Communication (1)

(Lec.4)

Presented by:
Dr. Radwa Adel

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 Angle Modulation (FM & PhM)
 (t )  wc t   Carrier angle
m(t ) Modulating signal
c (t )  Ac cos  (t )
c (t )  Ac cos wc t   t1  t  t 2
s (t )  Ac cos  i (t )
the angular frequency of " (t )  wc t   " is " wc "
then the angular frequency " i (t )" is then :
d i (t )
wi (t ) 
dt
 i (t )   wi (t ) dt

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 Phase Modulation (PhM)
Phase modulation (PhM) is that form of angle modulation in which the instantaneous
angle “θi (t)” is varied linearly with the information signal m(t)

 (t )  wct  2k p m(t )

s(t )  Ac cos( wct  2k p m(t ))

Angle of factor Kp : Phase

un-modulated sensitivity
carrier (radian/volt)

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 Frequency Modulation (FM)
Frquency modulation (FM) is that form of angle modulation in which the instantaneous
frequency “wi (t)” is varied linearly with the information signal m(t)

wi (t )  wc  2k f m(t )

Frequency of Kf : frequency sensitivity

un-modulated carrier factor (hertz/volt)

 i (t )   wi (t ) dt
  (w c  2k f m(t ))dt
 wc t  2k f  m(t )dt
s (t )  Ac cos( w t  2k  m(t ) dt )
c f
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5
PhM and FM waveforms

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PhM and FM waveforms

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PhM and FM waveforms

m`(t)

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 Angle modulation Power

*the amplitude of PhM and FM signals is maintained at a constant

value equal to the carrier amplitude Ac for all time t, irrespective of
the sensitivity factors. Consequently, the average transmitted power
of angle-modulated signals is constant
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Ac
PC 
2

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 Relation between PhM and FM

FM wave can be generated by:

1-integrating the modulating signal m(t) with respect to time t
2-using the resulting signal as the input to a phase modulator

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PM wave can be generated by:
1- differentiating with respect to time t
2-using the resulting signal as the input to a frequency modulator

It follows therefore that phase modulation and frequency modulation are

uniquely related to each other. This relationship, in turn, means that we may
deduce the properties of phase modulation from those of frequency
modulation and vice versa. For this reason, we will be focusing much of the
discussion on frequency modulation 11
 FM derivation
s (t )  Ac cos( wc t  2k f  m(t )dt )
m(t )  Am cos wm t
2k f Am
2k f  m(t )dt  wm
sin wm t

2k f Am
 sin wm t
2f m
Δf
 sin wm t
fm
  sin wm t
s (t )  Ac cos( wc t   sin wm t )
 : FM modulation index
Δf : frequency deviation f i from f c
note : cos(x  y)  cosx cosy - sinx siny
s (t )  Ac cos( wc t ) cos(  sin wm t )  Ac sin( wc t ) sin(  sin wm t )
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 FM Spectrum (Narrow band FM,NBFM)
s (t )  Ac cos( wc t ) cos(  sin wmt )  Ac sin( wc t ) sin(  sin wmt )
If the modulation index  is small compared to one radian(   1),
the following two approximat ions will be used for all times t :
cos(  sin wmt )  1
sin(  sin wmt )   sin wmt
s (t )  Ac cos( wc t )  Ac  sin( wc t ) sin wmt
Ac  A
 Ac cos( wc t )  cos( wc  wm )t  c cos( wc  wm )t
2 2

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 NBFM Modulator

The carrier wave (Ac coswct) is splitted into two paths. One path is direct; the other
path contains a -90 degree phase-shifting network and a product modulator, the
combination of which generates a DSB-SC modulated wave
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• Although the NBFM and AMDSB-SC have the same B.W (2fm) the
two modulation techniques are completely different
• In NBFM the information modulates the carrier frequency.
• In DSB-SC the information modulates the carrier amplitude

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 Fm Spectrum(Wide band FM, WBFM)

s(t )  Ac cos( wct ) cos(  sin wmt )  Ac sin( wct ) sin(  sin wmt )
J n (  ) : bessel function (n  0,1,2,3,...)
cos(  sin wmt )  J 0 (  ) sin( 0 * wmt )  2 J 2 (  ) sin( 2wmt )  2 J 4 (  ) sin( 4wmt )  ...
sin(  sin wmt )  J1 (  ) sin wmt  2 J 3 (  ) sin( 3wmt )  2 J 5 (  ) sin( 5wmt )  ...
s(t )  Ac cos( wct )[ J 0 (  ) sin( 0 * wmt )  2 J 2 (  ) sin( 2wmt )]
 Ac sin( wct )[ J1 (  ) sin wmt  2 J 3 (  ) sin( 3wmt )]
 Ac J 0 (  ) sin( 0 * wmt ) cos( wct )  2 Ac J 2 (  ) cos( wc t ) sin( 2wmt )
 Ac J1 (  ) sin( wct ) sin wmt  2 Ac J 3 (  ) sin( wct ) sin( 3wmt )
 Ac J 0 (  ) sin( 0 * wmt ) cos( wct )  Ac J 2 (  ) sin( wc  2wm )t  Ac J 2 (  ) sin( wc  2wm )t
Ac J1 (  ) A J ( )
 cos( wc  wm )t  c 1 cos( wc  wm )t  Ac J 3 (  ) sin( wc  3wm )t
2 2
 Ac J 3 (  ) sin( wc  3wm )t

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17
Bessel function

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 Transmission B.W of FM
1.For large values of the modulation index β:

the bandwidth approaches, and is only slightly greater than the total frequency
deviation (2Δf).
2. For small values of the modulation index β :

the spectrum of the FM wave is effectively limited to the carrier frequency fc and one pair of
side-frequencies at fc±fm so that the bandwidth equals to 2fm.

Based on the previous FM cases, we may define an approximate rule for the transmission
bandwidth of an FM wave generated by a single-tone modulating wave of frequency as

Carson’s rule B.WFM  2(f  f m )

 2 f m (   1)

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Example

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Example

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 Required

Sketch FM and PhM signal for the following m(t)

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Solution

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 FM Generation
1-Direct generation
*The main point in FM is that the frequency of carrier fc is modulated by the
modulating signal m(t). This means that m(t) controls the carrier frequency.
*the FM can be generated using what is called voltage controlled oscillator (VCO)
in which the oscillation frequency (fc) varies linearly with the controlled voltage
“m(t)”

VCO circuit can be implemented by:

Vary one of the
oscillator Reversed biased
Operational
resonance circuit diode act as a
amplifier and
reactive element capacitor
comparator
(L, C) [reactance [varactor diode]
valve modulator]
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 VCO (reactance valve ,varactor diode)

the direct method is therefore straightforward to implement. Moreover, it is capable of

providing large frequency deviations. However, a serious limitation of the direct method is
the tendency for the carrier frequency to drift, which is usually unacceptable for
commercial radio applications.

To overcome this limitation, frequency stabilization of the FM generator is required, which

is realized through the use of feedback around the oscillator.

Although the oscillator may itself be simple to build, the use of frequency stabilization
adds system complexity to the design of the frequency modulator.
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 1
fc  fr 
2 LC
1
f c  f 
2 L (C  C )
1
f c  f 
2 L (C  C )
1
f c  f 
C
2 LC (1  )
C
1 1
f c  f 
2 LC C
(1  )
C
1
f c  f  f c
C
(1  )
C
1
f C
1  (1  ) 2
fc C
f 1 C
1  1  ....
fc 2 C
f 1 C

fc 2 C 26
2-Indirect Method: Armstrong Modulator
*The message signal is first used to produce a narrow-band FM, which is followed
by frequency multiplication to increase the frequency deviation to the desired
level.

*In this second method, the carrier-frequency stability problem is solved by using a
crystal oscillator .

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A frequency multiplier consists of a memoryless nonlinear device followed by a
bandpass filter. The input–output relation of such a device is expressed by

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 FM Demodulation
*The frequency modulator is a circuit that produces a signal whose instantaneous
frequency varies linearly with the amplitude of the input message signal.

*In the FM demodulator we need a circuit whose output amplitude varies linearly with the
instantaneous frequency of the input FM wave.

*two techniques for FM demodulation are used:

1-discriminator.
2-phase-locked loop

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 1-Discriminator
s(t )  Ac cos( wct  2k f  m(t )dt )
ds(t )
  Ac [ wc  2k f m(t )] sin( wc t  2k f  m(t )dt )
dt

It is an AM signal with
amplitude Ac [ wc  2k f m(t )]

the message signal m(t) can be recovered with an envelope detector

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2-Phase Locked Loop (PLL)
The phase-locked loop is a feedback system.
Basically, the phase-locked loop consists of three major components:
1-Voltage-controlled oscillator (VCO), which performs frequency modulation on its
own control signal. VCO frequency is the same as fc and its output is a 90 phase shift with
respect to carrier wave.
2- Multiplier, which multiplies an incoming FM wave by the output of the voltage-
controlled oscillator.
3- Loop filter of a low-pass kind, the function of which is to remove the high-frequency
components contained in the multiplier’s output signal and thereby shape the overall
frequency response of the system.
*these three components are connected together to form a closed-loop feedback
system.

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s (t )  Ac cos( wc t  2k f  m(t )dt )
1 (t )  2k f  m(t )dt
r (t )  Av sin( wc t  2k v  v(t )dt )
2 (t )  2k v  v(t )dt
the function of feedback loop is to make 1 (t )  2 (t )
e(t )  s (t ) * r (t )
1 1
e(t )  k m Ac Av sin( wc t  1 (t )  2 (t ))  k m Ac Av sin( 1 (t )  2 (t ))
2 2
k m : is the multiplier gain
the loop - filter designed to suppress the high - frequency components in the multiplier ’ s
output the n
1
e(t )  k m Ac Av sin( 1 (t )  2 (t ))
2
e (t )  1 (t )  2 (t )
It is said to be near - phase - lock when the phase error e (t )  1 radian,
sin( e (t ))  e (t )
1 d2 (t )
v(t ) 
2k v dt
1 d1 (t )
v(t ) 
2k v dt
1 kf
v(t )  2k f m(t )  m(t )
2k v kv
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 FM Transmitter
1- FM Transmitter (Low level TX)

A low level FM transmitter performs the process of modulation near the

beginning of the transmitter
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