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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

ECE 4371, Fall, 2009

Zhu Han

Department of Electrical and Computer Engineering

Class 5

Sep. 8th, 2007

phase locked loop
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.
ideal model
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



fm basics
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
angle modulation vs am
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
angle modulation pro con application
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
instantaneous frequency
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
phase modulation
Phase Modulation
  • PM (phase modulation) signal
frequency modulation
Frequency Modulation
  • FM (frequency modulation) signal

(Assume zero initial phase)

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

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


% 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)')


% spectrum


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


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)')

frequency modulation18
Frequency Modulation
  • FM (frequency modulation) signal

(Assume zero initial phase)


Consider m(t)- a square wave- as shown. The FM wave for this m(t) is shown below.


0 T 2T

frequency deviation
Frequency deviation Δf

difference between the maximum instantaneous and carrier frequency


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).

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


narrow band angle modulation
Narrow Band Angle Modulation



  • 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)
A phasor comparison of narrowband FM and AM waves for sinusoidal modulation. (a) Narrowband FM wave. (b) AM wave.
wide band fm
Wide Band FM
  • Wideband FM signal
  • Fourier series representation
spectrum of wbfm
Spectrum of WBFM
  • Spectrum when m(t) is single-tone
  • Example 2.2
bandwidth of fm
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)
carson s rule
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