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ﺍﻟﺮﲪﻦ ﺍﻟﺮﺣﻴﻢ ﺑﺴﻢ ﺍ
بسم ا الرمحن الرحيم
LecturerAhmed H. Hadi
Training package inFrequency ModulationFor students of second class
Ministry of Higher Education and Scientific ResearchFoundation of Technical Education
Technical College / Al-Najaf
1 / B –Rationale :-FM signal, FM transmitter, FM receiver, andadvantages FM over AM
/ Over view1/ Over view1
1 / A –Target population :-For students of second class inCommunications Techniques Engineering Department
1 / D –Objectives:-• Understand the theory of frequency modulation• Draw an FM waveform.• Determine by calculation, the modulation index.• Analyze the frequency spectrum using Bessel
functions.
1 / C –Central Idea :
- Define FM wave
- Mathematical representation of FM signal
- Transmission bandwidth of an FM signal
2/ Pre test :-2/ Pre test :-
A frequency modulated carrier is represented byV=20 sin(6.28108t+4sin628t). The carrier frequency is
(a) 6.28108Hz (b) 3.14108Hz
(c) 108Hz (d) 2108Hz
A frequency modulated carrier is represented byV=20 sin(6.28108t+4sin628t). The carrier frequency is
(a) 6.28108Hz (b) 3.14108Hz
(c) 108Hz (d) 2108Hz
Multiple Choice Questions With Answer
١١ In frequency modulation, if the amplitude of the modulationvoltage is doubled, the maximum frequency deviation.
(a) Doubles (b) becomes four times.
(c) becomes half. (d) remains unaltered.
In frequency modulation, if the amplitude of the modulationvoltage is doubled, the maximum frequency deviation.
(a) Doubles (b) becomes four times.
(c) becomes half. (d) remains unaltered.
٢٢
٣٣ In frequency modulation, if the frequency of the modulationvoltage is
doubled, the maximum frequency deviation.(a) Doubles (b) becomes four times.
(c) becomes half. (d) remains unaltered.
In frequency modulation, if the frequency of the modulationvoltage is
doubled, the maximum frequency deviation.(a) Doubles (b) becomes four times.
(c) becomes half. (d) remains unaltered.
٤٤ In frequency modulation, if the amplitude of the modulatingvoltage is doubled, the rate of deviation of carrier frequency.
(a) Doubles (b) becomes four times.
(c) becomes half. (d) remains unaltered.
In frequency modulation, if the amplitude of the modulatingvoltage is doubled, the rate of deviation of carrier frequency.
(a) Doubles (b) becomes four times.
(c) becomes half. (d) remains unaltered.
3/ Performance Objectives :-3/ Performance Objectives :-
In frequency modulated (FM) radio, the frequency of the
carrier is varied about a fixed value in accordance with the
amplitude of the audio frequency. The amplitude of the
carrier is kept constant. The waveform of a sinusoidal
carrier modulated by a saw-tooth wave is shown in Figure
In frequency modulated (FM) radio, the frequency of the
carrier is varied about a fixed value in accordance with the
amplitude of the audio frequency. The amplitude of the
carrier is kept constant. The waveform of a sinusoidal
carrier modulated by a saw-tooth wave is shown in Figure
A sinusoidal voltage can be expressed as:A sinusoidal voltage can be expressed as:
the phase angle and theangular velocity
the phase angle and theangular velocity
the modulating signal which is assumed in this casealso to be a sinusoid:the modulating signal which is assumed in this casealso to be a sinusoid:
The instantaneous angular velocityThe instantaneous angular velocity
The resultThe result
Figure : A plot of Bessel functions of the firstkind, Jn(mf) against mf for n= 0; 1; 2 and 3. Thevalues of where Jn(mf) are used to calculate theamplitudes of the side-frequencies present in theFM signal.
Figure : A plot of Bessel functions of the firstkind, Jn(mf) against mf for n= 0; 1; 2 and 3. Thevalues of where Jn(mf) are used to calculate theamplitudes of the side-frequencies present in theFM signal.
Figure : Block diagram of the basic Armstrongsystem FM transmitter. This is an example of anindirect generation of FM signal.
Figure : Block diagram of the basic Armstrongsystem FM transmitter. This is an example of anindirect generation of FM signal.
The bandwidth for very large can then be approximated bytaking the last significant sideband at n= so thatThe bandwidth for very large can then be approximated bytaking the last significant sideband at n= so that
One such rule was proposed by J.R.CarsonOne such rule was proposed by J.R.Carson
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The bandwidthThe bandwidth
Max. and Min. frequencyMax. and Min. frequency
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Example: A 10 MHz carrier is frequency-modulated by asinusoidal signal such that the peak frequency deviation is50 kHz. Determine the approximate bandwidth of the FMsignal if the frequency of modulating sinusoid is (a) 500 kHz(b) 500 Hz (c) 10 kHz.
Example: A 10 MHz carrier is frequency-modulated by asinusoidal signal such that the peak frequency deviation is50 kHz. Determine the approximate bandwidth of the FMsignal if the frequency of modulating sinusoid is (a) 500 kHz(b) 500 Hz (c) 10 kHz.
10.010500
1050a)
3
3
mf
f
.12signal;FMnarrowbandaisThis MHzfB m
This is wideband case andThis is wideband case and;100500
1050b)
3
mf
f
This is wideband case andThis is wideband case andkHzfB 1002
;51010
1050c)
3
3
mf
f use of Carsson's rule givesuse of Carsson's rule gives
.120)(2 kHzB m
1. What is frequency modulation?
Quiz /Quiz /
2. Give the mathematical expression forbandwidth for a FM wave2. Give the mathematical expression forbandwidth for a FM wave
Bandwidth in FM =2 (Δfm+fm)Δfm=frequency deviationBandwidth in FM =2 (Δfm+fm)Δfm=frequency deviation
Frequency modulation is defined as the frequencyof the carrier wave is changed in accordance withthe variation of the modulating signal
-/ Post test :5
1. Give the mathematical expression for modulation index ofFM.
modulation index of FM is Therefore modulation
index of FM is inversely proportional to the modulating frequency
1. Give the mathematical expression for modulation index ofFM.
modulation index of FM is Therefore modulation
index of FM is inversely proportional to the modulating frequency
2. What are types of frequency modulation?
The frequency modulation are of two types. They area) Narrow band FM.b) Wideband FM.
2. What are types of frequency modulation?
The frequency modulation are of two types. They area) Narrow band FM.b) Wideband FM.
mf
f
3. Define narrowband FM.When the frequency sensitivity is small thebandwidth is also narrow which is twice thebaseband signal.
3. Define narrowband FM.When the frequency sensitivity is small thebandwidth is also narrow which is twice thebaseband signal.
4. Define FM demodulation and FM detectors.
The process of extracting a modulating signal fromfrequency modulated carrier is known as FMdemodulation. Electronic circuits that performs thedemodulation process are called FM detectors.
4. Define FM demodulation and FM detectors.
The process of extracting a modulating signal fromfrequency modulated carrier is known as FMdemodulation. Electronic circuits that performs thedemodulation process are called FM detectors.
References:References:
11
2
T. R. Ganesh Babu, and G. Srinivasan:“ Communication Theory and systems”, 2006.
Sanjay Sharma: “Communication Systems(Analog and Digital) ”.Sanjay Sharma: “Communication Systems(Analog and Digital) ”.
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