Transcript Power Gain - 4th semester

Decibel Gain
Power Gain
The power gain G of an amplifier is the ratio of output
power to the input power
If the output power is 15W and input power is 0.5W
then
The output power is 30 times greater then the input
power
Decibel Gain
The power gain of an audio amplifier is measured in the
units of ‘BEL’ in the honor of Graham Bell the inventor of
Telephones.
1 Bel= 10 deciBel
As a unit the Bel was actually devised as a convenient
way to represent power loss in he telephone system
wiring rather then gain in amplifiers. It is defined in
logarithmic scale since human ear is sensitive to sound
energy only in logarithmic scale.
The decibel power gain (G) is defined in terms of the
normal gain (G)
dB
Decibel Gain
Decibels:
If the circuit has a power gain of 100, its
decibels power gain is
dB
Decibel Gain
10 dB for each factor of 10:
If the power gain is 10; then the decibel power
gain is
If the power gain is 100; then the decibel power
gain is
If the power gain is 1000; then the decibel power
gain is
Decibel Gains
G
G/
1
10
100
1000
10000
0dB
10dB
20dB
30dB
40dB
Similar results applies to power gain of less than 1.
When the power gain is 0.1; the decibel gain is -10dB
Decibel Gain
3 dB for each factor of 2:
If the power gain is 2, then the decibel power gain is
G=4, the decibel power gain is
G=8, the decibel power gain is
When the normal power gain doubles, the decibel power
gain increases by approximately 3dB
Decibel Gains
Negative Decibels:
If power gain is less than 1 there is a power loss (attenuation), and
the decibel power gain is negative. For instance, if the output
power is 1.5W and the input power is 3W, then
And the decibel power gain is
When the power gain is 0.25,
When the power gain is 0.125,
Decibel Gain
Rs
+
VS
-
P1
G1
P2
G2
P3
RL
Ordinary Gain Multiply
The figure shows two stage s in an amplifier. The
first stage has an input power of P1, an output
power of P2, and a power gain
The second stage has an input power of p2,an
output power of P3, and a power gain of
G2 
P3
P2
The total power gain of the two stages is
For example, a first stage power gain is 100
and the second stage power gain is 200, the
total power gain is
100
200
20,000
Decibel Gain
Decibel Gains Add:
Since the total gain of two cascaded stages is
We can take the logarithm of both sides to get
Multiplying both sides by 10 gives
Which can be written as
20dB
23dB
43dB
Relation of power and voltage gains
The rms voltage across the amplifier input
terminal equals V1 and the rms voltage across
the amplifier output terminals equals V2.
therefore, the input power to the amplifier is
And the output power is
The power gain from input to out equals
Decibel Voltage Gain
Voltage measurements are more common than
power measurements. Therefore it is not surprising
that decibels are also used to specify voltage gain.
Decibel voltage gain (A/) is
For example if A is 40, then
A
A
1
2
4
8
0dB
6dB
12dB
18dB
1
0.5
0.25
0.125
0dB
-6dB
-12dB
-18dB
Factors of 2 and 10:
When A=2
When A=4
When A=8
When the voltage gain doubles the decibel gain
increases by 6dB.
If the voltage gain decreases by a factor of 2, hen the
decibel gain decreases by 6dB.
Also when the voltage gain increases by a factor of
10 , the decibel gain increases by 20 dB.
A
1
10
100
1000
0dB
20dB
40dB
60dB
Half power point:
The frequency at which the output power is half of
the input power is called the half power point. This is
also called the cutoff frequency
At the cut off frequency
A=0.707
As
For R1 =R2