Frequency Modulation FM

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Frequency Modulation (FM)
2
AM Waveform
ec Ec sin wct em Em sin wmt
AM signal es (Ec em) sin wct
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Modulation Types

• es Ec sin ( wct F )

AM
FM
PM
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Angle Modulation

• Angle modulation includes both frequency and
  phase modulation.
• FM , PM are used for radio broadcasting, sound
  signal in TV, two-way fixed and mobile radio
  systems, cellular telephone systems, and
  satellite communications.
• PM is used extensively in data communications

5
Comparison of FM or PM with AM

• Advantages over AM
• better SNR, and more resistant to noise
• less power is required to angle modulate
• capture effect reduces mutual interference
• Disadvantages
• much wider bandwidth is required
• slightly more complex circuitry is needed

6
Frequency Shift Keying (FSK)
Carrier
Modulating signal
FSK signal
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FSK (contd)

• The frequency of the FSK signal changes abruptly
  from one that is higher than that of the carrier
  to one that is lower.
• Note that the amplitude of the FSK signal remains
  constant.
• FSK can be used for transmission of digital data
  (1s and 0s) with slow speed modems.

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Frequency Modulation
Carrier
Modulating Signal
FM signal
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Frequency Modulation (contd)

• Frequency of the FM wave changes when the
  modulating signal amplitude changes.
• The frequency of the FM wave is maximum when the
  modulating signal is at its positive peak and is
  minimum when the modulating signal is at its
  negative peak.
• Amplitude of carrier is kept constant

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Frequency Deviation

• The amount by which the frequency of the FM
  signal varies with respect to its resting value
  (fc) is known as frequency deviation Df kf em,
  where kf is a system constant, and em is the
  instantaneous value of the modulating signal
  amplitude.
• Thus the frequency of the FM signal is
• fs (t) fc Df fc kf em(t)

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Frequency Deviation

• If the modulating signal is a sine wave, i.e.,
  em(t) Emsin wmt, then fs
  fc kfEmsin wmt.
• The peak or maximum frequency deviation d kf
  Em
• The modulation index of an FM signal is mf d
  / fm (FM)
• m Vm / Vc (AM)
• mf can be greater than 1.

12
Relationship between FM and PM

• For PM, phase deviation, Df kpem, and the peak
  phase deviation, fmax mp mf.
• Since frequency (in rad/s) is given by

the above equations suggest that FM can
be obtained by first integrating the
modulating signal, then applying it to a phase
modulator.
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Equation for FM Signal

• If ec Ec sin wct, and em Em sin wmt, then the
  equation for the FM signal is
• es Ec sin (wct mf sin wmt)
• In AM es (Ec Em sin wmt) sin wct
• sin wmt x sin wct
• makes use of the relation
• sin wmt sin wct ½ cos (wc-wm) t- ½ cos
  (wcwm)t

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Equation for FM Signal

• For FM
• es Ec sin (wct mf sin wmt)
• we need to deal with a more complex relation
• sin (. sin wmt )
• whose solution is the Bessel function
• This signal can be expressed as a series of
  sinusoids es EcJo(mf) sin wct
• - J1(mf)sin (wc - wm)t - sin (wc wm)t
• J2(mf)sin (wc - 2wm)t sin (wc 2wm)t
• - J3(mf)sin (wc - 3wm)t sin (wc 3wm)t
• .

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Bessel Functions

• The Js in the equation are known as Bessel
  functions of the first kind
• mf Jo J1 J2 J3 J4 J5 J6 . . .
• 0 1
• 0.5 .94 .24 .03
• 1 .77 .44 .11 .02
• 2.4 0.0 .52 .43 .20 .06 .02
• 5.5 0.0 -.34 -.12 .26 .40 .32 .19 . . .

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Notes on Bessel Functions

• Theoretically, there is an infinite number of
  side frequencies for any mf other than 0.
• However, only significant amplitudes, i.e. those
  ?0.01 are included in the table.
• Bessel-zero or carrier-null points occur when mf
  2.4, 5.5, 8.65, etc. These points are useful
  for determining the deviation and the value of kf
  of an FM modulator system.

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Graph of Bessel Functions
18
FM Side-Bands

• Each (J) value in the table gives rise to a pair
  of side-frequencies.
• The higher the value of mf, the more pairs of
  significant side- frequencies will be generated.

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Power and Bandwidth of FM Signal

• Regardless of mf , the total power of an FM
  signal remains constant because its amplitude is
  constant.
• The required BW of an FM signal is
• BW 2 x n x fm ,where n is the number of pairs
  of side-frequencies.
• If mf gt 6, a good estimate of the BW is given by
  Carsons rule
• BW 2(d fm (max) )

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Narrowband Wideband FM

• FM systems with a bandwidth lt 15 kHz, are
  considered to be NBFM. A more restricted
  definition is that their mf lt 0.5. These systems
  are used for voice communication.
• Other FM systems, such as FM broadcasting and
  satellite TV, with wider BW and/or higher mf are
  called WBFM.

21
Pre-emphasis

• Most common analog signals have high frequency
  components that are relatively low in amplitude
  than low frequency ones. Ambient electrical
  noise is uniformly distributed. Therefore, the
  SNR for high frequency components is lower.
• To correct the problem, em is pre-emphasized
  before frequency modulating ec.

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Pre-emphasis circuit

• In FM broadcasting, the high frequency components
  are boosted by passing the modulating signal
  through a HPF with a slope of 6 dB/octave

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De-emphasis Circuit

• At the FM receiver, the signal after demodulation
  must be corrected or de-emphasized by a filter
  with similar characteristics as the pre-emphasis
  filter to restore the original amplitudes of the
  modulating signal.

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FM Stereo Broadcasting Baseband Spectra

• To maintain compatibility with mon system, FM
  stereo uses a form of FDM or frequency-division
  multiplexing to combine the left and right
  channel information

19 kHz Pilot Carrier
SCA (optional)
LR (mono)
L-R
L-R
kHz
.05
15
23
38
53
60
74
67
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FM Stereo Broadcasting

• To enable the L and R channels to be reproduced
  at the receiver, the L-R and LR signals are
  required. These are sent as a DSBSC AM signal
  with a suppressed subcarrier at 38 kHz.
• The purpose of the 19 kHz pilot is for proper
  detection of the DSBSC AM signal.

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Block Diagram of FM Transmitter
FM Modulator
Frequency Multiplier(s)
Antenna
Buffer
Power Amp
Driver
Pre-emphasis
Audio
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Simple FM transmitter

• L and C m determine the frequency of LC
  oscillator
• C m of Capacitor Microphone changes in accordance
  to the speech

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Direct-FM Modulator

• A simple method of generating FM is to use a
  reactance modulator where a varactor is put in
  the frequency determining circuit.

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Varactor Diode Modulator

• Varactor Diode is used to deviate the frequency
  of a crystal oscillator
• R1/R2 develop dc voltage that reverse bias the
  varactor diode VD1 and determines the rest
  frequency (unmodulated)
• External voltage (audio) adds and subtracts from
  the dc bias and hence alters the capacitance of
  VD1

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Varactor Diode Modulator Contd

• mod. Signal increases the reverse bias hence
  reduce the capacitance and increases the
  frequency f c
• negative mod. Signal decreases the reverse bias
  hence increase the capacitance and reduces the
  frequency f c
• Because crystal is used, peak frequency deviation
  is limited
• Low-index application

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Non Crystal Oscillator

• For medium to high frequency deviation index
• Poor stability, therefore automatic frequency
  control (AFC) is used.
• AFC compares non-crystal carrier frequency with
  crystal reference oscillator and produces a
  correction voltage
• The correction frequency is fed back to the
  carrier oscillator to compensate for the drift.

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Crosby AFC System

• An LC oscillator operated as a VCO with automatic
  frequency control is known as the Crosby system.

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Phase-Locked Loop FM Generators

• The PLL system is more stable than the Crosby
  system and can produce wide-band FM without using
  frequency multipliers.

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Indirect-FM Modulators

• Recall earlier that FM and PM were shown to be
  closely related. In fact, FM can be produced
  using a phase modulator if the modulating signal
  is passed through a suitable LPF (i.e. an
  integrator) before it reaches the modulator.

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Indirect-FM Modulators Contd

• One reason for using indirect FM is that its
  easier to change the phase than the frequency of
  a crystal oscillator.
• However, the phase shift achievable is small,
  and frequency multipliers will be needed.

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Example of Indirect FM Generator
Armstrong Modulator
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Block Diagram of FM Receiver
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FM Receivers

• FM receivers, like AM receivers, utilize the
  superheterodyne principle, but they operate at
  much higher frequencies (88 - 108 MHz).
• A limiter is often used to ensure the received
  signal is constant in amplitude before it enters
  the discriminator or detector.

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FM Demodulators

• The FM demodulators must convert frequency
  variations of the input signal into amplitude
  variations at the output.
• The Foster-Seeley discriminator and its variant,
  the ratio detector are commonly found in older
  receivers. They are based on the principle of
  slope detection using resonant circuits.

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Slope Detector

• La Ca produce an output voltage proportional to
  the input frequency.
• Center frequency is place at the center of the
  most linear portion of the voltage
  versus-frequency curve
• When IF deviates above or below fc , output
  voltage increases or decreases
• Tuned circuit converts frequency variation to
  voltage variation

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S-curve Characteristics of FM Detectors
vo
Em
d
fi
fIF
d
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Balanced Slope Detector

• Two single-ended slope detectors connected in
  parallel and fed 180 o out of phase
• Phase inversion accomplished by center-tapping
  secondary winding
• Top tuned circuit is tuned to a frequency above
  the IF center frequency by approx. 1.33 X ? f
  (1.33 X 75 k 100kHz )
• Similarly, the lower to 100 kHz bellow the IF

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• At the IF center frequency, the output voltage
  from the two tuned circuits are equal in
  amplitude but opposite in polarity, v out 0 V
• When IF deviate above resonance, top tuned
  circuit produces a higher output voltage than the
  lower circuit and voltage goes positive
• When IF deviate below resonance, lower tuned
  circuit produces higher output than upper, and
  output goes negative

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Foster-Seely Discriminator

• Similar to balanced slope detector
• Output voltage versus frequency deviation is more
  linear
• Only one tuned circuit easier to tune
• Slope-detector and Foster-Seely discriminator
  respond to amplitude variation as well as
  frequency deviation must be preceded by a
  separate limiter circuit

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Ratio Detector

• Advantages over slope detector Foster-Seely It
  is insensitive to amplitude variation in input
  signal

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Phased Locked Loop (PLL)

• PLL initially locks to the IF frequency
• After locking, voltage controlled oscillator
  (VCO) would track frequency changes in the input
  signal by maintaining a phase error
• The PLL input is a deviated FM and the VCO
  natural frequency is equal to the IF center
  frequency
• The correction voltage produced at the output of
  the phase comparator is proportional to the
  frequency deviation that is equal to the
  demodulated information signal

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PLL FM Detector

• PLL detectors are commonly found in modern FM
  receivers.

Phase Detector
Demodulated output
FM IF Signal
f
LPF
VCO
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Quadrature Detector

• PLL detector is conveniently found as IC packages.

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Types of Transmission Lines

• Differential or balanced lines (where neither
  conductor is grounded) e.g. twin lead,
  twisted-cable pair, and shielded-cable pair.
• Single-ended or unbalanced lines (where one
  conductor is grounded) e.g. concentric or
  coaxial cable.
• Transmission lines for microwave use e.g.
  striplines, microstrips, and waveguides.

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Transmission Line Equivalent Circuit
L
L
L
L
R
R
Zo
Zo
C
C
C
C
G
G
Lossless Line
Lossy Line