Ch5 AngleModulation
Ch5 AngleModulation
Ch5 AngleModulation
Nonlinear Modulation
Bandwidth of Angle Modulation
Generating of FM Waves
Demodulation of FM Signals
Effects of Nonlinear Distortion and Interference
Superheterodyne Analog AM/FM Receivers
FM Broadcasting System
2
Baseband Vs. Carrier Communications
Angle Modulation: The generalized angle (t) of a sinusoidal
signal is varied in proportion the message signal m(t).
= ()
= cos + 0 1 < < 2
Instantaneous Frequency
() =
Frequency Modulation:
= + ()
= = +
= cos +
Power of an Angle-Modulated wave is constant and equal A2/2. 4
Example of FM and PM Modulation
Sketch FM and PM waves for the modulating signal m(t). The
constants kf and kp are 2 x105 and 10, respectively, and the
carrier frequency fc is 100 MHz.
5
Example of FM and PM Modulation
Sketch FM and PM waves for the digital modulating signal
m(t). The constants kf and kp are 2 x105 and /2, respectively,
and the carrier frequency fc is 100 MHz.
7
Bandwidth of Angle Modulated Waves
= cos + () where () =
= Re [ + ()] = Re ()
Expand () using power series expansion
2 2
= Re 1 + + + +
2! !
2 2 3 3
= + +
2! 3!
The bandwidth of a(t), a2(t), an(t) are B, 2B, and nB Hz,
respectively. From the above equation it seems the
bandwidth of angle modulation is infinite but for practical
reason most of the power reside at B Hz since higher terms 8
have small power because of n!.
Narrowband PM and FM
2 2 3 3
= + +
2! 3!
= cos + = cos + ()
m(t)
2 { + }
Fourier Transform
1 + + ( ) 1 ( )
+
2 4 2 4
1
= 2 + 8 Hz
2
=2 + 2 Hz
13
2
Wideband FM (WBFM)
Peak frequency
=2 + 2 =
2 2 deviation in hertz
= 2 + 2 Hz
15
Example
a) Estimate BFM and BPM for the modulating signal m(t) for kf =2
x105 and kp = 5. Assume the essential bandwidth of the
periodic m(t) as the frequency of its third harmonic.
b) Repeat the problem if the amplitude of m(t) is doubled.
16
Example
An angle-modulated signal with carrier frequency c = 2 105 is
described by the equation
= 10 + 5 3000 + 10 2000
= 1 + 2 2 () = 1 ()
()
()
= + = + 2 = +
2
1 + () 1 + 2 2 ()
= + 1 2 2 + 4 4 19
NBFM Generation
Bandpass Limiter
= ()
= +
+1 > 0
() =
1 < 0
4 1 1
= cos cos 3 + cos 5 +
3 5
20
Generating FM Waves
4 1 1
= cos cos 3 + cos 5 +
3 5
= +
4 1
= cos + cos 3 +
3
1
+ cos 5 + +
5
The output of the bandpass filter
4
= +
21
Indirect Method of Armstrong
NBFM is generated first and then converted to WBFM by using
additional frequency multipliers.
= 2 cos 2 +
= + ()
23
Example
Design an Armstrong indirect FM modulator to generate an FM
signal with carrier frequency 97.3 MHz and f = 10.24 kHz. A
NBFM generator of fc1 = 20 kHz and f = 5 Hz is available. Only
frequency doublers can be used as multipliers. Additionally, a
local oscillator (LO) with adjustable frequency between 400 and
500 kHz is readily available for frequency mixing.
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Direct Generation
1. The frequency of a voltage-controlled oscillator (VCO) is
controlled by the voltage m(t).
() = + ()
2. Use an operational amplifier to build an oscillator with
variable resonance frequency o. The resonance frequency
can be varied by variable capacitor or inductor. The
variable capacitor is controlled by m(t).
1 1 1
= = =
0 ()
0 1
0
1 1
= 1/2
1+ 1
0 20 0
0 1
0
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Direct Generation
1
= 1 + =
20 0
= + () =
20
= cos +
= cos +
= + () sin +
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Demodulation of FM Signals
= + () sin +
Differentiator
28
Practical Frequency Demodulators
2
= 2 if 2 1
1 + 2
1
< =
29
Instantaneous frequency = the rate of zero crossing
Effect of Nonlinear Distortion and
Interference
Immunity of Angle Modulation to Nonlinearities
= 0 + 1 + 2 2 + + ()
= cos + ()
= cos( ) + 3 () 3 ( )
3 3 3
= + () cos + (3 )
4 4
30
Interference Effect
Angle Modulation is less vulnerable than AM to small-signal
interference from adjacent channels.
= cos + ( + )
= ( + ) cos sin
= ( + ) cos sin
= () cos [ + ()]
= 1 for I << A
+
The output of ideal phase and frequency demodulators are
For PM =
Interference is inversely
proportional to the carrier
For FM =
amplitude (capture effect). 31
Preemphasis and Deemphasis in FM
With white noise, the
amplitude interference is
constant for PM but
increase with for FM.
Preemphasis Deemphasis
Filter Noise Filter
Preemphasis and Deemphasis (PDE) in FM
30 kHz
2.1 kHz
Preemphasis Filter
Deemphasis Filter
Preemphasis and Deemphasis (PDE) in FM
2 + 1
= Where K is the gain and = 2 / 1
2 + 2
For 2f << 1 1
2
For 1 << 2f << 2
1
1
=
2 + 1
Filter
200 KHz
Superheterodyne Analog AM/FM Receivers
90 desired signal
90.2
111.4
fc = 10.7 10.7
90 10.7 , 190.7
90.2 10.5 , 190.9
10.7, 212.1
90+10.7=100.7 fIF = 455KHz (AM radio);
10.7 MHz (FM);
38 MHz (TV)
AM stations that are 2 fIF apart are called image stations and
both would appear simultaneously at the IF output.
RF filter eliminates undesired image station, while IF filter
eliminates undesired neighboring stations.
FM Broadcasting System
cos
= + + +
2
FM Broadcasting System
= + + cos +
2
Homework Problem 5.4-2
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Homework Problem 5.6-2
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