Nonlinear Modulation
CHAPTER 5 ANGLE MODULATION AND DEMODULATION Fundamental of Communication Systems ELCT332 Fall2011 1 Nonlinear Modulation Frequency Modulation (FM) Phase Modulation (PM) Angle Modulation Exponential Modulation Instantaneous Angular Frequency Concept of instantaneous frequency. Phase Modulation Frequency Modulation Fundamental of Communication Systems ELCT332 Fall2011 2 Nonlinear Modulator Phase and frequency modulation are equivalent and interchangeable. Fundamental of Communication Systems ELCT332 Fall2011 3 Modulation and Demodulation Generalized phase modulation by means of the filter H(s) and recovery of the message from the modulated phase through the inverse filter 1/H(s). Fundamental of Communication Systems ELCT332 Fall2011 4 Example Sketch FM and PM waves for the modulating signal m(t), The constants kf and kp are 2π×105 and 10π, respectively, and the carrier frequency fc is 100MHz. FM and PM waveforms. Fundamental of Communication Systems ELCT332 Fall2011 5 Example Sketch FM and PM waves for the modulating signal m(t), The constants kf and kp are 2π×105 and π/2, respectively, and the carrier frequency fc is 100MHz. Frequency shift keying: modulating by a digital signal Fundamental of Communication Systems Phase shift keying ELCT332 Fall2011 6 Bandwidth of Angle Modulated Waves Narrowband FM (NBFM) Narrowband PM (NBPM) Fundamental of Communication Systems ELCT332 Fall2011 7 Bandwidth of Angle Modulated Waves: Wideband FM (WBFM) Peak Frequency Deviation Fundamental of Communication Systems ELCT332 Fall2011 8 Spectral Analysis of Frequency Modulation Fundamental of Communication Systems ELCT332 Fall2011 9 Example: Estimate BFM and BPM for the modulating signal m(t) for kf and kp are 2π×105 and 5π, respectively. Assume the essential bandwidth of the periodic m(t) as the frequency of its third harmonic. What will be the bandwidth if the amplitudde of m(t) is doubled? Fundamental of Communication Systems ELCT332 Fall2011 10 Generating FM Waves: NBFB Generation Narrowband PM generator. (b) Narrowband FM signal generator. Fundamental of Communication Systems ELCT332 Fall2011 11 Bandpass Limiter Eliminate the amplitude variations of an angle-modulated carrier 𝑡 𝑣𝑜 𝜃 𝑡 = 𝑣𝑜 𝜔𝑐 𝑡 + 𝑘𝑓 𝑚 𝛼 𝑑𝛼 −∞ = 4 cos 𝜔𝑐 𝑡 + 𝑘𝑓 𝜋 𝑡 1 𝑚 𝛼 𝑑𝛼 − cos 3 𝜔𝑐 𝑡 + 𝑘𝑓 3 −∞ 𝑡 𝑚 𝛼 𝑑𝛼 + ⋯ −∞ (a) Hard limiter and bandpass filter used to remove amplitude variations in FM wave. (b) Hard limiter input-output characteristic. (c) Hard limiter input and the corresponding output. (d) Hard limiter output as a function of θ. Modern Digital and Analog Communication Systems ELCT332 Fall2011 12 Indirect Method of Armstrong: WBFM Generation Generating NBFM first and then converted to WBFM by using additional frequency multipliers. Frequency multiplier can be realized by a nonlinear device followed by a bandpass filter. 𝑦 𝑡 = 𝑎2 𝑐𝑜𝑠 2 𝜔𝑐 𝑡 + 𝑘𝑓 𝑦 𝑡 = 𝑐0 + 𝑐1 cos 𝜔𝑐 𝑡 + 𝑘𝑓 𝑚 𝛼 𝑑𝛼 = 0.5𝑎2 + 0.5𝑎2 cos [2𝜔𝑐 𝑡 + 2𝑘𝑓 𝑚 𝛼 𝑑𝛼 + 𝑐2 cos2 𝜔𝑐 𝑡 + 𝑘𝑓 + 𝑐𝑛 cosn 𝜔𝑐 𝑡 + 𝑘𝑓 𝑚 𝛼 𝑑𝛼] 𝑚 𝛼 𝑑𝛼 + ⋯ 𝑚 𝛼 𝑑𝛼 Block diagram of the Armstrong indirect FM transmitter. Fundamentals of Communication Systems ELCT332 Fall2011 13 Example: Design an Armstrong indirect FM modulator to generate an FM signal with carrier frequency 97.3 MHz and Δf=10.24kHz. A NBFM generator of fc1=20 kHz and Δf=5Hz is available. Only frequency doublers can be used as multipliers. Additionally, a local oscillator with adjustable frequency 400 and 500 kHz is readily available for frequency mixing. 97.3𝑀𝐻𝑧 = 2𝑛 2 2𝑛 1 𝑓𝑐1 − 𝑓𝐿𝑂 97.3𝑀𝐻𝑧 = 2𝑛 2 2𝑛 1 𝑓𝑐1 + 𝑓𝐿𝑂 , 𝑓𝐿𝑂 = 2−𝑛 2 4.096 × 107 − 9.73 × 107 < 0 𝑓𝐿𝑂 = 2−𝑛 2 5.634 × 107 , 𝑛2 = 7, 𝑓𝐿𝑂 = 440𝑘𝐻𝑧 𝑀1 = 16, 𝑀2 = 128 Designing an Armstrong indirect modulator. Fundamentals of Communication Systems ELCT332 Fall2011 14 Demodulation of FM Signals Slope Detection 𝑗2𝜋𝑓𝑅𝐶 𝐻 𝑓 = ≈ 𝑗2𝜋𝑓𝑅𝐶 1 + 𝑗2𝜋𝑓𝑅𝐶 𝑖𝑓 2𝜋𝑓𝑅𝐶 ≪ 1 (a) FM demodulator frequency response. (b) Output of a differentiator to the input FM wave. (c) FM demodulation by direct differentiation. Fundamentals of Communication Systems ELCT332 Fall2011 15 Effects of Nonlinear Distortion and Interference Immunity of Angle Modulation to Nonlinearities Amplitude Modulation Fundamentals of Communication Systems ELCT332 Fall2011 16 Interference Effect Angle modulation is also less vulnerable than AM to small signal interference from adjacent channels Effect of interference in PM, FM, and FM with preemphasis-deemphasis (PDE). Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.15 Preemphasis-deemphasis in an FM system. Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.16 (a) Preemphasis filter and (b) its frequency response. (c) Deemphasis filter and (d) its frequency response. Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.17 Superheterodyne receiver. Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.18 (a) FM stereo transmitter. (b) Spectrum of a baseband stereo signal. (c) FM stereo receiver. Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.19 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.19 FM and PM signals in the time and frequency domains. Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.20 Signals at the demodulator: (a) after differentiator; (b) after rectifier. Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 5.21 FM modulation and demodulation: (a) original message; (b) recovered signal. Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P.5.1-1 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P.5.1-2 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P.5.1-3 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P.5.1-5 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P.5.4-1 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P.5.4-2 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.
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