decibel notation
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DECIBEL NOTATION
DECIBEL NOTATION
DECIBELS (dB) is the common form of gain and attenuation measurement and is used in
expressing communication system’s 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
Rix
Vi
Vo log 10 =Gp(dB)
L
2
R
Rix
Vi
Vo log 10 =Gp(dB)
L
2
R
Ri log 10
Vi
Vo log 10 =Gp(dB)
LL R
Rilog 10 Gv(dB)
R
Ri log 10
Vi
Volog 20 =Gp(dB)
since Po = Io2RL and Pi = Ii
2Ri ,
DECIBEL NOTATION
Ri
Rx
Ii
Io log 10 =Gp(dB) L
2
2
Ri
Rx
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) LL
VOLTAGE GAIN in dB, Gv (dB)
Mathematically, Gv (dB) = 20 log Av
Vi
Vo log 20 =Gv(dB)
CURRENT GAIN in dB, Gi (dB)
Mathematically, Gi (dB) = 20 log Ai
Ii
Io log 20 =(dB) Gi
DECIBEL NOTATION
For multi-stage communication system,
AVT = Av1 x Av2 x Av3
AiT = Ai1 x Ai2 x Ai3
ApT = Ap1 x Ap2 x Ap3
Total voltage gain in dB,
GVT = 20 log AVT
GVT = 20 log (Av1 x Av2 x Av3)
GVT = 20 log Av1 + 20 log Av2 + 20 log Av3
GVT = GV1 + GV2+ GV3
Total current gain in dB,
GiT = Gi1 + Gi2+ Gi3
Total power gain in dB,
GpT = Gp1 + Gp2+ Gp3
DECIBEL NOTATIONABSOLUTE 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 1mW
POWER IN dBn, P(dBn) – power with reference to 1nW.
W3-
1x10
P log 10 =P(dBm)
W6-
101x
P log 10 =)P(dBm
W9-
1x10
P log 10 =)nP(dB
ABSOLUTE VOLTAGE VALUE
VOLTAGE IN dBv, V(dBv) - voltage with reference to 1V1V
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. A new 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. A superheterodyne 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 20mV 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 system’s 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
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