (40 × 10-3) = 6.8W
Gain, Attenuation,
and Decibels
Attenuation
– Attenuation refers to a loss introduced by a circuit or
component. If the output signal is lower in amplitude
than the input, the circuit has loss or attenuation.
– The letter A is used to represent attenuation
– Attenuation A = output/input = Vout/Vin
– Circuits that introduce attenuation have a gain that is
less than 1.
– With cascaded circuits, the total attenuation is the
product of the individual attenuations.
Gain, Attenuation,
and Decibels
Figure 2-3: A voltage divider introduces attenuation.
Gain, Attenuation,
and Decibels
Figure 2-4: Total attenuation is the product of individual attenuations of each cascaded circuit.
Gain, Attenuation,
and Decibels
Decibels
– The decibel (dB) is a unit of measure used to express
the gain or loss of a circuit.
• The decibel was originally created to express hearing response.
• A decibel is one-tenth of a bel.
– When gain and attenuation are both converted into
decibels, the overall gain or attenuation of a circuit can
be computed by adding individual gains or
attenuations, expressed in decibels.
Gain, Attenuation,
and Decibels
Decibels: Decibel Calculations
– Voltage Gain or Attenuation
dB = 20 log Vout/ Vin
– Current Gain or Attenuation
dB = 20 log Iout/ Iin
– Power Gain or Attenuation
dB = 10 log Pout/ Pin
Gain, Attenuation,
and Decibels
Decibels: Decibel Calculations
• Example:
An amplifier has an input of 3 mV and an output of 5
V. What is the gain in decibels?
dB = 20 log 5/0.003
= 20 log 1666.67
= 20 (3.22)
= 64.4
Gain, Attenuation,
and Decibels
Decibels: Decibel Calculations
• Example:
A filter has a power input of 50 mW and an output of 2
mW. What is the gain or attenuation?
dB = 10 log (2/50)
= 10 log (0.04)
= 10 (−1.398)
= −13.98
– If the decibel figure is positive, that denotes a gain.
Gain, Attenuation,
and Decibels
Decibels: Antilogs
– The antilog is the number obtained when the base is
raised to the logarithm which is the exponent.
– Antilogs are used to calculate input or output voltage
or power, given the decibel gain or attenuation and
the output or input.
– The antilog is the base 10 raised to the dB/10 power.
– The antilog is readily calculated on a scientific
calculator.
Gain, Attenuation,
and Decibels
Example: Antilog 4 = antilog (log (Pout/ Pin
A power amplifier with a 40 dB ))
gain has an output power of (Pout/ Pin ) =10^ dB/10
100 W. What is the input (Pout/ Pin ) =10^4
power?
= 10,000
Solution:
Pin =Pout/10000
dB = 10 log (Pout/ Pin ) = 100/10000
antilog = log^(-1)
= 0.01 W
dB/10 = log (Pout/ Pin )
40/10 = log (Pout/ Pin ) = 10 mW
4 = log (Pout/ Pin )
Gain, Attenuation,
and Decibels
Decibels: dBm and dBc
– When a decibel value is computed by comparing a
power value to 1 mW, the result is a value called
the dBm. This is a useful reference value.
– The value dBc is a decibel gain attenuation figure
where the reference is the carrier.
Exercises
• 1. What is the gain of an amplifier with an
output of 1.5V and an input of 30V?
• 2. What is the attenuation of a voltage divider
like that in Figure 2.3,where R1 is 3.3K-ohms
and R2 is 5.1K-ohms?
• 3. What is the overall gain or attenuation of
the combination formed by cascading the
circuit described in exercises 1 and 2?
Exercises (cont..)
4. The AM receiver radio have three-stages comprised of
two amplifiers and one filter with an input power Pin=-
10 dBm , and absolute power gains of Ap1 =100,
Ap2=0.7 and Ap3=2000. Determine:
(i) The dB gain of each stage and the overall gain
in dB.
(ii)Output power (Po ) in dBm and watts.
(iii) What is the difference between a positive and
negative decibel (dB)?
Exercises
• 5. Given a four-stage system with an input power of Pin =
-15dBm with the absolute power gain of Ap1 = 400, while
Ap2 = 2Ap1, Ap4 = 1x10-4Ap2 and Ap3 = 5Ap4.Determine:
• the overall gain in dB.
• the dB gain of each stage.
• the output power in dBm and watt.
