For Voltage
Consider a circuit with an rms ac input voltage of E
in
and an rms ac output voltage of E
out
, specified
in the same units as E
in
. Then the voltage gain of the circuit, in decibels, is given by this formula:
Gain (dB) = 20 log(E
out
/E
in
)
The base-10 logarithm of a value x is written log x. Log functions of base 10 and base e (another
type of logarithm sometimes used in physics and engineering) can be determined easily using scien-
tific calculators. From now on, when we say “logarithm,” we mean the base-10 logarithm unless
otherwise specified.
Problem 24-1
Suppose a circuit has an rms ac input of 1.00 V and an rms ac output of 14.0 V. What is the gain in
decibels?
First, find the ratio E
out
/E
in
. Because E
out
= 14.0 V rms and E
in
= 1.00 V rms, the ratio is
14.0/1.00, or 14.0. Next, find the logarithm of 14.0. This is about 1.146128036. Finally, multiply
this number by 20, getting something like 22.92256071. Round this off to three significant figures,
because that’s all you’re entitled to, getting 22.9 dB.
Problem 24-2
Suppose a circuit has an rms ac input voltage of 24.2 V and an rms ac output voltage of 19.9 V.
What is the gain in decibels?
Find the ratio E
out
/E
in
= 19.9/24.2 = 0.822... . (The three dots indicate extra digits introduced
by the calculator. You can leave them in until the final roundoff.) Find the logarithm of this: log
0.822...=−0.0849... . The gain is 20 times this, or −1.699...dB, which rounds off to −1.70 dB.
For Current
Current gain or loss is calculated in the same way as voltage gain or loss. If I
in
is the rms ac input cur-
rent and I
out
is the rms ac output current specified in the same units as I
in
, then:
Gain (dB) = 20 log(I
out
/I
in
)
For Power
The power gain of a circuit, in decibels, is calculated according to a slightly different formula. If P
in
is the input signal power and P
out
is the output signal power expressed in the same units as P
in
, then:
Gain (dB) = 10 log (P
out
/P
in
)
The coefficient (that is, the factor by which the logarithm is to be multiplied) in the formula for
power gain is 10, whereas for voltage and current gain it is 20.
Problem 24-3
Suppose a power amplifier has an input of 5.03 W and an output of 125 W. What is the gain in
decibels?
380 Amplifiers and Oscillators