3013S2L3 TELE3013: Lab 3 1

TELE3013 TELECOMMUNICATION SYSTEMS 1

Lab 3: Frequency Modulation

1. INTRODUCTION

A sinusoidal carrier signal Ac cos ωct frequency modulated by a message m(t) is defined by,

++++== ∫∫ 0

t

0fcc d)(mDtcosA)t(s θθττττωω (1)

where Df is the frequency modulator constant (or sensitivity) in radians per second per volt.

For a sinusoidal message m(t) = Am cos ωm t, equation (1) becomes (taking θo = 0 for simplicity),

)tsintcos(A)t(s mcc ωωββωω ++== (2)

where β = AmDf /ωm = � ω /ωm = �F / fm is the frequency modulation index and �F is the peak(instantaneous) frequency deviation from the carrier frequency fc.

When β « 1 we have a Narrow–Band Frequency Modulated (NBFM) signal,

tsintsinAtcosA|)t(s cmcccNBFM ωωωωββωω −−== (3)

2. PREPARATION

P1.P1. Consider an FM signal with a sinusoidal message as given by equation (2). Giventhat the message parameters Am = 2 volts, fm = 5 kHz and the carrier parametersAc = 1 volt, fc = 100 kHz and that the peak frequency deviation ∆F = 20 kHz,determine the following:

a. The instantaneous phase of the FM signal and the peak phase deviationfrom the carrier phase. Sketch the instantaneous phase as a function of time.

b. The instantaneous frequency of the FM signal. Sketch it as a function oftime.

c. The FM signal modulation index.

d. The approximate bandwidth of the FM signal.

e. The average power of the message signal (in 1 ohm).

f. The average power of the unmodulated carrier signal.

g. The average power of the FM signal.

P2.P2. Use Armstrong's method to generate Wide-Band Frequency Modulated (WBFM)signal from NBFM. Starting from a NBFM signal with a carrier frequency of 10kHz, a tone message signal of 2 kHz and a frequency deviation ∆F = 40 Hz givea block diagram for the generation of a WBFM signal with a carrier frequency of10 MHz and ∆F = 50kHz, showing the necessary frequency multipliers andfrequency converters (mixers).

3013S2L3 TELE3013: Lab 3 2

3. EXPERIMENTS

EQUIPMENT

MODULES QTY TRUNK SIGNALS

Audio Oscillator 1 Signal #1: Unknown Signal

Adder 2 Signal #2: Unknown Signal

Multiplier 2 Signal #3: Speech Signal

Voltage Controlled Oscillator (VCO) 2

Tuneable Low Pass Filter 1

3.1 Generation of Narrow–Band Frequency Modulation (NBFM)

The block diagram below shows how the TIMS system can be used to generate a NBFM signalgiven by equation (3) above.

Use a VCO module with its input grounded and its centre frequency set to 2 kHz as the messagesource. The quadrature outputs of the Audio Oscillator with its frequency set to about 10 kHzare used as the carrier source. Recall that this method will only work for small values of themodulation index β. For large values of β a combination AM/FM signal is obtained.

Observe and sketch the time domain waveform and amplitude spectrum of the NBFM signal.Observe and record the change resulting when in–phase carriers are used instead of quadraturecarriers. Draw phasor diagrams for the two cases.

3.2 WBFM generation using a Voltage Controlled Oscillator (VCO)

By definition a voltage controlled oscillator (VCO) is a frequency modulator. We now use theVCO module to investigate the properties of wideband FM.

Osc.(VCO)

AudioOsc.

βsinωmt

cosωct

sinωctmessage

NBFMsignal

addermultiplier

VCOAudioOsc.

message

FM signal

Centre freq. fc

carrier

3013S2L3 TELE3013: Lab 3 3

3.3 Characteristics of FM

3.3.1 Time Domain Waveform of Tone FM Signal

Set the VCO centre frequency to about 10 kHz and use the Audio Oscillator to modulate thisfrequency with a 1 kHz sine wave. Observe the time domain waveform – set the oscilloscope todisplay about ten carrier cycles. Note the effect of increasing the VCO sensitivity (gain) fromzero upwards.

Note: If the oscilloscope display is triggered on this waveform then the left most carrier cycleis ‘stationary’ more or less by definition. What is the next carrier cycle that isapproximately ‘stationary’ on the oscilloscope display? Vary the frequency of themodulating signal and see how this result changes. A tone modulated FM signal isdescribed by equation (2) which is repeated below

)tsintcos(A)t(s mcc ωωββωω ++==

A ‘stationary’ cycle corresponds to ωmt = nπ (n an integer), the maximum phasedeviation occurs when ωmt = (2n + 1)π/2 and successive peaks of the unmodulatedcarrier signal correspond to ωct = 2nπ. Triggering the FM signal at a certain level, theCRO displays a blurred signal with its maximum phase blur, Φ, corresponding to

ππ∆∆

φφ∆∆ΦΦ 2T

t4 ====

Here ∆φ =β is the peak phase deviation. ∆t is the maximum blur in time and T=2π /ωc

is the period of the carrier.

3.3.2 FM Signal Spectrum and Bandwidth

Using the time waveform set the VCO gain so that the peak (instantaneous) phase deviation ∆φ=β ~ 1 radian. What is the value of the modulation index β? Observe and sketch the amplitudespectrum of the of the FM signal. What is the measured bandwidth of the FM signal and howdoes it compare with the bandwidth predicted by Carson’s rule? Repeat the measurements ofpeak phase deviations ∆φ = 2.4, 3 and 3.8 radians. Draw up a table listing the modulation index,the measured FM signal bandwidth and the bandwidth predicted by Carson’s rule. Comment onthe validity of Carson’s rule.

Note: The FM signal in equation (2) can be expressed as a Fourier series,

t)ncos()(JA)t(s mn

cnc ωωωωββ ∑∑∞∞

−∞−∞==++==

where Jn(β) is an n-th order Bessel function of the first kind and it has therelation

J–n(ββ) = (–1)nJn(ββ).

You may find it instructive to use MATLAB to plot the values of a few Bessel functions, eg:

b = 0:0.1:10; {Modulation index β: 0 to 10 in 0.1 steps}

3013S2L3 TELE3013: Lab 3 4

j0 = besselj(0, b); {J0(β)}

j1 = besselj(1, b); {J1(β)}

j2 = besselj(2, b); {J2(β)}

plot ( b, [j0’ j1’ j2’] ), grid { J2’ means the transpose of J2}

What values of β give Jo(β) = 0?

3.4 FM Demodulation using a Phase–Locked Loop

Construct a first order Phase–Locked Loop (PLL) from a second VCO, a tuneable LPF and amultiplier, as shown in the following plot. Use this PLL to recover the message from the FMmodulated signal generated by the first VCO.

RecoveredMessage Multiplier

TuneableLowpassFilter

VCO

FM Signal

Phase Comparator

NOTE: You have initially to adjust the second VCO to obtain lock, i.e. you need toapproximately match the centre frequency and choose a reasonable value for thesensitivity. You may like to compare the analog level outputs of the two VCOs on youroscilloscope to observe when lock is obtained. Change the message frequency andcheck that the receiver recovers the message accurately. Drive the PLL just out oflock and note the transition time, Lock–No Lock–Lock.

3.5 Modulation and Demodulation using Speech Signals

Using the speech signal available from the trunk panel as your message, carry out FM modulationand demodulation as described in sections 3.2 and 3.4.

3.6 Recovery of Unknown FM Signals

There are two FM signals with unknown messages available from the trunks panel. Demodulatethese and identify the message signals.

Sketch and explain your strategies to demodulate the unknown FM signals.