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