© 2010 The McGraw-Hill Companies Communication Systems, 5e Chapter 5: Angle CW Modulation A. Bruce Carlson Paul B. Crilly (modified by J. H. Cho using Prof. W.J. Song’s lecture note)

© 2010 The McGraw-Hill Companies Chapter 5: Angle CW Modulatation  Phase and frequency modulation  Transmission bandwidth and distortion  Generation and detection of FM and PM  Interference

© 2010 The McGraw-Hill Companies 5.1 Phase and frequency modulation

Terms © 2010 The McGraw-Hill Companies Total instantaneous angle Angle modulation = exponential modulation Phase modulation (PM) Phase modulation index = phase deviation Instantaneous frequency vs. spectral frequency Frequency modulation (FM) Frequency deviation Zero-crossing rate

© 2010 The McGraw-Hill Companies  Exponential Modulation ( 각변조 ) Phase modulation Frequency Modulation (FM) Phase Modulation (PM)  PM & FM Signals

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Def ) 순간 주파수 (instantaneous frequency) 의 정의 Frequency modulation

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PM signals

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FM and PM Signals  Power is constant, and not a function of message power

© 2010 The McGraw-Hill Companies FM and PM  Message content resides in zero crossings not amplitude  Modulated waveform does not resemble message waveform  Amplitude is constant  we can use more efficient nonlinear amplifiers 

© 2010 The McGraw-Hill Companies Illustrative AM, FM, and PM waveforms

Terms © 2010 The McGraw-Hill Companies Narrowband PM and FM (NBPM and NBFM) Single-tone modulation Bessel function of the first kind of order n and argument beta Multitone modulation Periodic modulation

© 2010 The McGraw-Hill Companies  Narrowband PM & FM

© 2010 The McGraw-Hill Companies  Narrowband Condition 따라서 Note this is true only when is small. Then

© 2010 The McGraw-Hill Companies Narrowband PM and FM

© 2010 The McGraw-Hill Companies The spectrum of narrowband FM and PM looks like that of AM!

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Tone Modulation

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Narrowband modulation

© 2010 The McGraw-Hill Companies NBFM with tone modulation (a) Line spectrum; (b) Phasor diagram

© 2010 The McGraw-Hill Companies Let Then 일반적으로 임의의 에 대한 FM 의 대역폭을 구하는 것은 불가능하다. 최고 주파수

© 2010 The McGraw-Hill Companies FM/PM spectra with an arbitrary index value

© 2010 The McGraw-Hill Companies Note) Trigono. Fourier Series 주기함수 Bessel Function of the First Kind of order and argument

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Note)   determines the magnitude of the Fourier Coeff.’s  frequency spacing (decay rate of sideband harmonics)

© 2010 The McGraw-Hill Companies  Infinite Sideband ! 따라서  Up to N sidebands

© 2010 The McGraw-Hill Companies  99% POWER Note)

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Note: the lower sidebands alternate from + to -

© 2010 The McGraw-Hill Companies Magnitude of tone-modulated line spectra (a) FM or PM with ƒ m fixed; (b) FM with A m ƒ  fixed

© 2010 The McGraw-Hill Companies  Multitone Modulation  FM

© 2010 The McGraw-Hill Companies No superposition Intermodulation component ! because FM is a nonlinear modulation method.

© 2010 The McGraw-Hill Companies Chapter 5: Angle CW Modulatation  Phase and frequency modulation  Transmission bandwidth and distortion  Generation and detection of FM and PM  Interference

© 2010 The McGraw-Hill Companies 5.2 Transmission bandwidth and distortion

Bandwidth of Narrowband FM  Approximate spectrum of narrowband FM  Message bandwidth vs. transmission bandwidth © 2010 The McGraw-Hill Companies

Bandwidth of Tone Modulated FM  Spectrum of Single-tone modulated FM  M significant sideband pairs B=2Mf_m  M(beta) vs. beta +2 Beta = A_m f_delta/f_m=< f_delta/f_m  Deviation ratio = f_delta/W © 2010 The McGraw-Hill Companies

Transmission Bandwidth

© 2010 The McGraw-Hill Companies In all approximations, the transmission bandwidth is proportional to twice the transmission bandwidth. The proportionality constants are different.

© 2010 The McGraw-Hill Companies Commercial FM radio bandwidth example

© 2010 The McGraw-Hill Companies  Station engineer has set constants so B T conforms to the FCC limits dictated by their license

5.2.2 Linear and Nonlinear Distortion © 2010 The McGraw-Hill Companies  Wireless channel as an LTI system  FM-to-AM conversion  Controlled nonlinear distortion and filtering to remove unwanted amplitude variation  Memoryless nonlinear system

© 2010 The McGraw-Hill Companies Limiter

© 2010 The McGraw-Hill Companies Nonlinear processing circuits (a) Amplitude limiter; (b) frequency multiplier

© 2010 The McGraw-Hill Companies Amplitude Limiter and Noise Reduction FM signal processing using a limiter: Noiseless FM signal, (b) noisy FM signal, (c) limiter output with noisy input, (d) BPF output

© 2010 The McGraw-Hill Companies Output of Memoryless Nonlinear System to FM Input  V_in(t) = A_c cos{omega_ct+phi(t)}  Weierstrass Approximation Theorem For every epsilon, there exists a polynomial such that…  V_out(t) = …

© 2010 The McGraw-Hill Companies Limiter for frequency multiplier  Limiter or some other nonlinear device generates harmonics   BPF selects which integer multiple of  Nonlinear device also changes frequency/phase deviation constants

© 2010 The McGraw-Hill Companies Chapter 5: Angle CW Modulatation  Phase and frequency modulation  Transmission bandwidth and distortion  Generation and detection of FM and PM  Interference

© 2010 The McGraw-Hill Companies 5.3 Generation and detection of FM and PM

© 2010 The McGraw-Hill Companies Generation of FM and PM signals  Pros. Constant envelope  more power efficient nonlinear methods can be used  longer battery life  Cons. Required to have frequency vary linearly with the message amplitude. Not straightforward.

© 2010 The McGraw-Hill Companies Direct FM and Voltage Controlled Oscillator (VCO): Use a VCO!

© 2010 The McGraw-Hill Companies Important: frequency change must be linear with x(t)  sets a limit on maximum frequency deviation

© 2010 The McGraw-Hill Companies Tripler

© 2010 The McGraw-Hill Companies Important: Frequency multiplication is not the same as hetrodyning Hetrodyning is a linear process and does not affect the frequency or phase deviation constants

© 2010 The McGraw-Hill Companies Phase modulators and indirect FM: Generate a NBFM, use frequency multiplier, and down-convert! Convert a PM signal to an FM one by integrating The message signal

© 2010 The McGraw-Hill Companies Phase modulators and Indirect FM

© 2010 The McGraw-Hill Companies Frequency detection Produces output voltage that is proportional to the instantaneous frequency of the input  the message x(t).

© 2010 The McGraw-Hill Companies Frequency detector = Discriminator 1.FM-to-AM conversion 2.Phase-shift discrimination 3.Zero-crossing detection 4.Frequency feedback→ phase locked loops (Chap 7)

© 2010 The McGraw-Hill Companies FM to AM conversion

© 2010 The McGraw-Hill Companies FM to AM conversion  Take derivative of FM signal  Use an envelope detector

© 2010 The McGraw-Hill Companies FM Detection Waveforms (a)frequency detector with limiter and FM to AM conversion (b) waveforms

© 2010 The McGraw-Hill Companies FM to AM methods - Derivative  Slope detector via a BPF  Balanced discriminator

© 2010 The McGraw-Hill Companies Derivative function  Allows an AM receiver with a BPF to detect an FM signal

© 2010 The McGraw-Hill Companies Balanced discriminator To get the maximum response from the BPF we combine two BPF-envelope detectors to get a balanced discriminator (b) circuit, (c) voltage to frequency characteristic

© 2010 The McGraw-Hill Companies Phase shift discriminator

© 2010 The McGraw-Hill Companies Phase-shift discriminator

© 2010 The McGraw-Hill Companies Chapter 5: Angle CW Modulatation  Phase and frequency modulation  Transmission bandwidth and distortion  Generation and detection of FM and PM  Interference

© 2010 The McGraw-Hill Companies 5.4 Interference  Occurs when another signal is received concurrently in the receiver’s bandpass  Multipath: multiple versions of the transmitted signal with different delays can cause interference  Effects can be affected by the types of modulation and detectors used.  Interference: generally not random  Sometimes can be canceled out Is not the same as random noise

© 2010 The McGraw-Hill Companies Interfering sinusoids

© 2010 The McGraw-Hill Companies Interfering sinusoid in envelope-phase form

© 2010 The McGraw-Hill Companies The interfering sinusoid produces both amplitude and phase modulation This is why nearby AM/FM signals with unsuppressed carriers generate a disproportionate amount of obnoxious background “whistles.”

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Demodulated output with interference Observe how interference level of FM depends on spacing of interference carrier frequency

© 2010 The McGraw-Hill Companies Interference level as function of interference frequency spacing Note how with FM interference is reduced if the interference frequency spacing is reduced.

© 2010 The McGraw-Hill Companies Deemphasis and Preemphasis Filtering We exploit the property of FM that causes the interference level to be reduced as f i ↓ by deemphasis filtering of the high frequencies at detection  we preemphasize the high frequencies at the transmitter.

© 2010 The McGraw-Hill Companies Chapter 5: Angle CW Modulatation  Phase and frequency modulation  Transmission bandwidth and distortion  Generation and detection of FM and PM  Interference