ch 5 angle modulations and demodulations
DESCRIPTION
ENGR 4323/5323 Digital and Analog Communication. Ch 5 Angle Modulations and Demodulations. Engineering and Physics University of Central Oklahoma Dr. Mohamed Bingabr. Chapter Outline. Nonlinear Modulation Bandwidth of Angle Modulation Generating of FM Waves Demodulation of FM Signals - PowerPoint PPT PresentationTRANSCRIPT
Ch 5Angle Modulations and Demodulations
ENGR 4323/5323Digital and Analog Communication
Engineering and PhysicsUniversity of Central Oklahoma
Dr. Mohamed Bingabr
Chapter Outline
β’ Nonlinear Modulation
β’ Bandwidth of Angle Modulation
β’ Generating of FM Waves
β’ Demodulation of FM Signals
β’ Effects of Nonlinear Distortion and Interference
β’ Superheterodyne Analog AM/FM Receivers
β’ FM Broadcasting System
2
Baseband Vs. Carrier CommunicationsAngle Modulation: The generalized angle ΞΈ(t) of a sinusoidal signal is varied in proportion the message signal m(t).
Two types of Angle Modulationβ’ Frequency Modulation: The frequency of the carrier signal
is varied in proportion to the message signal.
β’ Phase Modulation: The phase of the carrier signal is varied in proportion to the message signal.
π (π‘ )=π΄πππ π(π‘ )π (π‘ )=π΄cos (ππΆπ‘+π0 ) π‘1<π‘<π‘2
Instantaneous Frequency
π π(π‘ )=ππππ‘
3
Frequency and Phase Modulation
Phase Modulation:
Frequency Modulation:
π (π‘ )=ππΆπ‘+πππ (π‘ )πππ (π‘ )=π΄ cos [ππΆπ‘+πππ (π‘)]
π π (π‘ )=ππ+π ππ(π‘)
π (π‘ )=β«β β
π‘
ππ (π‘ )ππ‘=ππ π‘+π π β«β β
π‘
π (πΌ )ππΌ
ππΉπ (π‘ )=π΄cos [ππΆπ‘+π π β«β β
π‘
π (πΌ )ππΌ]Power of an Angle-Modulated wave is constant and equal A2/2. 4
π (π‘ )=π΄πππ π(π‘)
Example of FM and PM Modulation
Sketch FM and PM waves for the modulating signal m(t). The constants kf and kp are 2Ο x105 and 10Ο, 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 2Ο x105 and Ο/2, respectively, and the carrier frequency fc is 100 MHz.
Frequency Shift Keying (FSK) Phase Shift Keying (PSK)
Note: for discontinuous signal kp should be small to restrict the phase change kpm(t) to the range (-Ο,Ο). 6
PSK
7
Bandwidth of Angle Modulated Waves
where
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 have small power because of n!.
ππΉπ (π‘ )=π΄cos [ππΆπ‘+π π π(π‘)] π(π‘)=β«ββ
π‘
π (πΌ )ππΌ
ππΉπ (π‘ )=π΄βΒΏΒΏExpand
π ππ π π (π‘ )using power series expansion
ππΉπ (π‘ )=π΄β[{1+ π ππ π (π‘ )βπ π
2
2!π2 (π‘ )+β¦+ ππ π π
π
π !ππ (π‘ )+β¦}π π ππΆπ‘ ]
ππΉπ (π‘ )=π΄ [πππ ππ π‘βπ π π (π‘ )π πππππ‘βπ π
2
2!π2 (π‘ )πππ πππ‘+
ππ3
3 !π3 (π‘ )π πππππ‘+β¦]
8
Narrowband PM and FM
When kf a(t) << 1
ππΉπ (π‘ )=π΄ [πππ ππ π‘βπ π π (π‘ )π πππππ‘βπ π
2
2!π2 (π‘ )πππ πππ‘+
ππ3
3 !π3 (π‘ )π πππππ‘+β¦]
ππΉπ (π‘ ) β π΄ [πππ ππ π‘βπ π π (π‘ )π ππππ π‘ ]The above signal is Narrowband FM and its bandwidth is 2B Hz.
πππ (π‘ )β π΄ [πππ πππ‘βπππ (π‘ )π ππππ π‘ ]
9
Same steps can be carried out to find the Narrowband PM.
Note: the above equation is similar to amplitude modulation but the waveform are different.
πππ (π‘ )=π΄ cos [ππΆπ‘+πππ (π‘)]ππΉπ (π‘ )=π΄cos [ππΆπ‘+π π β«β β
π‘
π (πΌ )ππΌ]
m(t)
fc = 300 FM modulation kf = 120 kf a(t) = 6 NBFM (kf a(t)max <<1)
fc = 300 PM modulation kp = 10 kp mp = 31.4 NBPM (kpm(t)max << 1)
fc = 300 FM modulation kf = 10 kf a(t) = 0.5 NBFM (kf a(t)max <<1)
fc = 300 PM modulation kp = 0.1 kp mp = 0.314 NBPM (kpm(t)max << 1)
m(t)
πππ΅πΉπ (π‘ )β π΄ [πππ πππ‘βπ π π (π‘ ) π πππππ‘ ]πππ΅ππ (π‘ ) β π΄ [πππ ππ π‘βπππ (π‘ )π πππππ‘ ]
π (π‘ )=β«β β
π‘
π (πΌ )ππΌ
12
ts=1.e-4; kf = 10*pi; kp = 0.1*pi;fc = 300; t=-0.05:ts:0.05; Ta = 0.02;triangle = @(z)(1-abs(z)).*(z>=-1).*(z<1); m_sig = 1*(triangle((t+0.01)/Ta) - triangle((t-0.01)/Ta));m_intg = ts*cumsum(m_sig);s_fm = cos(2*pi*fc*t + kf*m_intg);s_pm = cos(2*pi*fc*t + kp*m_sig);subplot(311);plot(t, m_sig)subplot(312);plot(t, s_fm)subplot(313);plot(t, s_pm)s_nbfm = cos(2*pi*fc*t) - kf*m_intg.*sin(2*pi*fc*t);s_nbpm = cos(2*pi*fc*t) - kp*m_sig.*sin(2*pi*fc*t);figure;subplot(311);plot(t, m_sig)subplot(312);plot(t,s_nbfm)subplot(313);plot(t, s_nbpm)figure; plot(t, m_intg)
Code to demonstrate the effect of the condition for NBFM (kf a(t)max <<1) and NBPM (kpm(t)max << 1)
Wideband FM (WBFM)
In many application FM signal is meaningful only if its frequency deviation is large enough, so kf a(t) << 1 is not satisfied, and narrowband analysis is not valid.
ππππ‘ (2π΅π‘ )πππ [{ππ+ππ π( π‘π ) }π‘ ]Fourier Transform
Hz
13
+
π΅πΉπ=2(π πππ
2π +2π΅) Hz
Wideband FM (WBFM)
Hz
ΒΏ2π΅ (π½+1 ) π½=β ππ΅ is the deviation ratioWhere
When Ξf >> B the modulation is WBFM and the bandwidth is BFM = 2 Ξf
When Ξf << B the modulation is NBFM and the bandwidth is BFM = 2B 14
A better estimate: Carsonβs rule
Hz
β π =π πππ
2πPeak frequency deviation in hertzπ΅πΉπ=2(π πππ
2π +2π΅)
Wideband PM (WBPM)
The instantaneous frequency
π π=ππ+πποΏ½ΜοΏ½(π‘)
β π =πποΏ½ΜοΏ½π
2π Hz
15
Example
a) Estimate BFM and BPM for the modulating signal m(t) for kf =2Ο x105 and kp = 5Ο. 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.
c) Repeat the problem if the time expanded by a factor of 2: that is, if the period of m(t) is 0.4 msec.
16
Example
An angle-modulated signal with carrier frequency Οc = 2 105 is described by the equation
ππΈπ (π‘ )=10πππ (πππ‘+5 π ππ3000 π‘+10 π ππ2 000ππ‘ )
a) Find the power of the modulated signal.b) Find the frequency deviation Ξf.c) Find the deviation ration .d) Find the phase deviation ΞΓΈ.e) Estimate the bandwidth of .
17
Read the Historical Note: Edwin H. Armstrong (page 270)
Generating FM Waves
Two Methods: 1) Indirect method using NBFM Generation 2) Direct method
ππΉπ (π‘ ) β π΄ [πππ ππ π‘βπ π π (π‘ )π ππππ π‘ ]πππ (π‘ )β π΄ [πππ πππ‘βπππ (π‘ )π ππππ π‘ ]
18With the NBFM generation, the amplitude of the NBFM modulator will have some amplitude variation due to approximation.
NBFM Generation
Distortion with NBFM Generation
Example 5.6: Discuss the nature of distortion inherent in the Armstrong indirect FM generator.
Amplitude and frequency distortions.
19
ππΉπ (π‘ )=π΄ [πππ ππ π‘βπ π π (π‘ )π ππππ π‘ ]ππΉπ (π‘ )=π΄πΈ (π‘ )πππ [ππ π‘+π(π‘ ) ]
πΈ (π‘ )=β1+π π2 π2(π‘) π (π‘ )=π‘ππβ1 [π π π(π‘)]
π π (π‘ )=ππ+ππππ‘ =ππ+
π π οΏ½ΜοΏ½(π‘)1+π π
2 π2(π‘)=ππ+
π ππ (π‘)1+π π
2 π2(π‘)
π π (π‘ )=ππ+π ππ (π‘ ) [1 βπ π2 π2 (π‘ )+π π
4 π4 (π‘ )β β¦ ]
NBFM Generation
Bandpass Limiter
π (π‘ )=πππ‘+ππ β«ββ
π‘
π (πΌ )ππΌ
π£ π (π‘ )=π΄ (π‘ )πππ π(π‘ )
π£π(π)={+1πππ π>0β 1πππ π<0
π£π (π )= 4π (cosπβ 1
3cos 3π+1
5cos5 π+β¦)
20
Generating FM Waves
π£π (π )= 4π {cos [πππ‘+ππ β«
ββ
π‘
π (πΌ )ππΌ ]β 13
cos3 [πππ‘+π π β«ββ
π‘
π (πΌ )ππΌ]+15
cos5 [πππ‘+π π β«ββ
π‘
π (πΌ )ππΌ]+β¦}ππ (π‘ )= 4
π πππ [ππ π‘+π π β«β β
π‘
π (πΌ )ππΌ ] 21
The output of the bandpass filter
π£π (π )= 4π (cosπβ 1
3cos 3π+1
5cos5 π+β¦)
π (π‘ )=πππ‘+ππ β«ββ
π‘
π (πΌ )ππΌ
Indirect Method of Armstrong
NBFM is generated first and then converted to WBFM by using additional frequency multipliers.
Example of frequency multiplier is a nonlinear device
22
π¦ (π‘ )=π2π₯2(π‘ )
π¦ (π‘ )=π2 cos2 [πππ‘+π πβ«π (πΌ )ππΌ ]π¦ (π‘ )=0.5 π2+0.5π2cos [2πππ‘+2π πβ«π (πΌ )ππΌ ]π¦ (π‘ )=π0+π1π₯ (π‘ ) +π2π₯2 (π‘ )+β¦+ππ π₯π (π‘ )
Devices of higher multiplier
Indirect Method of Armstrong
For NBFM << 1. For speech fmin = 50Hz, so if Ξf = 25 then 25/50 = 0.5,
23
ππΉπ (π‘ ) β π΄ [πππ ππ π‘βπ π π (π‘ )π ππππ π‘ ]ππΉπ (π‘ )=π΄πΈ (π‘ )πππ [ππ π‘+π(π‘ ) ]
Example
Design an Armstrong indirect FM modulator to generate an FM signal with carrier frequency 97.3 MHz and Ξf = 10.24 kHz. A NBFM generator of fc1 = 20 kHz and Ξf = 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.
24
Direct Generation
1. The frequency of a voltage-controlled oscillator (VCO) is controlled by the voltage m(t).
π π(π‘)=ππ+π ππ(π‘ )
25
2. Use an operational amplifier to build an oscillator with variable resonance frequency Οo. The resonance frequency can be varied by variable capacitor or inductor. The variable capacitor is controlled by m(t).
ππ=1
βπΏπΆ=
1
βπΏ (πΆ0 βππ(π‘) )=
1
βπΏπΆ0(1 βππ (π‘ )πΆ0 )
ππ=1
βπΏπΆ0[1β ππ (π‘ )πΆ0 ]
1 /2 β 1βπΏπΆ0
[1+ππ (π‘ )2πΆ0 ] ππ (π‘ )
πΆ0βͺ1
Direct Generation
26
ππ=ππ [1+ππ (π‘ )2πΆ0 ] ππ=
1βπΏπΆ0
ππ=ππ+π ππ(π‘ ) π π=πππ
2πΆ0
πΆ=πΆ0 βππ(π‘)The maximum capacitance deviation is
βπΆ=πππ=2π π πΆ0ππ
ππ
βπΆπΆ0
=2π πππ
ππ=2 β π
π π
In practice Ξf << fc
Demodulation of FM Signals
A frequency-selective network with a transfer function of the form |H(f)|=2af + b over the FM band would yield an output proportional to the instantaneous frequency.
οΏ½ΜοΏ½πΉπ (π‘ )= πππ‘ {π΄cos [ππΆπ‘+π π β«
β β
π‘
π (πΌ ) ππΌ]}
27
ππΉπ (π‘ )=π΄cos [ππΆπ‘+π π β«β β
π‘
π (πΌ )ππΌ]
οΏ½ΜοΏ½πΉπ (π‘ )=π΄ [ππ+π ππ (π‘)] sin [ππΆπ‘+π π β«β β
π‘
π (πΌ )ππΌ ]
Demodulation of FM Signals
οΏ½ΜοΏ½πΉπ (π‘ )=π΄ [ππ+π ππ (π‘)] sin [ππΆπ‘+π π β«β β
π‘
π (πΌ )ππΌ ]
28
Differentiator
Practical Frequency Demodulators
π» ( π )= π 2π ππ πΆ1+ π2π ππ πΆ β π2π ππ πΆ if 2π ππ πΆβͺ1
ππππππππ<πππ’π‘πππ=1
π πΆ
The slope is linear over small band, so distortion occurs if the signal band is larger than the linear band.Zero-crossing detectors: First step is to use amplitude limiter and then the zero-crossing detector.
29Instantaneous frequency = the rate of zero crossing
Effect of Nonlinear Distortion and Interference
30
Immunity of Angle Modulation to Nonlinearities
π¦ (π‘ )=π0+π1π₯ (π‘ )+π2π₯2 (π‘ )+β¦+πππ₯π(π‘)
π₯ (π‘ )=π΄ cos [ππΆπ‘+π (π‘ )]
Vulnerability of Amplitude Modulation to Nonlinearities
π¦ (π‘ )=ππ (π‘ ) cos (ππΆπ‘)+ππ3(π‘)πππ 3(ππΆπ‘)
π¦ (π‘ )=[ππ (π‘ )+ 3π4
π3(π‘)] cos (ππΆ π‘ )+π4 π3 (π‘ )πππ (3ππΆπ‘)
Interference Effect
31
Angle Modulation is less vulnerable than AM to small-signal interference from adjacent channels.
π (π‘ )=π΄ cosπππ‘+πΌπππ ΒΏπ (π‘ )=( π΄+ πΌ πππ ππ‘)cosππ π‘β πΌ π ππππ‘ sinπππ‘π (π‘ )=( π΄+ πΌ πππ ππ‘ )cosππ π‘β πΌ π ππππ‘ sinπππ‘
ππ (π‘ )=π‘ππβ1 πΌ π ππππ‘π΄+πΌ πππ ππ‘ for I << A
The output of ideal phase and frequency demodulators are For PM
For FM
Interference is inversely proportional to the carrier amplitude (capture effect).
Preemphasis and Deemphasis in FM
For audio signal the PSD is concentrated at low frequency below 2.1 kHz, so interference at high frequency will greatly deteriorate the quality of audio signal.
PreemphasisFilter
DeemphasisFilterNoise
πΌπ΄
πΌππ΄With white noise, the
amplitude interference is constant for PM but increase with Ο for FM.
Preemphasis and Deemphasis (PDE) in FM
Preemphasis Filter
Deemphasis Filter
2.1 kHz
30 kHz
Preemphasis and Deemphasis (PDE) in FM
π»π ( π )=πΎπ2π π +π1
π2π π +π2
π»π ( π )=π1
π 2π π +π1
For 2f << Ο1 π»π ( π )β 1
For Ο1 << 2f << Ο2π»π ( π )β π2π π
π1
Where K is the gain and = Ο2 / Ο1
PDE is used in many applications such as recording of audiotape and photograph recording, where PDE depends on the band.
FM Broadcasting Standard
Federal Communications Commission (FCC) specifications for FM communication- Frequency range = 88 to 108 MHz- Channel separations = 200 kHz,- Peak frequency deviation = 75 kHz- Transmitted signal should be received by monophonic and
stereophonic receivers.
9088 108 MHz90.2
200 KHz
75 KHz150 KHz
Filter
89.8
Superheterodyne Analog AM/FM Receivers
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.
90 desired signal90.2111.4
90+10.7=100.7
fc = 10.7
10.7 , 190.710.5 , 190.9
9090.2
10.7, 212.1
10.7
FM Broadcasting System
π (π‘ )=(πΏ+π )β²+(πΏβ π )β² cosπππ‘+πΌπππ ππ
2π‘
FM Broadcasting System
π (π‘ )=(πΏ+π )β²+(πΏβ π )β² cosπππ‘+πΌπππ ππ
2π‘
39
Homework Problem 5.4-2
40
Homework Problem 5.6-2