TE 0224 ANALOG COMMUNICATION LAB. Laboratory Manual

Transcription

1 TE 0224 ANALOG COMMUNICATION LAB Laboratory Manual DEPARTMENT OF TELECOMMUNICATION ENGINEERING SRM UNIVERSITY S.R.M. NAGAR, KATTANKULATHUR FOR PRIVATE CIRCULATION ONLY ALL RIGHTS RESERVED

2 DEPARTMENT OF TELECOMMUNICATION ENGINEERING TE0224 ANALOG COMMUNICATION LAB ( ) Revision No: 2 Date: PREPARED BY, Mrs.Kavitha Narayanan Mrs.S.Murugaveni HOD/TCE

3 TEO224 ANALOG COMMUNICATION LAB List of Experiments 1. AM Modulation and Demodulation(Envelope Detector) 2. FM Modulation using PLL 3. Pulse Amplitude Modulation and Demodulation 4. Pre-emphasis and De-emphasis 5. Analog Multiplexing. 6. Study of FM detection 7. Amplitude Modulation using Pspice 8. AM Modulation using Matlab 9. FM Modulation using Matlab

4 AIM 1. AM MODULATOR & ENVELOPE DETECTOR To study the amplitude modulation and demodulation and to calculate the modulation index values for various modulating voltages APPARATUS REQUIRED 1. Transistor BC Resistors 3. Capacitors 4. AFO 5. CRO 6. Diode OA79 7. Millimeter 8. Regulated power supply 9. Breadboard and connecting wires THEORY Modulation is defined as the process by which some characteristics of a carrier signal is varied in accordance with a modulating signal. The base band signal is referred to as the modulating signal and the output of the modulation process is called as the modulation signal. Amplitude modulation is defined as the process in which is the amplitude of the carrier wave is varied about a means values linearly with the base band signal. The envelope of the modulating wave has the same shape as the base band signal provided the following two requirements are satisfied (1). the carrier frequency fc must be much greater then the highest frequency components fm of the message signal m (t) i.e. fc >> fm (II) The modulation index must be less than unity. if the modulation index is greater than unity, the carrier wave becomes over modulated. PROCEDURE 1. The circuit connection is made as shown in the circuit. 2. The power supply is connected to the collector of the transistor 3. Modulated Output is taken from the collector of the Transistor 4. Calculate Vmax and Vmin from the Output

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8 Vc = 63mv fc = 500Khz fm = 1Khz Modulating signal Vm(v) (V) Emax(V) Modulation index M = Emax-Emin x 100 Emax + Emin AM DETECTION THEORY: The process of detection provides a means of recovering the modulating Signal from modulating signal. Demodulation is the reverse process of modulation. The detector circuit is employed to separate the carrier wave and eliminate the side bands. Since the envelope of an AM wave has the same shape as the message, independent of the carrier frequency and phase, demodulation can be accomplished by extracting envelope. An increased time constant RC results in a marginal output follows the modulation envelope. A further increase in time constant the discharge curve become horizontal if the rate of modulation envelope during negative half cycle of the modulation voltage is faster than the rate of voltage RC combination,the output fails to follow the modulation resulting distorted output is called as diagonal clipping : this will occur even high modulation index. The depth of modulation at the detector output greater than unity and circuit impedance is less than circuit load (Rl > Zm) results in clipping of negative peaks of modulating signal. It is called negative clipping

9 PROCEDURE 1. T he circuit connection are made as shown in the circuit diagram. 2. The amplitude modulated signal from AM generator is give as input to the circuit. 3. The demodulated output is observed on the CRO 4. The various values modulating voltage signal frequency corresponding demodulated voltage and frequency are noted and the readings are tabulated. SAMPLE READING Fc = 500 KHz fm = 1 KHz Emin (v) Emax (V) Em(p-p) Modulation index M = Emax-Emin x 100 Emax + Emin RESULT: Thus the amplitude modulation and demodulation circuit were designed and the modulation index for various modulating voltage were calculated.

10 REVIEW QUESTIONS 1. Define Modulation. 2. What is modulation index? 3. Differentiate under modulation & over modulation. 4. List the advantages of AM modulation. 5. What are the different AM modulations Techniques? 6. What is detector? 7. When Diagonal clipping and Negative clipping occur in demodulation and how it is overcome?

11 AIM: 2. FREQUENCY MODULATION To generate a frequency modulated wave-using IC 566 APPARATUS REQUIRED 1. AFO 2. IC NE Resistors 4. Capacitor 5. CRO 6. Bread board and connection 7. RPS THEORY: Frequency modulation is a process of changing the frequency of a carrier wave in accordance with the slowly varying base band signal. The main advantage of this modulation is that it can provide better discrimination against noise. FREQUENCY MODULATION USING IC 566 A VCO is a circuit that provides an oscillating signal whose frequency can be adjusted over a control by Dc voltage. VCO can generate both square and triangular Wave signal whose frequency is set by an external capacitor and resistor and then varied by an applied DC voltage. IC 566 contains a current source to charge and discharge an external capacitor C1 at a rate set by an external resistor. R1 and a modulating DC output voltage. The Schmitt trigger circuit present in the IC is used to switch the current source between charge and discharge capacitor and triangular voltage developed across the capacitor and the square wave from the Schmitt trigger are provide as the output of the buffer amplifier. The R2 and R3 combination is a voltage divider, the voltage VC must be in the range ¾ VCC < VC < VCC. The modulating voltage must be less than ¾ VCC the frequency Fc can be calculated using the formula Fo = 2 (Vcc-Vc) R1 C1 Vcc For a fixed value of Vc and a constant C1 the frequency can be varied at 10:1 similarly for a constant R! C1 product value the frequency modulation can be done at 10:1 ratio

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14 FORMULA: Modulation index: β = f/fm where f = Fmax Fmin /2 PROCEDURE: 1. The circuit connection is made as shown in the circuit diagram. 2. The modulating signal FM is given from an AFO (1KHZ) 3. For various values of modulating voltage Vm the values of Fmax and Fmin are noted 4. The values of the modulation index are calculated. SAMPLE READING V m T min T max F max F min Modulation Index Β = / f / fm , RESULTS: The FM circuit using IC566 was designed and the modulation index for practical and Theoretical.

15 REVIEW QUESTIONS 1. Define Frequency Modulation. 2. What is Frequency deviation? 3. Differentiate under modulation & over modulation. 4. List the advantages of FM modulation over AM modulation. 5. What are the different AM modulations Techniques? 6. What is detector? 7. When Diagonal clipping and Negative clipping occur in demodulation and how it is overcome?

16 3. PULSE AMPLITUDE MODULATION & DEMODULATION AIM: To study and obtain pulse amplitude modulation and demodulation APPARATUS REQUIRED 1. Transistor 2. AFO 3. IC NE Resistors 5. Capacitor 5. CRO 6. RPS THEORY: Pulse amplitude modulation is a scheme, which alters the amplitude of regularly spaced rectangular pulses in accordance with the instantaneous values of a continuous message signal. Then amplitude of the modulated pulses represents the amplitude of the intelligence. A train of very short pulses of constant amplitude and fast repetition rate is chosen the amplitude of these pulse is made to vary in accordance with that of a slower modulating signal the result is that of multiplying the train by the modulating signal the envelope of the pulse height corresponds to the modulating wave.the Pam wave contain upper and lower side band frequencies.besides the modulating and pulse signals. The demodulated PAM waves, the signal is passed through a low pass filter having a cut off frequencies equal to the highest frequency in the modulating signal. At the output of the filter is available the modulating signal along with the DC component PAM has the same signal to noise ratio as AM and so it is not employed in practical circuits PROCEDURE: MODULATION

17 1. Make the circuit as shown in circuit diagram fig A 2. Set the pulse generated s output to be 41vpp at 100HZ 3. Set AFO s output at 2 vpp 100HZ 4. Observe the output wave form on a CRO 5. Tabulate the reading.

18 DEMODULATION: 1. Connect the circuit as shown in fig (b) 2. Given the modulated output with AFO used to the input of the circuit. 3. Vary the potentiometer so that modulating signal is obtained. 4. Measure the amplitude of the signal and verify with that of the input.

19 SAMPLE READING: PAM Modulating voltage Vm (V) Pulse Amplitude modulation (V) SAMPLE READING: DEMODULATION Modulating voltage Vm (V) Pulse Amplitude demodulation (V) RESULT: The pulse amplitude modulation circuit is circuit assembled and studied and demodulated wave also done.

20 AIM: 4. PRE EMPHASIS AND DE-EMPHASIS CIRCUITS To study and test the chateristics of pre-emphasis and de-emphasis circuits APPARATUS REQUIRED 1. Transistor 2. AFO 3. IC NE Resistors 5. Capacitor 5. CRO 6. RPS THEORY: PRE-EMPHASIS CIRCUITS The circuits are the transmitting side of the frequency modulator. It is used to increase the gain of the higher frequency component as the input signal frequency increased, the impendence of the collector voltage increase. If the signal frequency is lesser then the impendence decrease which increase the collector current and hence decrease the voltage. DE-EMPHASIS CIRCUITS: The circuit is placed at the receiving side. It acts as allow pass filter. The boosting gain for higher frequency signal in the transmitting side is done by the pre-emphasis circuit is filtered to the same value by the low pass filter. The cut off frequency is given by the formula Fc = 1/2π RC

21 Where R = 2 π fc L DESIGN FORMULA: Fc = 1/2 π R C (assume =R = 10 KΩ, C = 0.01μf) R = 2 π fc L; L = R/2 π fc

22 PROCEDURE: 1. The circuit connection are made as shown in the circuit diagram for the preemphasis and de-emphasis circuits 2. A power supply of 10V is given to the circuit

23 3. For a constant value of input voltage the values of the frequency is varied and the output is noted on the CRO 4. A graph is plotted between gain and frequency 5. The cut frequencies are practical values of the values of cut off frequency \are found, compared and verified. SAMPLE READING Pre emphasis De emphasis Frequency Vo (v) Gain (db) Vo (v) Gain (db) RESULTS: The characteristics of pre emphasis and de emphasis circuits were studied and a graphs was drawn between gain (in db) and frequency and fc was found.

24 5. ANALOG MULTIPLEXING TIME DIVISION MULTIPLEXING AIM: To perform time division multiplexing and de- multiplexing using PAM signals. APPARATUS REQUIRED: 1. TDM Trainer Kit ST CRO 3. Patch Chords 4. Probes THEORY: An important feature of pulse-amplitude modulation is a conservation of time. That is, for a given message signal, transmission of the associated PAM wave engages the communication channel for only a fraction of the sampling interval on a periodic basis. Hence, some of the time interval between adjacent pulses of the PAM wave is cleared fro use by the other independent message signals on a time shared basis. By so doing, we obtain a time division multiplex system (TDM), which enables the joint utilization of a common channel by a plurality of independent message signals without mutual interference. Each input message signal is first restricted in bandwidth by a low- pass pre-alias filter to remove the frequencies that are nonessential to an adequate signal representation. The pre-alias filter outputs are then applied to commutator, which is usually implemented using electronic switching circuitry. The function of the commutator is two-fold: (1) to take a narrow sample of each of the N input messages at a rate f that is slightly higher

25 than 2 wave, where W are the cutoff frequencies of the pre-alias filter, and (2) to sequentially interleave these N samples inside a sampling interval Ts = 1/fs. Indeed, this latter function is the essence of the time division multiplexing operation.following the commutation process, the multiplexed signal is applied to a pulse amplitude modulator, The purpose of which is to transform the multiplexed signal into a form suitable for transmission over the communication channel. At the receiving end of the system, the received signal is applied to a pulse amplitude demodulator, which performs the reverse operation of the pulse amplitude modulator. The short pulses produced at the pulse demodulator output are distributed to the appropriate low-pass reconstruction filters by means of a decommutator, which operates in synchronism with the commutator in the transmitter. This synchronization is essential for satisfactory operation of the TDM system, and provisions have to be made for it PROCEDURE: 1. Take the inputs from the function generator and give it to the channel in the transmitter (Ch0..Ch3)using a patch chords 2. Note down the amplitude and time period of each signal that is available in (Ch0...Ch3). 3. Measure the voltage and time period at the transmitter output. 4. Using a patch chord, connect transmitter output to receiver input. 5. For synchronization purpose, connect the transmitter clock and receiver clock and also Txch0 and Rx0. 6. See the output before the filter and the filter for all the channels connected.

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30 RESULTS: Time division multiplexing and de-multiplexing using PAM signals was performed and respect ion forms were plotted.

31 6. STUDY OF FM DEMODULATION In fm demodulators, the intelligence to be recovered is not in amplitude variations; it is in the variation of the instantaneous frequency of the carrier, either above or below the center frequency. The detecting device must be constructed so that its output amplitude will vary linearly according to the instantaneous frequency of the incoming signal. Several types of fm detectors have been developed and are in use, but in this section we will study two of the most common: (1) the slope detector, (2) Foster-seeley discriminator. SLOPE DETECTION To be able to understand the principles of operation for fm detectors, you need to first study the simplest form of frequency-modulation detector, the SLOPE DETECTOR. The slope detector is essentially a tank circuit which is tuned to a frequency either slightly above or below the fm carrier frequency. View (a) of figure (a)is a plot of voltage versus frequency for a tank circuit. The resonant frequency of the tank is the frequency at point 4. Components are selected so that the resonant frequency is higher than the frequency of the fm carrier signal at point 2. The entire frequency deviation for the fm signal falls on the lower slope of the band pass curve between points 1 and 3. As the fm signal is applied to the tank circuit in view (b), the output amplitude of the signal varies as its frequency swings closer to, or further from, the resonant frequency of the tank. Frequency variations will still be present in this waveform, but it will also develop amplitude variations, as shown in view (b). This is because of the response of the tank circuit as it varies with the input frequency. This signal is then applied to the diode detector in view (c) and the detected waveform is the output. This circuit has the major disadvantage that any amplitude variations in the RF waveform will pass through the tank circuit and be detected. This disadvantage can be eliminated by placing a limiter circuit before the tank input. This circuit is basically the same as an AM detector with the tank tuned to a higher or lower frequency than the received carrier. Figure (a) - Slope detector. VOLTAGE VERSUS FREQUENCY PLOT

32 Figure (b) - Slope detector. TANK CIRCUIT Figure (c) - Slope detector. DIODE DETECTOR FOSTER-SEELEY DISCRIMINATOR The FOSTER-SEELEY DISCRIMINATOR is also known as the PHASE-SHIFT DISCRIMINATOR. It uses a double-tuned RF transformer to convert frequency variations in the received fm signal to amplitude variations. These amplitude variations are then rectified and filtered to provide a dc output voltage. This voltage varies in both amplitude and polarity as the input signal varies in frequency. A typical discriminator response curve is shown in figure (d). The output voltage is 0 when the input frequency is equal to the carrier frequency (f r ). When the input frequency rises above the center

33 frequency, the output increases in the positive direction. When the input frequency drops below the center frequency, the output increases in the negative direction. Figure (d) - Discriminator response curve. The output of the Foster-Seeley discriminator is affected not only by the input frequency, but also to a certain extent by the input amplitude. Therefore, using limiter stages before the detector is necessary. CIRCUIT OPERATION OF A FOSTER-SEELEY DISCRIMINATOR Figure (e) shows a typical Foster-Seeley discriminator. The collector circuit of the preceding limiter/amplifier circuit (Q1) is shown. The limiter/amplifier circuit is a special amplifier circuit which limits the amplitude of the signal. This limiting keeps interfering noise low by removing excessive amplitude variations from signals. The collector circuit tank consists of C1 and L1. C2 and L2 form the secondary tank circuit. Both tank circuits are tuned to the center frequency of the incoming fm signal. Choke L3 is the dc return path for diode rectifiers CR1 and CR2. R1 and R2 are not always necessary but are usually used when the back (reverse bias) resistance of the two diodes is different. Resistors R3 and R4 are the load resistors and are bypassed by C3 and C4 to remove RF. C5 is the output coupling capacitor. Figure (e) - Foster-Seeley discriminator.

34 CIRCUIT OPERATION AT RESONANCE The operation of the Foster-Seeley discriminator can best be explained using vector diagrams figure (e), view (B) that show phase relationships between the voltages and currents in the circuit. Let's look at the phase relationships when the input frequency is equal to the center frequency of the resonant tank circuit. The input signal applied to the primary tank circuit is shown as vector e p. Since coupling capacitor C8 has negligible reactance at the input frequency, RF choke L3 is effectively in parallel with the primary tank circuit. Also, because L3 is effectively in parallel with the primary tank circuit, input voltage e p also appears across L3. With voltage e p applied to the primary of T1, a voltage is induced in the secondary which causes current to flow in the secondary tank circuit. When the input frequency is equal to the center frequency, the tank is at resonance and acts resistive. Current and voltage are in phase in a resistance circuit, as shown by i s and e p. The current flowing in the tank causes voltage drops across each half of the balanced secondary winding of transformer T1. These voltage drops are of equal amplitude and opposite polarity with respect to the center tap of the winding. Because the winding is inductive, the voltage across it is 90 degrees out of phase with the current through it. Because of the center-tap arrangement,

35 the voltages at each end of the secondary winding of T1 are 180 degrees out of phase and are shown as e 1 and e 2 on the vector diagram. The voltage applied to the anode of CR1 is the vector sum of voltages e p and e 1, shown as e 3 on the diagram. Likewise, the voltage applied to the anode of CR2 is the vector sum of voltages e p and e 2, shown as e 4 on the diagram. At resonance e 3 and e 4 are equal, as shown by vectors of the same length. Equal anode voltages on diodes CR1 and CR2 produce equal currents and, with equal load resistors, equal and opposite voltages will be developed across R3 and R4. The output is taken across R3 and R4 and will be 0 at resonance since these voltages are equal and of appositive polarity. The diodes conduct on opposite half cycles of the input waveform and produce a series of dc pulses at the RF rate. This RF ripple is filtered out by capacitors C3 and C4. OPERATION ABOVE RESONANCE A phase shift occurs when an input frequency higher than the center frequency is applied to the discriminator circuit and the current and voltage phase relationships change. When a series-tuned circuit operates at a frequency above resonance, the inductive reactance of the coil increases and the capacitive reactance of the capacitor decreases. Above resonance the tank circuit acts like an inductor. Secondary current lags the primary tank voltage, e p. Notice that secondary voltages e 1 and e 2 are still 180 degrees out of phase with the current (i S ) that produces them. The change to a lagging secondary current rotates the vectors in a clockwise direction. This causes el to become more in phase with e p while e 2 is shifted further out of phase with e p. The vector sum of e p and e 2 is less than that of e p and e 1. Above the center frequency, diode CR1 conducts more than diode CR2. Because of this heavier conduction, the voltage developed across R3 is greater than the voltage developed across R4; the output voltage is positive. OPERATION BELOW RESONANCE When the input frequency is lower than the center frequency, the current and voltage phase relationships change. When the tuned circuit is operated at a frequency lower than resonance, the capacitive reactance increases and the inductive reactance decreases. Below resonance the tank acts like a capacitor and the secondary current leads primary tank voltage e p. This change to a leading secondary current rotates the vectors in

36 a counterclockwise direction. From the vector diagram you should see that e 2 is brought nearer in phase with e p, while el is shifted further out of phase with e p. The vector sum of e p and e 2 is larger than that of e p and e 1. Diode CR2 conducts more than diode CR1 below the center frequency. The voltage drop across R4 is larger than that across R3 and the output across both is negative. DISADVANTAGES These voltage outputs can be plotted to show the response curve of the discriminator discussed earlier (figure (d)). When weak AM signals (too small in amplitude to reach the circuit limiting level) pass through the limiter stages, they can appear in the output. These unwanted amplitude variations will cause primary voltage e p [view (A) of figure (e)] to fluctuate with the modulation and to induce a similar voltage in the secondary of T1. Since the diodes are connected as half-wave rectifiers, these small AM signals will be detected as they would be in a diode detector and will appear in the output. This unwanted AM interference is cancelled out in the ratio detector and is the main disadvantage of the Foster-Seeley circuit.

37 DESCRIPTION: 7. AM MODULATOR USING PSPICE This circuit uses two signal generators to simulate an Amplitude Modulated RF carrier wave. The output can be used to simulate the response of LC and tank circuits. Two signal generators are used in this circuit, one representing a high frequency (200 khz) RF carrier, VG2; the other signal generator is used to inject a 1 KHz audio signal. The two signals are mixed and amplified by the transistor and an amplitude modulated signal appears at the collector of the T1 (2N 2222). The DC component is removed by C2 and R3 and the RF output now appears across the load resistor R3.

38 SPICE NETLIST: The spice net list is shown below. Copy all lines between *AM and.end and paste into a new text file called Vmod.circuit or similar. Vcc VG2 2 0 DC 0 AC 1 0 SIN (0 10M 200K ) VG1 4 0 DC 0 AC 1 0 SIN ( 0 5 1K ) C N C P C N R K R K R K R K R K QT Q2N2222. LIB EVAL.LIB.

39 .TRAN 2us 10 ms..probe.end To produce an output in Spice Opus start the program and load the new Vmod.cir the modulated signal appears across R3 which is now node 3 and earth. After loading the circuit the command "listing" will display the net list. The command "run" will then simulate the circuit; "display" will print a list of all variables in the circuit. The command plot v(3) will display the AM wave between node 3 and 0 i.e. the load resistor R3. Note to speed up simulation, the RF carrier has been limited to 200KHz only, and the output waveform just shows two complete cycles of the audio wave, i.e. 2ms as the modulating frequency is 1k. RESULT: Thus Amplitude Modulation using Pspice was generated.

40 AIM: 8. AMPLITUDE MODULATION To generate the waveform for Amplitude modulation using Mat lab Simulation. THEORY: In Amplitude Modulation or AM, the carrier signal Has its amplitude Modulated in proportion to the message bearing (lower frequency) signal To give The magnitude of Is chosen to be less than or equal to 1, from reasons having to do with demodulation, i.e. recovery of the signal From the received signal. The modulation index is then defined to be Figures 1 and 2 are some mat lab plots of what the modulated signal looks like for. The frequency of the modulating signal is chosen to be much smaller than that of the carrier signal. Try to think of what would happen if the modulating index were bigger than 1.

41 Figure 1: AM modulation with modulation index.2 Note that the AM signal is of the form This has frequency components at frequencies. Figure 2: AM modulation index.4 Matlab code for modulation with

42 PROGRAM: t=0:0.001:1; vd=8*cos(2*pi*5*t); vc=0.1*cos(2*pi*15*t); ft=vc.*vd; am=ft+vc; figure(1) plot(t,vd); figure(2) plot(t,vc); figure(3) plot(t,am);

43 Carrier signal Original singal(informationsignal) Amplitude Modulated signal

44 The AM waveform in time and frequency domain. fm=20hz,fc=500hz,vm=1v,vc=1v,t=0: : fm=20; fc=500; vm=1; vc=1; interval=0.001; % x-axis:time(second) t=0: : ; f=0:1:9999; % y-axis:voltage(volt) wc=2*pi*fc; wm=2*pi*fm; V1=vc+vm*sin(wm*t); V2=-(vc+vm*sin(wm*t)); Vm=vm*sin(wm*t); Vc=vc*sin(wc*t); Vam=(1+sin(wm*t)).*(sin(wc*t)); Vf=abs(fft(Vam,10000))/10000; % Plot figure in time domain figure; plot(t,vam); hold on; plot(t,v1,'r'),plot(t,v2,'r'); title('am waveform time-domain'); xlabel('time'), ylabel('amplitude'); grid on; % Plot figure in frequency domain figure; plot(f*10,vf);

45 axis([(fc-2*fm) (fc+2*fm) 0 0.6]); title('am waveform frequency-domain'); xlabel('frequency'), ylabel('amplitude'); grid on; %Plot modulating signal figure; plot(t,vm); title('am modulating signal'); xlabel('time'), ylabel('amplitude'); grid on; %Plot carrier signal figure; plot(t, Vc); title('am carrier signal'); xlabel('time'), ylabel('amplitude'); grid on; clear; Result: Thus the waveform for Amplitude Modulation is generated using Mat lab

46 AIM: 9. FREQUENCY MODULATION To generate the waveform for frequency modulation using Matlab Simulation. THEORY: Frequency modulation uses the information signal, V m (t) to vary the carrier frequency within some small range about its original value. Here are the three signals in mathematical form Information: V m (t) Carrier: V c (t) = V co sin ( 2 π f c t + φ ) FM: V FM (t) = V co sin (2 π [f c + (Δf/V mo ) V m (t) ] t + φ) We have replaced the carrier frequency term, with a time-varying frequency. We have also introduced a new term: Δf, the peak frequency deviation. In this form, you should be able to see that the carrier frequency term: f c + (Δf/V mo ) V m (t) now varies between the extremes of f c - Δf and f c + Δf. The interpretation of Δf becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the "swing" in the frequency. We can also define a modulation index for FM, analogous to AM: β = Δf/f m, where f m is the maximum modulating frequency used. The simplest interpretation of the modulation index, β, is as a measure of the peak frequency deviation, Δf. In other words, β represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, f m, i.e. Δf = β f m. Example: suppose in FM radio that the audio signal to be transmitted ranges from 20 to 15,000 Hz (it does). If the FM system used a maximum modulating index, β, of 5.0, then the frequency would "swing" by a maximum of 5 x 15 khz = 75 khz above and below the carrier frequency. Here is a simple FM signal:

47 Here, the carrier is at 30 Hz, and the modulating frequency is 5 Hz. The modulation index is about 3, making the peak frequency deviation about 15 Hz. That means the frequency will vary somewhere between 15 and 45 Hz. How fast the cycle is completed is a function of the modulating frequency. PROGRAM: The frequency modulation (FM) waveform in time and frequency domain. fm=250hz,fc=5khz,vm=1v,vc=1v,m=10,t=0: : % setting vc=1; vm=1; fm=250; fc=5000; m=10; % x-axis: Time(second) t=0: : ; f=0:10:99990; % y-axis: Voltage(volt) wc=2*pi*fc; wm=2*pi*fm; sc_t=vc*cos(wc*t); sm_t=vm*cos(wm*t); kf=1000;

48 s_fm=vc*cos((wc*t)+10*sin(wm*t)); vf=abs(fft(s_fm,10^4))/5000; % Plot figure in time domain figure; plot(t,s_fm); hold on; plot(t,sm_t,'r'); axis([ ]); xlabel('time(second)'),ylabel('amplitude'); title('fm time-domain'); grid on; % Plot figure in frequency domain figure; plot(f,vf); axis([ 0 10^ ]); xlabel('frequency'), ylabel('amplitude'); title('fm frequency-domain'); grid on; %Plot modulating signal figure; plot(t,sm_t); axis([ ]); title('fm modulating signal'); RESULT: Thus the waveform for frequency Modulation is generated using Mat lab