DECIBEL NOTATION
DECIBEL NOTATION
DECIBELS (dB) is the common form of gain and attenuation measurement and is used in
expressing communication systems response.
POWER GAIN in dB , Gp(dB)
Mathematically, Gp(dB) = 10 log Ap
Pi
Po
log 10 = Gp(dB)
L
2
R
Vo
= Po
Ri
Vi
= Pi
2
since and
|
|
.
|
\
|
L
2
2
R
Ri
x
Vi
Vo
log 10 = Gp(dB)
(
(
|
.
|
\
|
L
2
R
Ri
x
Vi
Vo
log 10 = Gp(dB)
L
2
R
Ri
log 10
Vi
Vo
log 10 = Gp(dB) +
|
.
|
\
|
L L
R
Ri
log 10 Gv(dB)
R
Ri
log 10
Vi
Vo
log 20 = Gp(dB) + = +
since P
o
= I
o
2
R
L
and P
i
= I
i
2
R
i
,
DECIBEL NOTATION
|
|
.
|
\
|
Ri
R
x
Ii
Io
log 10 = Gp(dB)
L
2
2
(
(
|
.
|
\
|
Ri
R
x
Ii
Io
log 10 = Gp(dB)
L
2
Ri
R
log 10
Ii
Io
log 10 = Gp(dB)
L
2
+
|
.
|
\
|
Ri
R
log 10 Gi(dB)
Ri
R
log 10
Ii
Io
log 20 = Gp(dB)
L L
+ = +
VOLTAGE GAIN in dB, Gv (dB)
Mathematically, G
v
(dB) = 20 log A
v
Vi
Vo
log 20 = Gv(dB)
CURRENT GAIN in dB, Gi (dB)
Mathematically, G
i
(dB) = 20 log A
i
Ii
Io
log 20 = (dB) Gi
DECIBEL NOTATION
For multi-stage communication system,
A
VT
= A
v1
x A
v2
x A
v3
A
iT
= A
i1
x A
i2
x A
i3
A
pT
= A
p1
x A
p2
x A
p3
Total voltage gain in dB,
G
VT
= 20 log A
VT
G
VT
= 20 log (A
v1
x A
v2
x A
v3
)
G
VT
= 20 log A
v1
+ 20 log A
v2
+ 20 log
Av3
G
VT
= G
V1
+ G
V2
+ G
V3
Total current gain in dB,
G
iT
= G
i1
+ G
i2
+ G
i3
Total power gain in dB,
G
pT
= G
p1
+ G
p2
+ G
p3
DECIBEL NOTATION
ABSOLUTE POWER VALUES
1W
P
log 10 = P(dBW) POWER IN dBW, P(dBW) power with reference to 1W.
POWER IN dBm, P(dBm) power with reference to 1mW
POWER IN dBm, P(dBm) power with reference to 1W
POWER IN dBn, P(dBn) power with reference to 1nW.
W
3 -
1x10
P
log 10 = P(dBm)
W
6 -
10 1x
P
log 10 = ) P(dB
W
9 -
1x10
P
log 10 = ) n P(dB
ABSOLUTE VOLTAGE VALUE
VOLTAGE IN dBv, V(dBv) - voltage with reference to 1V
1V
V
log 20 = V(dBv)
Note: dB + dB = dB
dBm + dB = dBm
dBV + dB = dBV
DRILL PROBLEM:
# 1. A signal enters the circuit with a value of 0.2 V and to amplified to 10 V. What is
the voltage gain in dB?
(a) 50 dB (b) 16.99 dB (c) 33.98 dB (d) 1.7 dB
# 2. Anew communication cable is installed and the 1V input signal is increased by 75%.
What is the increase in dB?
(a) 1.25 dB (b) 2.5 dB (c) 2.43 dB (d) 4.86 dB
# 3. A 20 W signal is transmitted and suffers a 10% power loss due to attenuation in the
cable. What is the attenuation level in dB?
(a) -10 dB (b) 0.46 dB (c) -0.92 dB (d) -0.41 dB
#4. Asuperheterodyne receiver has the following specification:
RF amplifier:
Gp = 10 dB, Ri = 50 ohms
Mixer: Gp = 6 dB
(3) IF amplifier: Gp = 27dB each at 455KHz
Detector: Gp = -5 dB
AF amplifier: Gp = 15 dB
The antenna delivers a 20V signal to the RF amplifier. The input and output resistance
of the receiver is equal.
4.1 The input power to the receiver in dBm is ______.
(a) -80.97 dBm (b)-161.94 dBm (c) 33.98 dBm (d) 67.96 dBm
4.2 The total systems gain in dB is _____.
(a) 53 dB (b) 158.95 dB (c) 101.69 dB (d) 107 dB
4.3 The output power of the receiver in dBm is ______.
(a) 26.03 dBm (b) -54.94 dBm (c) 77.98 dBm (d) 27.97 dBm
4.4 The output voltage of the receiver in dBv is ______.
(a) 13.02 dBv (b) -40.98 dBv (c) 64.97 dBv (d) 7.71 dBv
#5. If a voltage change equal to twice its original value, what is the corresponding
change in dB? (ECE Board April 1997)
(a) 9 dB (b) 6 dB (c) 10 dB (d) 3 dB
#6. If you have available number of power amplifiers with a gain of 100 each, how
many such amplifier do you need to cascade to give an over-all gain of 60 dB? (ECE
Board April 1997)
(a) 1 (b) 3 (c) 4 (d) 2
REFERENCES
Electronic Communication Systems Through Advanced
by W. Tomasi
Lecture Notes in Principles of Communication by A.H.
Ballado and M.M. Sejera
Electronic Devices and Circuit Theory by Boylestad and
Nashelsky
