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FREQUENCY MODULATION

OBJECTIVE: To plot the modulation characteristic of varactor modulator. To calculate the modulation sensitivity of varactor modulator.

To observe and measure frequency deviation and modulation index of FM. To study frequency modulation using reactance modulator and measure

the frequency deviation.

EQUIPMENT: ACL-03 Kit. Power supply. E-lab. Connective links. Frequency meter.

THEORY:

FREQUENCY MODULATION:It is a type of modulation in which the frequency of the high frequency (Carrier) isvaried in accordance with the instantaneous value of the modulating signal.

MAIN ASPECTS:Consider a sine wave signal vm(t) with pulse w FIG-1.

vm(t) = B sin(Wt)and another sine wave vc(t) with upper W pulse:

vc(t) = A sin(Wt)

The signal vm(t) is called modulating signal, the signal vc(t) is called carriersignal.Vary the frequency of the carrier vc(t) in a way proportional to the amplitude ofthe modulating signal vm(t). You obtain a vm(t) frequency modulated diagonal,which can be expressed by the relation:

vm(t) = A sin [q(t)]with q(t) instantaneous angle function of vm(t).

MATHEMATICAL EXPRESSION OF THE FREQUENCY MODULATEDSIGNAL:

The instantaneous pulse W(t) of the FM signal, by definition, isW(t) = W + K vm(t)

with W= carrier pulseK= modulation sensitivity

The instantaneous angle W(t) to be used as subject of the sine to obtain themathematical operation of the FM signal, is detected by integrating W(t):

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(t) =Integral [W(t) dt]

In the case of modulating sine wave signal [vm (t) = B.sin (W.t)], q (t) it results:

q(t) = W(t) (KB/w) cos(wt)

The expression of the frequency modulated signal vm (t) becomes:

vm(t) = A sin[W (t)- (KB/w) cos(wt)]

FREQUENCY DEVIATION DF AND MODULATION INDEX MF:

The instantaneous frequency F(t) of the carrier modulated by a sine wave,results:

F(t) = W(t)/2p= W2p + KBsin(wt)

and oscillates between a minimum Fmin and a maximum value Fmax:Fmin = W/(2p) - (KB)/(2p)Fmax = W/(2p) + (KB)/(2p)

The frequency deviation DF represents the maximum shift between themodulated signal frequency, over and under the frequency of the carrier:

DF = (Fmax Fmin)/2We define modulation index mf as the ratio between DF and the modulatingfrequency f:

mf = DF/f

FREQUENCY MODULATION GENERATION:The circuits used to generate a frequency modulation must vary the frequency ofa high frequency signal (carrier) as function of the amplitude of a low frequencysignal (modulating signal). In practice, there are two main methods used togenerate the FM:

DIRECT METHOD:An oscilloscope is used in which the reactance of one of the elements of theresonant circuit depends on the modulating voltage. The most common devicewith variable reactance is the Varactor or Varicap, which is a particular diodewhose capacity varies as a function of the reverse bias voltage. The frequency ofthe carrier is established with AFC circuits (Automatic Frequency Control) or PLL(Phase Locked Loop).

INDIRECT METHOD:

In this case, FM is done by Phase Modulation, after the modulating signal hasbeen integrated. In the phase modulator the carrier can be generated by a quartzoscillator and so its frequency stabilization is easier.In the circuit used for the exercise, the frequency modulation is generated by a

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Hartley oscillator, whose frequency is determined by a fixed inductance and by acapacitance (variable) supplied by Varicap diodes.

THE ADVANTAGES OF FM:There are three advantages of frequency modulation for a communication

system.

1.We saw that the information signal controls the frequency of the carrier but hasno effect on its amplitude. Now, when any transmission is affected by electricalnoise, the noise signal is superimposed on the transmitted signal. In an AMsystem, the demodulator is designed to respond to changes in amplitude of thereceived signal but in an FM receiver, the demodulator is only watching forchanges in frequency and therefore ignores any changes in amplitude. Electricalnoise thus has little or no effect on an FM communication system.

2. The bandwidth of the FM signal is very wide compared to an AM transmission.

Typical broadcast bandwidths are in the order of 250kHz. This allows a muchbetter sound quality, so signals like music sound significantly better if frequencymodulation is being used.

3. When an FM demodulator is receiving an FM signal, it follows the variations infrequency of the incoming signal and is said to lock on to the receivedtransmission. This has a great advantage when two transmissions are receivedat the same time. The receiver locks on to the stronger of the two signals andignores the other. This is called the captured effect and it means that we canlisten to an FM station on a radio without interference from other stations.

THE DISADVANTAGE OF FM:This is the wide bandwidth of the transmission.The medium frequency broadcast band extends from about 550kHz to 1,600kHzand therefore only a little over 1MHz in width. If we tried to use FM using abandwidth 250kHz for each station, it would mean that no more than four stationscould be accommodated. This wide bandwidth forces us to use higher carrierfrequencies, usually in the VHF band, which extends from about 85MHz to110MHz. This is a width of 25MHz and would hold many more stations.

THE BANDWIDTH OF AN FM SIGNAL:The frequency modulation process generates a large number of sidefrequencies. Theoretically, the sidebands are infinitely wide with the power levelsbecoming lower and lower as we move away from the carrier frequency. Thebandwidth of 250kHz was chosen as a convenient value to ensure a low value ofdistortion in the received signal while allowing many stations to beaccommodated in the VHF broadcast band.

Communication signals, which do not require the high quality, associated withbroadcast stations can adopt a narrower bandwidth, to enable more

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transmissions within their allotted frequency band. Marine communications forship to shop communications, for example, use a bandwidth of only 25kHz butthis is only for speech and the quality is not important.These bandwidth figures bear no easy relationship with the frequency of theinformation signal or with the frequency deviation or anything else. FM is unlike

AM in this respect.

AN FM TRANSMITTER:The audio oscillator supplies the information signal and could, if we wish, bereplaced by a microphone and AF amplifier to provide speech and music insteadof the sinewave signals that we are using with ACL-03.The FM modulator is used to combine the carrier wave and the informationsignal in the same way as in the AM transmitter. The only difference in this caseis that the generation of the carrier wave and the modulation process is carriedout in the same block. It doesnt have to be, but in our case, it is.

The only real difference between the AM and FM transmitters are themodulators, so we are only going to consider this part of the transmitter.

We are going to investigate three types ofmodulator, they are called theVARACTOR MODULATOR, REACTANCE MODULATOR and the FM isobtained in this case by a Phase Modulation.

THE VARICAP DIODE:The Varicap (or Varactor) is a diode whose terminals are supplied with a capacitydepending on the applied reverse voltage.The symbol and the equivalent circuitof the varicap diode are shown in FIG.4, where: Cj = junction capacity Rs= series resistance (it drops as the applied reverse voltage increases)The junction capacity Cj depends on the reverse voltage VR applied to the diode,according to the relation:Cj = C0 (1 + VR)/VD X hwhere:VR = reverse voltage applied to VaricapC0 = junction capacity for VR=0VD = junction potential (0.6 V in the silicon diodes)h = it depends on the manufacturing process; it ranges between 0.3 and0.6approx.The factor of merit Q of the diode is expressed by:Q = 1/(wCj Rs)The factor of merit Q of the diode is expressed by :Q=1/wCjRs).FIG.5 shows the capacity/ VR and merit factor/ VR curves of the Varicapdiode used in the FM modulator.

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BLOCK DIAGRAM FOR STUDY OF VARACTOR MODULATOR

SF1

OFF

ON

1

SWITCH FAULTS SELECTION SWITCH

2 3 4

( ACL-03 )

P5 P6

LEVELFREQ.

FM MODULATOR

400KHz-1500KHz 0-2Vpp

500KHz 1500KHz

VF

RF/FM

OUT

SW2

MOD IN

PROCEDURE: Refer to the block diagram & Carry out the following connections and

settings. Connect the power supply with proper polarity to the kit ACL-03 and

switch it on. Keep all Switch Faults in OFF position. Keep switch SW2 at 1500KHz position.

Using pot P5 keep frequency at minimum and using pot P6 keepamplitude at 2Vpp.

Connect the oscilloscope and frequency meter to the output of themodulator FM/RF OUT.

Connect the voltmeter to the cursor of the frequency regulationpotentiometer post Vf below SW2.

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Vary the voltage in steps of 0.5 Volt and fill a table with the voltage valuesand the corresponding frequencies.

Plot a graph with the measured voltage and frequency values.

From the analysis of the curve you can note that some segments havenot a linear behavior, while if you consider the whole characteristic youfind a high non-linearity.

MODULATION SENSITIVITY OF VARACTOR MODULATOR:

Consider the modulator operation in the segment of curve within 700 to1300 KHz, with central frequency of 1000 KHz. From the analysis of thecurve it is possible to calculate the modulation sensitivity of the modulator.

The modulation sensitivity S is defined as:S= dF(v)/dvWhere F(v) is the instantaneous frequency function of the modulatingvoltage v. The last relation can be approximated writing the incrementalratio: S= DF/DVDF= 50kHz V = 125 mV from which: So = 50/125 = 0.4 KHz/ mv.