082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

88 Chapter 2 Engineering functions
the third system be P o3
. Suppose the three are connected so that the power output
from system 1,P o1
, is used as input to system 2, that isP i2
=P o1
. The power output
from system 2,P o2
, is then used as input to system 3, that isP i3
= P o2
. We wish to
find the overall power gain, 10log(P o3
/P i1
). Now
P o3
= P o3P o2
P o1
P i1
P i3
P i2
P i1
becauseP i3
=P o2
andP i2
=P o1
. Therefore,
( ) ( )
Po3 Po3 P
10log = 10log o2
P o1
P i1
P i3
P i2
P i1
thatis
10log
(
Po3
P i1
)
( ) ( ) ( )
Po3 Po2 Po1
= 10log +10log +10log
P i3
P i2
P i1
usingthe laws of logarithms.
It follows that the overall power gain is equal to the sum of the individual power
gains. Often engineers are more interested in voltage gain rather than power gain.
The power of a signal is proportional to the square of its voltage. We definevoltage
gain (dB) by
( ) V
2
voltage gain (dB) = 10log
o
V 2
i
( )
Vo
= 20log
V i
Engineeringapplication2.11
TheuseofdBminradiofrequencyengineering
Inthepreviousengineeringapplicationitwasshownhowthedecibelcanbeusedto
express a ratio of the power of two signal levelsP o
andP i
. It is possible to specify
a fixed value for the input signalP i
. This is termed a reference level. When this is
done the decibel becomes an absolute quantity. The notation is normally changed
slightly to indicate the assumed reference level. For example, dBm is used as an
absolutemeasureofpowerinthefieldofradiofrequency(RF)engineering.Amobile
telephone handset, a microwave oven and a radar transmitter on an airfield are all
devices that might have their output power quoted in dBm. The definition of power
gain measured indBmisasfollows:
( )
Po
power gain (dBm) = 10log
10 −3
Herethe reference level chosen is1mWor 10 −3 W.
If a device is quoted as having an output power of 15 dBm we can convert this
into a power value inwatts as follows:
( )
Po
15 (dBm) = 10log
10 −3
Dividing both sides by 10
( )
Po
1.5 = log
10 −3