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# FREQUENCY AND PHASE MODULATION (ANGLE MODULATION)

FREQUENCY AND PHASE MODULATION (ANGLE MODULATION). ANGLE MODULATION – When frequency or phase of the carrier is varied by the modulating signal , then it is called angle modulation.

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## FREQUENCY AND PHASE MODULATION (ANGLE MODULATION)

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1. FREQUENCY AND PHASE MODULATION(ANGLE MODULATION)

2. ANGLE MODULATION – • When frequency or phase of the carrier is varied by the modulating signal , then it is called angle modulation. • Frequency Modulation – When the frequency of the carrier varies as per amplitude of modulating signal, then it is called frequency modulation (FM). • Phase Modulation - When the phase of the carrier varies as per amplitude of modulating signal, then it is called phase modulation (PM). • Amplitude of the modulated carrier remains constant in both modulation systems. BDG(xx)

3. An important feature of angle modulation: • It can provide a better discrimination (robustness) against noise and interference than AM. • This improvement is achieved at the expense of increased transmission bandwidth. • In case of angle modulation, channel bandwidth may be exchanged for improved noise performance • Such trade-oﬀ is not possible with AM BDG(xx)

4. BASIC DEFINITIONS -Relationship between the angle and frequency of a sinusoidal signal • Sinusoidal carrier c(t) =Ac cos[θi(t)] • Angle of carrier θi(t)[rad] • Instantaneous frequency of carrier fi(t) =(1/2π)ωi(t) =(1/2π)di(t)/dt • =(1/2π)˙ θi(t)[Hz]. • In the case of an un-modulated carrier, the angle becomes θi(t) = 2πfct + θc BDG(xx)

5. Time domain representation BDG(xx)

6. Compare FM-PM – • The basic difference between FM & PM lies in which property of the carrier is directly varied by modulating signal. • In FM, the frequency of carrier is varied directly. • In PM, phase of the carrier is varied directly. Instantaneous phase deviation is represented by θ(t). • Instantaneous phase= ωct + θ(t) rad. BDG(xx)

7. Instantaneous frequency deviation = • d/dt {θ(t)} = θ’(t) Hz. • The instantaneous frequency deviation is the instantaneous change in carrier frequency and is equal to the rate at which instantaneous phase deviation takes place. • Instantaneous frequency is defined as frequency of the carrier at a given instant of time and is given as ωi(t) =d/dt [ωc.t + θ(t)] = ωc + θ’(t) rad/sec. BDG(xx)

8. Instantaneous phase deviation θ (t) is proportional to modulating signal voltage, θ (t) = k em(t) rad. ( k is deviation sensitivity of phase.). • Instantaneous frequency deviation θ’ (t) is proportional to modulating signal voltage, θ’ (t) = k1 em(t) rad. ( k1 is deviation sensitivity of frequency.)##2 BDG(xx)

9. Frequency modulation

10. Observations from the FM & PM waveforms – • 1. Both FM & PM waveforms are identical except the phase shift. • 2. For FM, the maximum frequency deviation takes place when modulating signal is at +ve and –ve peaks. • 3. For PM, the maximum frequency deviation takes place near zero crossing of the modulating signal. • 4. It is diffcult to know from modulated waveform whether the modulation is FM or PM. (##3) BDG(xx)

11. Bandwidth Requirement – for FM- • The BW requirement can be obtained depending on the modulation index (M.I). • The M.I. can be classified as high(more than 10), medium (1 to 10) and low (less than 1). • The low index systems are called narrowband FM in which frequency spectrum resembles AM. BW (fm) =2fm Hz. • For high index modulation, BW = 2*δ.(Freq. dev.) • BW can also be found out by Bessel table- BWfm = 2.n.fm where n is the number of sidebands obtained from table. BDG(xx)

12. Carson’s Rule – • Rule gives approximate minimum BW of angle modulated signal as • BW fm = 2{δ + fm(max)} Hz. • From the above equation, it is found that the BW accommodates almost 98% of the total transmitted power BDG(xx)

13. Bandwidth for PM – • BW for PM is expressed as • BWpm = 2(mp+1)fm. BDG(xx)

14. Block Diagram of NBFM Generator – • Carrier is Ec cos ωc .t Integrator Product Modulator Adder M(t) NBFM signal 90 degree Phase Shifter Carrier Generator BDG(xx)

15. Phasor Diagram of NBFM – • USB phasor at an angle of (ωm .t) and LSB phasor at an angle of (- ωm .t) Resultant Phasor LSB Phasor USB Phasor Phase Shift Carrier Phasor BDG(xx)

16. Carrier phasor is Ec cos ωc .t (always fixed). • USB phasor in clockwise direction (ωm) • LSB phasor in counter clockwise direction (-ωm) • Resultant of two sideband phasor is always perpendicular to carrier phasor. • The net resultant phasor of NBFM due to Carrier and sidebands is as shown in the diagram. BDG(xx)

17. Wideband Frequency Modulation – • If the modulation index is higher than 10, then it is called wideband FM. • Spectrum contains infinite numbers of sidebands and carrier as against two sidebands and carrier in NBFM. • BW is = 2{δ+fm(max)} as against 2fm for NBFM. • Used for broadcast and entertainment as against for mobile communication for NBFM. • ##5. BDG(xx)

18. Advantages of Angle Modulation over AM- • 1. As the amplitude of FM carrier is constant, the noise interference is minimum. • 2. The amplitude of FM carrier is constant and is independent of depth of modulation. Hence transmitter power remains constant in FM whereas it varies in AM. • 3. As against the limitation of depth of modulation in AM, in FM depth of modulation can be increased to any value, without causing any distortion. BDG(xx)

19. 4. Because of guard bands provided in FM, adjacent channel interference is very less. • 5. Since FM uses VHF and UHF bands of frequencies, the noise interference is minimum as compared to AM which uses MF and HF ranges. • 6. Radius of propagation is limited as FM uses space waves with line of sight. So it is possible to operate many independent transmitters on the same frequency with minimum interference. BDG(xx)

20. Disadvantages of FM compared to AM- • 1. BW requirement of FM is very high as compared to AM. • 2. FM equipments are more complex and hence costly. • Area covered by FM is limited, to line of sight area but AM coverage area is large. BDG(xx)

21. BDG(xx)

22. Modulators – • Carrier frequency can be generated by LC oscillator. • By varying the values of L or C of tank circuit, carrier frequency can be changed. • Properties of BJT,FET and varactor diodes can be varied by changing the voltage across them. • When these components are used with LC tank circuits, we are able to vary frequency of oscillator by changing the reactance of L or C. BDG(xx)

23. TWO types of FM Modulators – • 1. Indirect FM – Modulation is obtained by phase modulation of the carrier. An instantaneous phase of the carrier is directly proportional to the amplitude of the modulating signal. • 2. Direct FM- The frequency of carrier is varied directly by modulating signal. An instantaneous frequency variation is directly proportional to the amplitude of the modulating signal. BDG(xx)

24. There are two methods to derive FM by using FET and varactor. • 1. Frequency modulation using Varactor Diode – • There exists small junction capacitance in the reverse biased condition of all the diodes. • The varactor diodes are designed to optimise this characteristic. • As the reverse bias across varactor diode is varied, its junction capacitance changes. • These changes are linear and wide (1 to 200pF) BDG(xx)

25. Frequency modulation using varactor diode – • All diodes show small junction capacitance in the reverse biased condition. • ##6 BDG(xx)

26. Advantages of FM using Varactor Diode – • 1. High frequency stability as crystal oscillator is isolated from modulator. • Disadvantages – • 1. To avoid distortion, the amplitude of modulating signal is to be kept small. • 2. The varactor diode must have non linear characteristics of capacitance vs. voltage. • Use – • This method is used for low index narrow band FM generation. BDG(xx)

27. FET Reactance Modulator – • There are a number of devices whose reactance can be varied by the application of voltage. These include FET and BJT, varactor diode etc. • If such a device is placed across the tank circuit of the L-C oscillator, then FM will be produced when the reactance of the device is varied by the modulating voltage. • At the carrier frequency, the oscillator inductance is tuned by its own capacitance in parallel with the average reactance to the variable reactance device. BDG(xx)

28. Advantages of FET Reactance Modulator – • 1. Due to FET characteristics, linear relationship between modulating voltage and transconductance can be achieved. • 2 This method produces enough frequency deviation and hence no frequency multiplication is required. • Disadvantages - Frequency stability is poor as lumped components are used. • Use – This method is used for low modulation index application. BDG(xx)

29. Indirect FM – • Phase modulation is used to achieve frequency modulation in the indirect method, • It is necessary to integrate the modulating signal prior to applying it to the phase modulator, • This transmitter is widely used in VHF and UHF radio telephone equipment. • ##7 BDG(xx)

30. Advantage – • 1. The crystal oscillator is isolated from modulator, so frequency stability is very good. • Disadvantages – • 1. Because of nonlinear capacitance Vs. voltage characteristics of varactor diode, there is a distortion in the modulated output waveform. • 2. Amplitude of modulating signal should be kept small to avoid distortion. • Use –Used for narrow band low index FM. BDG(xx)

31. FM Transmitters – • Two types of transmitters – Indirect FM and Direct FM Transmitters. • Indirect FM Transmitters – Produces the FM whose phase deviation is directly proportional to modulating signal amplitude. Frequency of oscillator is not directly varied. Hence crystal oscillators can be used. • Direct FM Transmitters – Frequency deviation is directly proportional to modulating signal. Carrier frequency is directly deviated. BDG(xx)

32. Need for Automatic Frequency Correction – • In FM transmitters, the frequency of the oscillator is directly varied. • To obtain very stable frequency of oscillator, automatic frequency correction technique is employed. BDG(xx)

33. FM Transmitters – • Block Diagram –##8 • The modulating signal is given to frequency modulator ( may be reactance modulator or VCO ) and oscillator. • Let fc = F Mhz. Multiplied by 18 to generate the transmitted frequency F*18 Mhz. • AFC loop is to maintain stable centre frequency. • Multiplier output given to mixer is F*6. BDG(xx)

34. The crystal frequency oscillator - reference frequency is {(6*fc) – 2MHz.} • The mixer generates 2 MHz difference frequency which is given to discriminator, which is tuned to 2 MHz. • If there is a difference in the output frequency of mixer, discriminator generates d. c. correction voltage. • If multiplier frequency is exactly 6*fc, then no correction is required and hence correction voltage must be zero. BDG(xx)

35. But with FM, there is a frequency deviation in 6*fc, which is proportional to modulating signal amplitude. • So d.c. correction voltage also have corresponding variation. • Therefore this d.c. voltage is passed through low pass filter to remove effect of frequency variation due to modulation. • The filtered voltage is used for frequency correction. BDG(xx)

36. Phase Locked Loop direct FM transmitter – • This type is used to produce WBFM with high mod index. • When both the input frequencies to phase comparator are same , they are locked and output is zero. • The modulating signal is used to control the output frequency of VCO. • The frequency of output FM of VCO is a function of modulating signal. BDG(xx)

37. If there is a deviation in the centre frequency of VCO, correction voltage is generated. • This d.c. voltage, passing through LPF, is added to modulating signal to correct the VCO output. • Function of LPF is to remove rapid changes in correction voltage due to frequency variations in FM signal. BDG(xx)

38. Indirect FM Transmitter – Armstrong Method - • ( Phase Mod. is employed to produce FM) • Stability of the frequency is a major issue in FM. So direct methods of FM generation are not suitable for broadcasting . • To overcome this drawback, indirect method to generate FM from PM is employed. (block dia.) • To get the modulating signal of same frequency of carrier, AM signal is generated and shifted by 90degrees and added to fc signal vector. BDG(xx)

39. The resultant vector output is phase modulated. • Since AM and carrier vectors are having same frequency(fc), the out put is FM. • Thus phase modulation produces FM. • The phase modulated signal can be defined as e(pm) = Ec sin (ωc t + m cos ωm t). • ## BDG(xx)

40. FOSTER SEELEY DISCRIMINATOR – (Phase discriminator)- • The Foster Seeley Discriminator is a common type of FM detector circuit used mainly within radio sets constructed using discrete components. • The Foster Seeley detector (or the Foster Seeley discriminator) has many similarities to the ratio detector. The circuit topology looks very similar, having a transformer and a pair of diodes, but there is no third winding and instead a choke is used. BDG(xx)

41. Cc,C1 & C2 offers short circuit for IF center frequency. • Right side of L3 is at ground potential and IF(Vin) is fed directly (in phase)across L3.(VL3) • 180 degree phase out by T1 – La & Lb equal division. • At resonant frequency of tank circuit(IF) secondary current (Is) is in phase with Vs and 180degree out of phase with VL3. BDG(xx)

42. Like the ratio detector, the Foster-Seeley circuit operates using a phase difference between signals. • To obtain the different phased signals a connection is made to the primary side of the transformer using a capacitor, and this is taken to the center tap of the transformer. • This gives a signal that is 90 degrees out of phase. BDG(xx)

43. Due to loose coupling , primary of T1 acts as inductor and Ip is 90 degree out of phase with Vin. • Voltage induced in secondary is 90 degree out of phase with Vin(VL3) • VLa and Vlb are 180 degree out of phase with each other and 90 degree out of phase with VL3. • Voltage across VD1 is vector sum of VL3 and VLa and VD2 is vector sum of VL3 and VLb. BDG(xx)

44. When IF > resonance, secondary tank circuit impedance becomes inductive and secondary current lags voltage by theta which is proportional to frequency deviation. • When IF < resonance, secondary current leads secondary voltage by theta which is proportional to frequency deviation. • F.S.D. is tunned by injecting a frequency equal to the IF center frequency and tunning Co for zero volts output. BDG(xx)

45. Ratio Detector – • Ratio detector or discriminator is widely used for FM demodulation within radio sets using discrete components. It was capable of providing a good level of performance. • In recent years the Ratio detector has been less widely used. • The main reason for this is that it requires the use of wire wound inductors and these are expensive to manufacture. BDG(xx)

46. Ratio Detector Circuit – BDG(xx)

47. Other types of FM demodulator have overtaken them, mainly as a result of the fact that the other FM demodulator configurations lend themselves more easily to being incorporated into integrated circuits. • Ratio FM detector basics - • When circuits employing discrete components were more widely used, the Ratio and Foster-Seeley detectors were widely used. Of these the ratio detector was the most popular as it offers a better level of amplitude modulation rejection. BDG(xx)

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