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EE104: Lecture 22 Outline

EE104: Lecture 22 Outline. Announcements HW due, final HW posted (due Monday, 3/17) Final exam Thursday, 3/20, 8:30-11:30am More details next week Review of Last Lecture Spectral Analysis of FM FM Bandwidth and Carson’s Rule Narrowband FM Modulation Wideband FM Modulation FM Detection.

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EE104: Lecture 22 Outline

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  1. EE104: Lecture 22 Outline • Announcements • HW due, final HW posted (due Monday, 3/17) • Final exam Thursday, 3/20, 8:30-11:30am • More details next week • Review of Last Lecture • Spectral Analysis of FM • FM Bandwidth and Carson’s Rule • Narrowband FM Modulation • Wideband FM Modulation • FM Detection

  2. Review of Last Lecture • Vestigial Sideband Modulation • Transmits a small part of unwanted sideband • Does not cause distortion at baseband • Can use a carrier or suppress the carrier • Standard envelope detection or DSBSC demod. • AM Radio • Superheterodyne Receivers • Use IF downconversion and processing • Gets around reradiation and processing at fc. • Introduction to FM

  3. Introduction to FM • Information signal encoded in carrier frequency (or phase): s(t)=Accos(q(t)) • q(t)=f(m(t)) • Standard FM: q(t)=2pfct+2pkf m(t)dt • Signal robust to amplitude variations • Robust to signal reflections and refractions • Instantaneous frequency: fi=fc+kfm(t) • Maximum Deviation:Df=fc+kf|m(t)| • Bandwidth of S(f) depends on Df.

  4. B2Df WBFM B2Bm NBFM Spectral Analysis of FM • s(t)=Accos(2pfct+2pkf m(t)dt) • Nonlinear function of m(t) • Very hard to analyze for general m(t). • Let m(t)=cos(2pfmt): Bandwidth fm • Spectrum S(f) is a sequence of delta functions at multiples of fm from fc S(f) for m(t)=cos(2pfmt) … … f fc -4fm fc+fm fc -3fm fc+3fm fc fc -2fm fc+2fm fc+ 4fm fc-fm

  5. FM Bandwidth and Carson’s Rule • Frequency Deviation: Df=kf max|m(t)| • Maximum deviation of fi from fc: fi=fc+kfm(t) • Carson’s Rule: • B depends on maximum deviation from fcAND how fast fi changes • Narrowband FM: Df<<BmB2Bm • Wideband FM: Df>>BmB2Df B2Df+2Bm

  6. Generating FM Signals • NBFM • WBFM • Direct Method: Modulate a VCO with m(t) • Indirect Method: Use a NBFM modulator, followed by a nonlinear device and BPF f(t) s(t) m(t) - Product Modulator 2pkf(·)dt + + Accos(2pfct) Acsin(2pfct) LO -90o

  7. FM Detection • Differentiator and Envelope Detector • Zero Crossing Detector • Uses rate of zero crossings to estimate fi • Phase Lock Loop (PLL) • Uses VCO and feedback to extract m(t)

  8. Main Points • Spectral analysis of FM difficult. For a simple cosine information signal, FM spectrum is discrete and infinite. • FM signal bandwidth depends on information signal amplitude. Carson’s rule yields B=2Bm+2Df. • NBFM easy to analyze and is generated with a simple product modulator. WBFM harder to generate and to analyze. • In theory just need a differentiator and envelope detector for FM demodulation. Multiple methods used in practice

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