#### Transcript Electromagnetic Signal - Western Carolina University

TEL312 Electronic Communications Fundamentals
FM Signal Generation
They are two basic methods of generating frequency-Modulated signals
1.Direct FM
f i  f c  k m(t )
f
•In a direct FM system the instantaneous frequency is directly varied with the information signal.
•To vary the frequency of the carrier is to use an Oscillator whose resonant frequency is
determined by components that can be varied.
•The oscillator frequency is thus changed by the modulating signal amplitude.
•For example, an electronic Oscillator has an output frequency that depends on
energy-storage devices.
•There are a wide variety of oscillators whose frequencies depend on a particular capacitor value.
•By varying the capacitor value, the frequency of oscillation varies.
•If the capacitor variations are controlled by m(t), the result is an FM waveform
TEL312 Electronic Communications Fundamentals
Figure 6-23, page 262.
Crosby Direct FM modulator
TEL312 Electronic Communications Fundamentals
Example: Problem 6-16.
Crosby Direct FM modulator
Given: Kf = frequency deviation sensitivity = 450Hz/V,
Am = message signal amplitude = 3 V
fm = message signal frequency = 5000 Hz
1. Peak Frequency Deviation at the VCO output = ∆fVCO = AmKf = 3  450 =1350 Hz
Peak Frequency Deviation at the Amplifier Output
= ∆fOUT = N1N2N3AmKf = 3  2  3  3  450 Hz = 24300 Hz
2. Modulation index at the VCO output = βVCO = ∆fVCO /fm = 1350/5000 = 0.27
Modulation index at the Amplifier output = βOUT = ∆fOUT /fm = 24300 /5000 = 4.86
3. Bandwidth using Carson’s Rule = BW = 2  ∆fOUT + 2  fm
= 2  23.6 +10 kHz = 58.6 kHz
Bandwidth using Bessel functions = BW = 2  n  fm
For βOUT = 4.86, we can round βOUT to 5. From the Bessel Table, there are 7
significant terms past the carrier for βOUT = 5. So n = 7.
Bandwidth using Bessel functions = BW = 2  n  fm = 2  7  5 kHz = 70 kHz.
TEL312 Electronic Communications Fundamentals
Example: Problem 6-16.
Crosby Direct FM modulator
Bessel Function Jn() vs. n for  = 4.86
0.5
MATLAB Code to generate
Bessel Functions:
0.4
0.3
title('Bessel Function
J_n(\beta) vs. n for
\beta = 4.86')
0.2
n
J (4.86)
n = 0:0.01:9;
plot(n, bessel(n, 4.86));
grid;
xlabel('n');
ylabel('J_n(\beta)')
0.1
0
-0.1
-0.2
-0.3
-0.4
0
1
2
3
4
5
n
6
7
8
9
TEL312 Electronic Communications Fundamentals
Example: Problem 6-16.
Crosby Direct FM modulator
Zoomed-In Plot
Bessel Function Jn() vs. n for  = 4.86
0.045
0.04
0.035
n
J (4.86)
Notice that the Bessel function
falls below 0.02 for n > = 8.
So we say that n = 7 = # of
significant terms of the
Bessel functions past the
carrier.
Bandwidth using Bessel
functions = 2  n  fm
= 2  7  5 kHz
= 70 kHz.
0.03
0.025
0.02
0.015
0.01
All Bessel functions equal
to 8 or higher are below 0.02
0.005
7
7.5
8
n
8.5
9
TEL312 Electronic Communications Fundamentals
Figure 6-27.
Armstrong indirect
FM modulator
TEL312 Electronic Communications Fundamentals
Problem 6-27. Armstrong indirect FM modulator
Given Information: crystal carrier oscillator = 210 kHz
crystal reference oscillator = 10.2 MHz
Vm = sideband voltage = 0.018 volts
Carrier input voltage, Vc = 5 volts
First multiplier = 40
Second multiplier = 50
Modulating signal frequency, fm = 2 kHz
a) β = modulation index at the output of the combining network =
arctan(Vm/Vc) = arctan(0.018/5) = 0.0036 radians
After two multipliers: m = 0.0036*40*50 = 7.2 radians
2. Df = m*fm = 0.0036*2000 = 7.2 Hz
At antenna, df = Df*40*50 = 7.2*2000 = 14.4 kHz
TEL312 Electronic Communications Fundamentals
Indirect FM
x(t ) = Ac cos [2fct + (t) ]
 (t)  2 k m(t)
p
 (t )  2k f
t
 m( )d
0
1.Angle modulation includes frequency modulation FM and phase modulation PM.
FM and PM are interrelated; one cannot change without the other changing.
2.The information signal frequency also deviates the carrier frequency in PM.
3.Phase modulation produces frequency modulation. Since the amount of phase
shift is varying, the effect is as if the frequency is changed.
4. Since FM is produced by PM , the later is referred to as indirect FM.
5. The information signal is first integrated and then used to phase modulate
a crystal-controlled oscillator, which provides frequency stability.
6. In order to minimize the distortion in the phase modulator, the modulation index
is kept small, thereby is resulting in a narrow-band FM-signal
7. The narrow-band FM signal is multiplied in frequency by means of frequency
multiplier so as to produce the desired wide-band FM signal.
8. The frequency multiplier is used to perform narrow band to wideband conversion.
9. The frequency deviation of this new waveform is “M” times that of the old, while the
rate at which the instantaneous frequency varies has not changed
TEL312 Electronic Communications Fundamentals
For high enough values of m, frequency multiplication changes
narrowband FM into wideband FM.
It also moves the carrier frequency, but the carrier has no effect
on whether an FM wave is narrowband or wideband
TEL312 Electronic Communications Fundamentals – Spring 2004
Modulator for narrowband FM
Narrowband FM :
x(t )  Ac cos(2f ct )  Ac sin(2f ct )  sin(2f mt )