2 There are three parameters of a carrier that may carry information: IntroductionThere are three parameters of a carrier that may carry information:AmplitudeFrequencyPhaseFrequency and Phase modulation are closely related and grouped together as Angle modulation
3 Frequency ModulationIn this the instantaneous frequency of the carrier is caused to vary by an amount proportional to the amplitude of the modulating signal. The amplitude is kept constant.
7 Some key ObservationsMore complex than AM this is because it involves minute changes in frequencyPower in an FM signal does not vary with modulationFM signals do not have an envelope that reproduces the modulationFM is more immune to effects of noise
8 Frequency Deviation e(t) = E sin (t +) Frequency deviation of the carrier is proportional to the amplitude of the modulating signal as illustratedkf= frequency deviation/V = kf kHz/VMaximum freq deviation
9 Deviation ratio KfThis shift in frequency compared with the amplitude of the modulating voltage is called the deviation ratio.ExampleGiven that the deviation constant is 1kHz/10mV, what is the shift in frequency for a voltage level of 50 mV?Frequency deviation =
10 Mathematical Expression for FM e(t) = E sin (t +)Maximum freq deviationWhere modulation index is
11 % modulation FM% Modulation = Actual freq deviation/ allowed freq deviationExample:An FM broadcast-band transmitter has a peak deviation of ±60 kHz for a particular input signal. Determine the percentage of modulation.
12 Important Definitions -Frequency Deviation is maximum departure of instantaneous freq. of FM wave from career frequencyMaximum Freq of FM is fmax= fc+is independent of modulating freq. and proportional to only amplitude of informationModulation index is proportional to deviation and inversely proportional to modulating freq.This decides the BW of the FM wave also decides the no of side bands In FM the modulation index can be greater than 1
13 Deviation Ratio DR =Maximum deviation /maximum modulating freq in FM is 75KHzis 15KHzDeviation Ratio
14 ExamplesIn an FM system when the audio frequency is 300 Hz and the audio voltage is 2.0V, the deviation is 5kHz. If the audio voltage is now increased to 6V what is the new deviation? If the voltage is now increased to 9V and the frequency dropped to 100Hz what is the deviation? Find the modulation index in each case.
15 Find the carrier and modulating frequencies, the modulating index, and the max. deviation of an FM wave below. What power will the wave dissipate in a 10 ohm resistor?Compare this with:Modulating index =5 as given.Power,
16 Frequency spectrum of FM Wave – Sin of sin function is solved by Bessel functionFc+3fmJ0EcJ1EcJ2EcJ3EcfcFc+fmFc+2fmFc-fmFc-2fmFc-3fm
19 Carson’s RuleThis is an approximate method used to predict the required bandwidth necessary for FM transmissionAbout 98% of the total power is included in the approximation.
20 What bandwidth is required to transmit an FM signal with intelligence at 12KHz and max deviation 24 kHzConsult Bessel function table to note that for modulating index of 2, components which exist are J1,J2,J3,J4 apart from J0.This means that apart from the carrier you get J1 at +/-10kHz, J2 at +/- 20kHz, J3 at +/- 30kHz and J4 at +/- 40 kHz.Total bandwidth is therefore 2x40=80kHz.
21 For an FM signal given by If this signal is input into a 30 ohm antenna, findthe carrier frequencythe transmitted powerthe modulating indexthe intelligence frequencythe required bandwidth using Carson's rule and tablesthe power in the largest and smallest sidebands
22 AM Vs FM systemsIn both systems a carrier wave is modulated by an audio signal to produce a carrier and sidebands. The technique can be applied to various communication systems eg telephony and telegraphySpecial techniques applied to AM can also be applied to FMBoth systems use receivers based on the superheterodyne principle
23 In AM, the carrier amplitude is varied whereas in FM the carrier frequency is varied AM produces two sets of sidebands and is said to be a narrowband system. FM produces a large set of sidebands and is a broad band systemFM gives a better signal to noise ratio than AM under similar operating conditionsFM systems are more sophisticated and expensive than AM systems
24 TransmittersIn an AM transmitter, provision must be made for varying the carrier amplitude whilst for FM the carrier frequency is varied.AM and FM modulators are therefore essentially different in design. FM can be produced by direct frequency modulation or by indirectly phase modulation.The FM carrier must be high usually in the VHF band as it requires large bandwidth which is not available in the lower bands.
25 ReceiversThe FM and AM receivers are basically the same, however the FM receiver uses a limiter and a discriminator to remove AM variations and to convert frequency changes to amplitude variations respectively. As a result they (FM) have higher gain than AM.FM receivers give high fidelity reproduction due to their large audio bandwidth up to 15 kHz compared with about 8 kHz for AM receivers.
26 Frequency Modulation Index Another term common to FM is the modulation index, as determined by the formula:
27 Phase ModulationIn phase modulation, the phase shift is proportional to the instantaneous amplitude of the modulating signal, according to the formula:
28 Relationship Between FM and Phase Modulation Frequency is the derivative of phase, or, in other words, frequency is the rate of change of phaseThe modulation index is proportional to frequency deviation and inversely proportional to modulating frequency
30 Converting PM to FMAn integrator can be used as a means of converting phase modulation to frequency modulation
31 This solution may be shown to be given by To evaluate the individual values of J is quite tedious and so tables are used.
32 The sidebands at equal distances from fc have equal amplitudes ObservationsUnlike AM where there are only three frequencies, FM has an infinite number of sidebandsThe J coefficients decrease with n but not in any simple form and represent the amplitude of a particular sideband. The modulation index determines how many sideband components have significant amplitudesThe sidebands at equal distances from fc have equal amplitudesIn AM increase depth of modulation increases sideband power and hence total transmitted power. In FM total transmitted power remains constant, increase depth of modulation increases bandwidthThe theoretical bandwidth required for FM transmission is infinite.