NATIONAL COLLEGE OF SCIENCE AND TECHNOLOGY Amafel Bldg. Aguinaldo Highway Dasmariñas City, Cavite ASSIGNMENT # 3 “FREQUENCY MODULATION”Cauan, Sarah Krystelle P. July 11, 2011Communications 1 / BSECE 41A1 Score: Eng‟r. Grace Ramones Instructor
FREQUENCY MODULATIONFrequency Modulation Principles While changing the amplitude of a radio signal is the most obvious method to modulateit, it is by no means the only way. It is also possible to change the frequency of a signal to givefrequency modulation or FM. Frequency modulation is widely used on frequencies above 30MHz, and it is particularly well known for its use for VHF FM broadcasting. In FM, the carrier amplitude remains constant, while the carrier frequency is changed bythe modulating signal. As the amplitude of the information signal varies, the carrier frequencywill shift in proportion. As the modulating signal amplitude increases, the carrier frequencyincreases. If the amplitude of the modulating signal, decreases the carrier frequency decreases.The reverse relationship can also be implemented. A decreasing modulating signal will increasethe carrier frequency above its center value, whereas an increasing modulating signal amplitudevaries, the carrier frequency varies above and below its normal center frequency with nomodulation. The amount of change in carrier frequency produced by the modulating signal isknown as the frequency deviation. Maximum frequency deviation occurs at the maximumamplitude of the modulating signal. The frequency of the modulating signal determines how many times per second thecarrier frequency deviates above and below its nominal center frequency. If the modulatingsignal is 100-Hz sine wave, then the carrier frequency will shift above and below the centerfrequency 100 times per second. This is called the frequency deviation rate. An FM signal is illustrated in Figure 1. With no modulating signal applied, the carrierfrequency is a constant-amplitude sine wave at its normal constant center frequency. The modulating information signal is a low-frequency sine wave. As the sine wave goespositive, the frequency of the carrier increases proportionately. The highest frequency occurs atthe peak amplitude of the modulating signal. As the modulating signal amplitude decreases, thecarrier frequency decreases. When the modulating signal is zero amplitude, the carrier will be atits center frequency point.
Now when the modulating signal goes negative, the carrier frequency will decrease. Thecarrier frequency will continue to decrease until the peak of the negative half cycle of themodulating sine wave is reached. Then, as the modulating signal increases toward zero, thefrequency will again increase. Note in Figure 1 how the carrier sine waves seem to be first“compressed” and then “stretched” by the modulating signal. a) b) c) Figure 1 The principle of frequency modulation: (a) carrier signal, (b) modulating signal (c) Modulated signal (Frequency Modulation)
Phase Modulation Another way to produce angle modulation is to vary the amount of phase shift of aconstant frequency carrier in accordance with a modulating signal. The resulting output is a PMsignal. Imagine a modulator circuit whose basic function is to produce a phase shift. Rememberthat a phase shift refers to a time separation between two sine waves of the same frequency.Assume that we can build a phase shifter that causes the amount of phase shift to vary with theamplitude of the modulating signal. The greater the amplitude of the modulating signals, thegreater the phase shifts. Assume further that positive alternations of the modulating signalproduce a lagging phase shift and negative signals produce a leading phase shift. If a constant-amplitude frequency carrier sine wave is applied to the phase shifter, theoutput of the phase shifter will be a PM wave. As the modulating signal goes positive, theamount of phase lag increase with the amplitude modulating signal. This means that the carrieroutput is delayed. That delay increases with the amplitude of the modulating signal. The result atthe output is as if the constant-frequency carrier signal had been stretched out or its frequencylowered. When the modulating signal goes negative, the phase shift becomes leading. This causesthe carrier sine wave to be effectively speeded up or compressed. The result is as if the carrierfrequency had been increased. Phase modulation produces frequency modulation. Since the amount of phase shift isvarying, the effect is as is the carrier frequency is changed. Since FM is produced by PM, thelater is often referred to as indirect FM. It is important to point out that it is the dynamic nature of the modulating that causes thefrequency variation at the output of the phase shifter. In other words, FM is only reduced as longas the phase shift is being varied. In FM, maximum deviation occurs at the peak positive and negative amplitudes of themodulating signal. In PM, the maximum amount of leading ang lagging shift occurs at the peakamplitude of the modulating signal. The faster the modulating signal voltage varies the greaterthe frequency deviation produced. Because of this, the frequency deviation produced in PMincreases with the frequency of the modulating signal. The higher the modulating signalfrequency, naturally the shorter its period and the faster the voltage changes. Higher modulatingvoltages produce greater frequency deviation. However, higher modulating frequencies producea faster rate of change of modulating voltage and, therefore, also produce greater frequencydeviation.
Deviation When the audio signal is modulated onto the radio frequency carrier, the new radiofrequency signal moves up and down in frequency. The amount by which the signal moves upand down is important. It is known as the deviation and is normally quoted as the number ofkilohertz deviation. As an example the signal may have a deviation of ±3 kHz. In this case thecarrier is made to move up and down by 3 kHz. Assume a carrier frequency of 50 MHz .if the peak amplitude of the modulating signalcauses a maximum frequency shift of 200 kHz, the carrier frequency will deviate up to 50.2 MHzand down to 59.8 MHz. The total frequency deviation is 50.2 – 49.8 = 0.4 MHz = 400 kHz. Inpractice, however, the frequency deviation is expressed as the amount of frequency shift of thecarrier above or below the center frequency. Therefore, the frequency deviation in the exampleabove is said to be 200 kHz. This means that the modulating signal varies the carrier above andbelow its center frequency to 200 kHz. The frequency of the modulating signal determines therate of frequency deviation but has no effect on the amount of deviation which is strictly afunction of the amplitude of the modulating signal.
Advantages of frequency modulation, FMAlthough it may not be quite as straightforward as amplitude modulation, nevertheless frequencymodulation, FM, offers some distinct advantages. It is able to provide near interference freereception, and it was for this reason that it was adopted for the VHF sound broadcasts. Thesetransmissions could offer high fidelity audio, and for this reason, frequency modulation is farmore popular than the older transmissions on the long, medium and short wave bands.In addition to its widespread use for high quality audio broadcasts, FM is also sued for a varietyof two way radio communication systems. Whether for fixed or mobile radio communicationsystems, or for use in portable applications, FM is widely used at VHF and above.FM is used for a number of reasons and there are several advantages of frequency modulation. Inview of this it is widely used in a number of areas to which it is ideally suited. Some of theadvantages of frequency modulation are noted below: Resilience to noise: One particular advantage of frequency modulation is its resilience to signal level variations. The modulation is carried only as variations in frequency. This means that any signal level variations will not affect the audio output, provided that the signal does not fall to a level where the receiver cannot cope. As a result this makes FM ideal for mobile radio communication applications including more general two-way radio communication or portable applications where signal levels are likely to vary considerably. The other advantage of FM is its resilience to noise and interference. It is for this reason that FM is used for high quality broadcast transmissions. Easy to apply modulation at a low power stage of the transmitter: Another advantage of frequency modulation is associated with the transmitters. It is possible to apply the modulation to a low power stage of the transmitter, and it is not necessary to use a linear form of amplification to increase the power level of the signal to its final value. It is possible to use efficient RF amplifiers with frequency modulated signals: It is possible to use non-linear RF amplifiers to amplify FM signals in a transmitter and these are more efficient than the linear ones required for signals with any amplitude variations (e.g. AM and SSB). This means that for a given power output, less battery power is required and this makes the use of FM more viable for portable two-way radio applications.
Sidebands Any modulation process produces sidebands. As you saw in AM, when a constant-frequency sine wave modulates a carrier, two side frequencies are produced. The sidefrequencies are the sum and difference of the carrier and the modulating frequency. In FM andPM too, sum and difference sideband frequencies are produced. In addition, a theoreticallyinfinite number of pairs of upper and lower sidebands are also generated. As a result, thespectrum of an FM/PM signal usually wider than an equivalent AM signal. A specialnarrowband FM signal whose bandwidth is only slightly wider than that of an AM signal canalso be generated. Figure 2 shows an example of the spectrum of a typical FM signal produced bymodulating a carrier with a single-frequency sine wave. Note that the sidebands are spaced fromthe carrier fc and are space from one another by a frequency equal to the modulating frequencyfm. If the modulating frequency is 500 Hz, the first pair of sidebands are above and below thecarrier by 500 Hz. The second pair of sidebands are above and below the carrier by 2 500 Hz1000 Hz or 1 kHz, and so on. Note also that the amplitudes/intensities of the sidebands vary. Iseach sideband is assumed to be sine wave with a frequency and amplitude as indicated in Fig 1and all these sine waves were added together, then the FM signal producing them would becreated. Figure 2. Frequency Domain Display, fc and sidebands
As the amplitude of the modulating signal varies, of course, the frequency deviation willchange. The number of sidebands produced, their amplitude, and their spacing depend upon thefrequency deviation and modulating frequency. Keep in mind that an FM signal has a constantamplitude. If that FM signal is a summation of the sideband frequencies, then you can see thatthe sideband amplitudes must vary with frequency deviation and modulating frequency if theirsum is to produced a fixed amplitude FM signal. Although the FM process produces an infinite number of upper and lower sidebands, onlythose with the largest amplitudes are significant in carrying the information. Typically anysideband whose amplitude is less than 1 percent of the unmodulated carrier is consideredinsignificant. As a result, this markedly narrows the bandwidth of an FM signal.
MODULATION INDEXModulation IndexAs indicated earlier, the number of significant sidebands and their amplitudes are dependentupon the amount of frequency deviation and the modulating frequency. The ratio so thefrequency deviation to the modulating frequency is known as the modulation index, m.where fd is the frequency deviation and fm is the modulating frequency.For example, assume that the maximum frequency deviation of the carrier is 25 kHz while themaximum modulating frequency is 10 kHz. The modulating index, therefore, isIn most communication systems using FM, maximum limits are put on both the frequencydeviation and the modulating frequency. For example, in standard FM broadcasting, themaximum permitted frequency deviation is 75 kHz, while the maximum permitted modulatingfrequency is 15 kHz. This produce a modulating index ofWhenever the maximum allowable frequency deviation and maximum modulating frequency areused in computing the modulation index, m is known as the deviation ratio.Knowing the modulation index, you can compute the number and amplitudes of the significantsidebands. This is done through a complex mathematical process known as the Bessel function.
BESSEL FUNCTION TABLE Figure 3. the left-hand column gives the modulation index. The remaining columnsindicate the relative amplitudes of the carrier and the various parts of sidebands. Any sidebandwith relative carrier amplitude of less than 1 percent has been eliminated. Note that some of thecarrier and sideband amplitudes have negative signs. This means that the signal represented bythe amplitude is simply shifted in phase 180o (phase inversion) As you can see, the spectrum of an FM signal varies considerably in bandwidthdepending upon the modulation index. The higher the modulation index, the wider the bandwidthof an FM signals nay be deliberately by putting an upper limit on the modulation index.Modulation Sideband index Carrier 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.00 1.00 0.25 0.98 0.12 0.5 0.94 0.24 0.03 1.0 0.77 0.44 0.11 0.02 1.5 0.51 0.56 0.23 0.06 0.01 2.0 0.22 0.58 0.35 0.13 0.03 2.41 0 0.52 0.43 0.20 0.06 0.02 2.5 −0.05 0.50 0.45 0.22 0.07 0.02 0.01 3.0 −0.26 0.34 0.49 0.31 0.13 0.04 0.01 4.0 −0.40 −0.07 0.36 0.43 0.28 0.13 0.05 0.02 5.0 −0.18 −0.33 0.05 0.36 0.39 0.26 0.13 0.05 0.02 5.53 0 −0.34 −0.13 0.25 0.40 0.32 0.19 0.09 0.03 0.01 6.0 0.15 −0.28 −0.24 0.11 0.36 0.36 0.25 0.13 0.06 0.02 7.0 0.30 0.00 −0.30 −0.17 0.16 0.35 0.34 0.23 0.13 0.06 0.02 8.0 0.17 0.23 −0.11 −0.29 −0.10 0.19 0.34 0.32 0.22 0.13 0.06 0.03 8.65 0 0.27 0.06 −0.24 −0.23 0.03 0.26 0.34 0.28 0.18 0.10 0.05 0.02 9.0 −0.09 0.25 0.14 −0.18 −0.27 −0.06 0.20 0.33 0.31 0.21 0.12 0.06 0.03 0.01 10.0 −0.25 0.04 0.25 0.06 −0.22 −0.23 −0.01 0.22 0.32 0.29 0.21 0.12 0.06 0.03 0.01 12.0 0.05 −0.22 −0.08 0.20 0.18 −0.07 −0.24 −0.17 0.05 0.23 0.30 0.27 0.20 0.12 0.07 0.03 0.01Figure 3 A table showing carrier and sideband amplitudes for different modulation indexes ofFM signals. Based on the Bessel Function.
TYPES OF FREQUENCY MODULATION Wide Band Frequency Modulation – Broadcast stations in the VHF portion of thefrequency spectrum between 88.5 and 108 MHz use large values of deviation, typically ±75 kHz.This is known as wide-band FM (WBFM). These signals are capable of supporting high qualitytransmissions, but occupy a large amount of bandwidth. Usually 200 kHz is allowed for eachwide-band FM transmission. For > 0.3 there are more than 2 significant sidebands. As increases the number ofsidebands increases. This is referred to as wideband FM (WBFM). Narrow Band Frequency Modulation – For communications purposes less bandwidth isused. Narrow band FM (NBFM) often uses deviation figures of around ±3 kHz. It is narrow bandFM that is typically used for two-way radio communication applications. Having a narrowerband it is not able to provide the high quality of the wideband transmissions, but this is notneeded for applications such as mobile radio communication. From the graph/table of Bessel functions it may be seen that for small , ( 0.3) there isonly the carrier and 2 significant sidebands, i.e. BW = 2fm. FM with 0.3 is referred to asnarrowband FM (NBFM) (Note, the bandwidth is the same as DSBAM). The block diagrams satisfy the corresponding expression for FM.
POWER IN FREQUENCY MOULATIONFrom the equation for FM vs (t ) Vc J n ( ) cos( c n m )t nwe see that the peak value of the components is VcJn( ) for the nth component. 2Single normalised average power = V pk 2 then the nth component is (VRMS ) 2 2 2 Vc J n ( ) Vc J n ( ) 2 2Hence, the total power in the infinite spectrum is Total power (Vc J n ( ))2 PT n 2By this method we would need to carry out an infinite number of calculations to find PT. But,considering the waveform, the peak value is Vc, which is constant. 2 V pk VcSince we know that the RMS value of a sine wave is 2 2 2 2 Vc Vc2 Vc J n ( ) 2and power = (VRMS) then we may deduce that PT 2 2 n 2Hence, if we know Vc for the FM signal, we can find the total power PT for the infinite spectrumwith a simple calculation.Now consider – if we generate an FM signal, it will contain an infinite number of sidebands.However, if we wish to transfer this signal, e.g. over a radio or cable, this implies that we requirean infinite bandwidth channel. Even if there was an infinite channel bandwidth it would not allbe allocated to one user. Only a limited bandwidth is available for any particular signal. Thus wehave to make the signal spectrum fit into the available channel bandwidth. We can think of thesignal spectrum as a „train‟ and the channel bandwidth as a tunnel – obviously we make the trainslightly less wider than the tunnel if we can.
However, many signals (e.g. FM, square waves, digital signals) contain an infinite number ofcomponents. If we transfer such a signal via a limited channel bandwidth, we will lose some ofthe components and the output signal will be distorted. If we put an infinitely wide train througha tunnel, the train would come out distorted, the question is how much distortion can betolerated? Generally speaking, spectral components decrease in amplitude as we move awayfrom the spectrum „centre‟.In general distortion may be defined as Power in total spectrum- Power in Bandlimite spectrum d D Power in total spectrum PT PBL D PTWith reference to FM the minimum channel bandwidth required would be just wide enough topass the spectrum of significant components. For a bandlimited FM spectrum, let a = the numberof sideband pairs, e.g. for = 5, a = 8 pairs (16 components). Hence, power in the bandlimitedspectrum PBL is a (Vc J n ( ))2 = carrier power + sideband powers. PBL n a 2
Vc2Since PT 2 Vc2 Vc2 a ( J n ( ))2 a 2 2 n aDistortion D 1 ( J n ( ))2 Vc2 n a 2Also, it is easily seen that the ratio a Power in Bandlimite spectrum PBL d D ( J n ( ))2 = 1 – Distortion Power in total spectrum PT n a ai.e. proportion pf power in band limited spectrum to total power = ( J n ( ))2 n a