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ECE 4371, Fall, 2009

ECE 4371, Fall, 2009. Zhu Han Department of Electrical and Computer Engineering Class 5 Sep. 8 th , 2007. Phase-Locked Loop. Can be a whole course. The most important part of receiver.

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ECE 4371, Fall, 2009

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  1. ECE 4371, Fall, 2009 Zhu Han Department of Electrical and Computer Engineering Class 5 Sep. 8th, 2007

  2. Phase-Locked Loop • Can be a whole course. The most important part of receiver. • Definition: a closed-loop feedback control system that generates and outputs a signal in relation to the frequency and phase of an input ("reference") signal • A phase-locked loop circuit responds both to the frequency and phase of the input signals, automatically raising or lowering the frequency of a controlled oscillator until it is matched to the reference in both frequency and phase.

  3. Ideal Model • Model • Si=Acos(wct+1(t)), Sv=Avcos(wct+c(t)) • Sp=0.5AAv[sin(2wct+1+c)+sin(1-c)] • So=0.5AAvsin(1-c)=AAv(1-c) • Capture Range and Lock Range LPF VCO

  4. Type of waves

  5. GPS Orbits

  6. FM Basics • VHF (30M-300M) high-fidelity broadcast • Wideband FM, (FM TV), narrow band FM (two-way radio) • 1933 FM and angle modulation proposed by Armstrong, but success by 1949. • Digital: Frequency Shift Key (FSK), Phase Shift Key (BPSK, QPSK, 8PSK,…) • AM/FM: Transverse wave/Longitudinal wave

  7. Angle Modulation vs. AM • Summarize: properties of amplitude modulation • Amplitude modulation is linear • just move to new frequency band, spectrum shape does not change. No new frequencies generated. • Spectrum: S(f) is a translated version of M(f) • Bandwidth ≤ 2W • Properties of angle modulation • They are nonlinear • spectrum shape does change, new frequencies generated. • S(f) is not just a translated version of M(f) • Bandwidth is usually much larger than 2W

  8. Angle Modulation Pro/Con Application • Why need angle modulation? • Better noise reduction • Improved system fidelity • Disadvantages • Low bandwidth efficiency • Complex implementations • Applications • FM radio broadcast • TV sound signal • Two-way mobile radio • Cellular radio • Microwave and satellite communications

  9. Instantaneous Frequency • Angle modulation has two forms • - Frequency modulation (FM): message is represented as the variation of the instantaneous frequency of a carrier • - Phase modulation (PM): message is represented as the variation of the instantaneous phase of a carrier

  10. Phase Modulation • PM (phase modulation) signal

  11. Frequency Modulation • FM (frequency modulation) signal (Assume zero initial phase)

  12. FM Characteristics • Characteristics of FM signals • Zero-crossings are not regular • Envelope is constant • FM and PM signals are similar

  13. Relations between FM and PM

  14. FM/PM Example (Time)

  15. FM/PM Example (Frequency)

  16. Matlab fc=1000; Ac=1; % carrier frequency (Hz) and magnitude fm=250; Am=0.1; % message frequency (Hz) and magnitude k=4; % modulation parameter % generage single tone message signal t=0:1/10000:0.02; % time with sampling at 10KHz mt=Am*cos(2*pi*fm*t); % message signal % Phase modulation sp=Ac*cos(2*pi*fc*t+2*pi*k*mt); % Frequency modulation dmt=Am*sin(2*pi*fm*t); % integration sf=Ac*cos(2*pi*fc*t+2*pi*k*dmt); % PM % Plot the signal subplot(311), plot(t,mt,'b'), grid, title('message m(t)') subplot(312), plot(t,sf,'r'), grid, ylabel('FM s(t)') subplot(313), plot(t,sp,'m'), grid, ylabel('PM s(t)')

  17. Matlab % spectrum w=((0:length(t)-1)/length(t)-0.5)*10000; Pm=abs(fftshift(fft(mt))); % spectrum of message Pp=abs(fftshift(fft(sp))); % spectrum of PM signal Pf=abs(fftshift(fft(sf))); % spectrum of FM signal % plot the spectrums figure(2) subplot(311), plot(w,Pm,'b'), axis([-3000 3000 min(Pm) max(Pm)]), grid, title('message spectrum M(f)'), subplot(312), plot(w,Pf,'r'), axis([-3000 3000 min(Pf) max(Pf)]), grid, ylabel('FM S(f)') subplot(313), plot(w,Pp,'m'), axis([-3000 3000 min(Pp) max(Pp)]), grid, ylabel('PM S(f)')

  18. Frequency Modulation • FM (frequency modulation) signal (Assume zero initial phase)

  19. Example Consider m(t)- a square wave- as shown. The FM wave for this m(t) is shown below. m(t) 0 T 2T

  20. Frequency deviation Δf difference between the maximum instantaneous and carrier frequency Definition: Relationship with instantaneous frequency Question: Is bandwidth of s(t) just 2Δf? Frequency Deviation No, instantaneous frequency is not equivalent to spectrum frequency (with non-zero power)! S(t) has ∞ spectrum frequency (with non-zero power).

  21. Modulation Index • Indicate by how much the modulated variable (instantaneous frequency) varies around its unmodulated level (message frequency) • Bandwidth A

  22. Narrow Band Angle Modulation Definition Equation • Comparison with AM • Only phase difference of Pi/2 • Frequency: similar • Time: AM: frequency constant • FM: amplitude constant • Conclusion: NBFM signal is similar to AM signal • NBFM has also bandwidth 2W. (twice message signal bandwidth)

  23. Example

  24. Block diagram of a method for generating a narrowband FM signal.

  25. A phasor comparison of narrowband FM and AM waves for sinusoidal modulation. (a) Narrowband FM wave. (b) AM wave.

  26. Wide Band FM • Wideband FM signal • Fourier series representation

  27. Example

  28. Bessel Function of First Kind

  29. Spectrum of WBFM • Spectrum when m(t) is single-tone • Example 2.2

  30. Spectrum Properties <<

  31. Bandwidth of FM • Facts • FM has side frequencies extending to infinite frequency  theoretically infinite bandwidth • But side frequencies become negligibly small beyond a point  practically finite bandwidth • FM signal bandwidth equals the required transmission (channel) bandwidth • Bandwidth of FM signal is approximately by • Carson’s Rule (which gives lower-bound)

  32. Carson’s Rule • Nearly all power lies within a bandwidth of • For single-tone message signal with frequency fm • For general message signal m(t) with bandwidth (or highest frequency) W

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