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4/12/2018
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Lecture 15: Frequency and Phase Modulation (FM and PM)
Dr. Mohammed HawaElectrical Engineering Department
University of Jordan
EE421: Communications I: Lecture 15. For more information read Chapter 5 in your textbook or visit http://wikipedia.org/.
Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Just like earlier…
• Time domain expression.
• Time domain sketch.
• Average power of modulated signal.
• Frequency domain representation.
• Bandwidth of modulated signal.
• Signal-to-Noise Ratio and Quality.
• Practical Applications.
• Modulators and Demodulators (hardware).
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Angle Modulation (FM and PM)
• θ(t) is generalized angle of the modulated signal.
• ωi(t) is instantaneous frequency of modulated signal.
• θi(t) is instantaneous phase of modulated signal.
���������� �� = � cos��� + �0�
��� �� �� �� = � cos ���
�� �� ≜ �����
�� �� ≜ ��� − ��
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Frequency Modulation (FM)
• The instantaneous frequency of the modulated signal changes in proportion to the message.
���� �� = �� + � ���
����� = �� + � ! ����−∞
��� �� = � cos #�� + � ! ����−∞
$
���� �� = � ! ����−∞
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Phase Modulation (PM)
• The instantaneous phase of the modulated signal changes in proportion to the message.
���� �� = �%���
��� �� = �� + �% ���
��� �� = � cos &�� + �% ���'
���� �� = �� + ������
� = �� + ���′��
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM and PM Equivalence
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• PM– Constant
amplitude �– Constant carrier
frequency �)– Variable
instantaneousfrequency �* ∝ �′
– Variable instantaneous phase �* ∝ �
• FM– Constant
amplitude �– Constant carrier
frequency �)– Variable
instantaneousfrequency �* ∝ �
– Variable instantaneous phase �* ∝ , � �-
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Example 1• For the following message signal m(t) and a 100 MHz
carrier:a) Sketch the FM modulated signal. Use kf = 2π×105 rad/s/V.
b) Sketch the PM modulated signal. Use kp = 5π rad/V.
c) Find ∆f for both modulated signals.
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Solution: FM
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
PM
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m’(t)
t
0 V
ϕPM(t)
t
0 V
0° 0°
80,000
−80,000
200 µs
m(t)
t0 V
4
− 4
200 µs
A
−A
fmax fmin fmax fmin
Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM vs. PM
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan 11
Peak Frequency Deviation
• For FM:
∆ ≜ /01 − /*22 = �425 6 � /01 − � /*22∆ = �445 6 � 89:89 ;<=>
• For PM:
∆ ≜ /01 − /*22 = �825 6 �′ /01 − �′ /*22∆ = �845 6 �′ 89:89 ;<=>
Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Example 2
• For the following message signal m(t) and a 100 MHz carrier:a) Sketch the FM modulated signal. Use kf = 2π×105 rad/s/V.b) Sketch the PM modulated signal. Use kp = π/4 rad/V.c) Find ∆f for both modulated signals.
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Solution: FM or FSK
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
PMor
BPSK
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m’(t)
t
0 V
ϕPM(t)
t
0 V
χ° χ°
200 µs
m(t)
t0 V
2
− 2
200 µs
A
−A
χ°
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Homework: P.5.1-2• For the following message signal m(t) and a
200 MHz carrier:a) Sketch the FM modulated signal. Use kf = 2000π rad/s/V.b) Sketch the PM modulated signal. Use kp = π/2 rad/V.c) Try other kf and kp values. What is the effect?d) Find ∆f for both modulated signals.
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Hint: For PM
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Rules of Thumb
• Smooth change in instantaneous frequency always means smooth change in instantaneous phase.
• Sudden change in instantaneous frequency (i.e., unit step change) does not mean a sudden change in phase, i.e., it means 0° sudden phase shift.
• Impulse change in instantaneous frequency (i.e., infinity frequency) might cause a sudden change in phase. To determine the sudden phase shift (or lack thereof) see kpm(t) for PM or kf ∫m(t)dt for FM.
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM and PM Average Power
?���� = � cos #�� + � ! ����−∞
$
?�� �� = � cos &�� + �% ���'
���2 ��@@@@@@@@@ = �22
���2 ��@@@@@@@@@ = �22
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM and PM Bandwidth
• Mathematically speaking:– BFM = ∞– BPM = ∞
• Practically speaking, use Carson’s Rule:– BFM ≈ 2∆f + 2B = 2B(β+1)– BPM ≈ 2∆f + 2B = 2B(β+1)
• FM Modulation Index: – A = Δ /D– Narrow-Band FM (NBFM) has A ≪ 1 or Δ ≪ D– Wide-Band FM (WBFM) has A ≫ 1 or Δ ≫ D– FM radio uses WBFM with A = 5
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM Bandwidth: Semi-proof
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan 21
Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Bandwidth: Example 1
• Estimate the bandwidth BFM and BPM for the modulating signal m(t) shown below. Assume kf = π×104 rad/s/V and kp = π/4 rad/V.
• Answers: BFM = 60 kHz; BPM = 40 kHz.
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Bandwidth: Example 2
• Estimate the bandwidth BFM and BPM for the modulating signal m(t) shown below. Assume kf = π×105 rad/s/V and kp = 5π rad/V.
• Answers: 220 kHz; 20 kHz; 104 kHz; 4 kHz;
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM Signal-to-Noise Ratio
IJK�� = #3A2��2 $ I��J0D
I�� = �2��@@@@@@@ = �22
��2 = �%2�2��@@@@@@@@
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM (and PM) vs. AM
• FM (and PM) Advantages:
– FM is capable of exchanging SNR for bandwidth.
– The constant amplitude of FM makes it less susceptible to nonlinearities.
– Due to the constant amplitude, FM is less vulnerable than AM to adjacent-channel interference.
– The constant amplitude of FM gives it a kind of immunity against rapid fading (even with the larger bandwidth).
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM (and PM) vs. AM
• FM (and PM) Disadvantages:
–WBFM (which provides better quality) requires large transmission bandwidth.
–FM modulators and demodulators are relatively more expensive that AM hardware.
–PM demodulation requires synchronous detection (relatively expensive).
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Applications: FM Radio
• FM + FDM– The baseband message is 15 kHz (voice + music).
– With β = 5, the bandwidth of each FM station is 200 kHz (both U.S. and Europe).
– The broadcast range is 88 – 108 MHz.
• FM radio sounds better than AM radio:– m(t) has a larger bandwidth.
– WBFM: exchanging SNR for bandwidth.
– Pre-emphasis/De-emphasis improves SNR.
– Stereo FM.
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM Superhetrodyne Receiver
• IF frequency = 10.7 MHz
• L.O. frequency = 88 + 10.7 MH to 108 + 10.7 MHz
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
FM Superhetrodyne Receiver
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Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan
Stereo FM vs. Mono FM
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