Electromagnetic Signal

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TEL312 Electronic Communications Fundamentals

• FM Signal Generation
• They are two basic methods of generating
  frequency-Modulated signals
• Direct FM

• 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

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TEL312 Electronic Communications Fundamentals
Figure 6-23, page 262. Crosby Direct FM
modulator
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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
• 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
• Modulation index at the VCO output ßVCO ?fVCO
  /fm 1350/5000 0.27
• Modulation index at the Amplifier output
  ßOUT ?fOUT /fm 24300 /5000 4.86
• Bandwidth using Carsons Rule BW 2 ? ?fOUT
  2 ? fm
• 
  2 ? 23.6 10 kHz 58.6 kHz
• Bandwidth using Bessel functions BW 2
  ? n ? fm
• For ßOUT 4.86, we can round ßOUT to 5.
  From the Bessel Table, there are 7 significant
  terms past the carrier for ßOUT 5. So n 7.
• Bandwidth using Bessel functions BW 2 ?
  n ? fm 2 ? 7 ? 5 kHz 70 kHz.

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TEL312 Electronic Communications Fundamentals
Example Problem 6-16. Crosby Direct FM
modulator
MATLAB Code to generate Bessel Functions n
00.019 plot(n, bessel(n, 4.86)) grid
xlabel('n') ylabel('J_n(\beta)') title('Bessel
Function J_n(\beta) vs. n for \beta 4.86')
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TEL312 Electronic Communications Fundamentals
Example Problem 6-16. Crosby Direct FM
modulator
Zoomed-In Plot
Notice that the Bessel function falls below 0.02
for n gt 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.
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TEL312 Electronic Communications Fundamentals
Figure 6-27. Armstrong indirect FM modulator
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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) ß modulation
index at the output of the combining network
arctan(Vm/Vc) arctan(0.018/5) 0.0036
radians After two multipliers m 0.00364050
7.2 radians 2. Df mfm 0.00362000 7.2 Hz
At antenna, df Df4050 7.22000 14.4
kHz 3. f2 210kHz40 10.2MHz 8.4 10.2
1.8MHz ft 1.850 90 MHz
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TEL312 Electronic Communications Fundamentals

• Indirect FM
• x(t ) Ac cos 2?fct ?(t)

• Angle modulation includes frequency modulation FM
  and phase modulation PM. FM and PM are
  interrelated one cannot change without the other
  changing.
• The information signal frequency also deviates
  the carrier frequency in PM.
• 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

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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
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TEL312 Electronic Communications Fundamentals
Spring 2004
Modulator for narrowband FM
Narrowband FM