Communication Systems 5 e Chapter 5 Angle CW

Chapter 5: Angle CW Modulatation o Phase and frequency modulation o Transmission bandwidth and

5. 1 Phase and frequency modulation © 2010 The Mc. Graw-Hill Companies

Terms 5. 1 -1 • Total instantaneous angle • Angle modulation = exponential modulation

q Exponential Modulation (각변조) Frequency Modulation (FM) Phase Modulation (PM) q PM & FM

Def ) 순간 주파수 (instantaneous frequency)의 정의 Frequency modulation © 2010 The Mc. Graw-Hill

PM signals © 2010 The Mc. Graw-Hill Companies

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

FM and PM o Message content resides in zero crossings not amplitude o Modulated

Illustrative AM, FM, and PM waveforms © 2010 The Mc. Graw-Hill Companies

Terms 5. 1 -2 • Narrowband PM and FM (NBPM and NBFM) • Single-tone

q Narrowband PM & FM © 2010 The Mc. Graw-Hill Companies

q Narrowband Condition Then 따라서 © 2010 The Mc. Graw-Hill Note this is true

Narrowband PM and FM © 2010 The Mc. Graw-Hill Companies

The spectrum of narrowband FM and PM looks like that of AM! © 2010

Tone Modulation © 2010 The Mc. Graw-Hill Companies

Narrowband modulation © 2010 The Mc. Graw-Hill Companies

NBFM with tone modulation (a) Line spectrum; (b) Phasor diagram © 2010 The Mc.

FM/PM spectra with an arbitrary index value © 2010 The Mc. Graw-Hill Companies

Note) Trigono. Fourier Series Bessel Function of the First Kind of order © 2010

Note) (decay rate of sideband harmonics) determines the magnitude of the Fourier Coeff. ’s

q Infinite Sideband ! 따라서 q Up to N sidebands © 2010 The Mc.

q 99% POWER Note) © 2010 The Mc. Graw-Hill Companies

Note: the lower sidebands alternate from + to © 2010 The Mc. Graw-Hill Companies

Magnitude of tone-modulated line spectra (a) FM or PM with ƒm fixed; (b) FM

q Multitone Modulation q FM © 2010 The Mc. Graw-Hill Companies

Intermodulation component ! because FM is a nonlinear modulation method. © 2010 The Mc.

5. 2 Transmission bandwidth and distortion © 2010 The Mc. Graw-Hill Companies

Bandwidth of Narrowband FM o Approximate spectrum of narrowband FM o Message bandwidth vs.

Bandwidth of Tone Modulated FM o Spectrum of Single-tone modulated FM o M significant

Transmission Bandwidth © 2010 The Mc. Graw-Hill Companies

• In all approximations, the transmission bandwidth is proportional to twice the transmission

Commercial FM radio bandwidth example © 2010 The Mc. Graw-Hill Companies

Station engineer has set constants so BT conforms to the FCC limits dictated

5. 2. 2 Linear and Nonlinear Distortion o Wireless channel as an LTI system

Limiter © 2010 The Mc. Graw-Hill Companies

Nonlinear processing circuits (a) Amplitude limiter; (b) frequency multiplier © 2010 The Mc. Graw-Hill

Amplitude Limiter and Noise Reduction FM signal processing using a limiter: Noiseless FM signal,

$Output of Memoryless Nonlinear System to FM Input o V_in(t) = A_c cos{omega_ct+phi(t)} o$

Limiter for frequency multiplier o Limiter or some other nonlinear device generates harmonics o

5. 3 Generation and detection of FM and PM © 2010 The Mc. Graw-Hill

Generation of FM and PM signals o Pros. Constant envelope more power efficient nonlinear

5. 3. 1 Direct FM and Voltage Controlled Oscillator (VCO): Use a VCO! ©

Important: frequency change must be linear with x(t) sets a limit on maximum frequency

Tripler © 2010 The Mc. Graw-Hill Companies

Important: Frequency multiplication is not the same as hetrodyning Hetrodyning is a linear process

5. 3. 2 Phase modulators and indirect FM: Generate a NBFM, use frequency multiplier,

Phase modulators and Indirect FM © 2010 The Mc. Graw-Hill Companies

5. 3. 4 Frequency detection Produces output voltage that is proportional to the instantaneous

Frequency detector = Discriminator 1. FM-to-AM conversion 2. Phase-shift discrimination 3. Zero-crossing detection 4.

5. 3. 4. 1 FM to AM conversion © 2010 The Mc. Graw-Hill Companies

FM to AM conversion o Take derivative of FM signal o Use an envelope

FM Detection Waveforms (a)frequency detector with limiter and FM to AM conversion (b) waveforms

FM to AM methods - Derivative o Slope detector via a BPF o Balanced

Derivative function Allows an AM receiver with a BPF to detect an FM signal

Balanced discriminator To get the maximum response from the BPF we combine two BPF-envelope

5. 3. 4. 2 Phase shift discriminator © 2010 The Mc. Graw-Hill Companies

Phase-shift discriminator © 2010 The Mc. Graw-Hill Companies

5. 4 Interference o Occurs when another signal is received concurrently in the receiver’s

Interfering sinusoids © 2010 The Mc. Graw-Hill Companies

Interfering sinusoid in envelope-phase form © 2010 The Mc. Graw-Hill Companies

The interfering sinusoid produces both amplitude and phase modulation This is why nearby AM/FM

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

Interference level as function of interference frequency spacing Note how with FM interference is

Deemphasis and Preemphasis Filtering We exploit the property of FM that causes the interference

Slides: 80

Download presentation

Terms 5. 1 -1 • 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 Mc. Graw-Hill Companies

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

Terms 5. 1 -2 • 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 Mc. Graw-Hill Companies

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

5. 2. 2 Linear and Nonlinear Distortion o Wireless channel as an LTI system o FM-to-AM conversion o Controlled nonlinear distortion and filtering to remove unwanted amplitude variation o Memoryless nonlinear system © 2010 The Mc. Graw-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 Mc. Graw-Hill Companies

$Output of Memoryless Nonlinear System to FM Input o V_in(t) = A_c cos{omega_ct+phi(t)} o$

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

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

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

5. 3. 2 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 Mc. Graw-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 Mc. Graw-Hill Companies

5. 4 Interference o Occurs when another signal is received concurrently in the receiver’s bandpass o Multipath: multiple versions of the transmitted signal with different delays can cause interference o Effects can be affected by the types of modulation and detectors used. o Interference: generally not random n Sometimes can be canceled out n Is not the same as random noise © 2010 The Mc. Graw-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. ” © 2010 The Mc. Graw-Hill Companies

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