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**ANGLE MODULATION CHAPTER 3 Review on Part 1 Part 2**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION ANGLE MODULATION CHAPTER 3 Review on Part 1 Part 2

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**Review on Part 1 ANGLE MODULATION**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Review on Part 1 ANGLE MODULATION

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**Amplitude modulation (AM) Angle modulation (FM,PM)**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Define the following….. Modulation Demodulation Amplitude modulation (AM) Angle modulation (FM,PM) Modulating signal Carrier signal Bandwidth

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION Introduction Angle modulation is the process by which the angle (frequency or Phase) of the carrier signal is changed in accordance with the instantaneous amplitude of modulating or message signal. also known as “Exponential modulation"

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**Cont’d… Classified into two types ; Used for :**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Cont’d… Classified into two types ; Frequency modulation (FM) Phase modulation (PM) Used for : Commercial radio broadcasting Television sound transmission Two way mobile radio Cellular radio Microwave and satellite communication system

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**Cont’d… Advantages over AM:**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Cont’d… Advantages over AM: Freedom from interference: all natural and external noise consist of amplitude variations, thus receiver usually cannot distinguish between amplitude of noise or desired signal. AM is noisy than FM. Operate in very high frequency band(VHF):88M-108MHz Can transmit musical programs with higher degree of fidelity.

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**FREQUENCY MODULATION PRINCIPLES**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION FREQUENCY MODULATION PRINCIPLES In FM the carrier amplitude remains constant, the carrier frequency varies with the amplitude of modulating signal. The amount of change (the relative displacement of carrier frequency in hertz in respect to it un-modulated value) in carrier frequency produced by the modulating signal is known as frequency deviation.

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**PHASE MODULATION (PM) PRINCIPLES**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION PHASE MODULATION (PM) PRINCIPLES The process by which changing the phase of carrier signal in accordance with the instantaneous of message signal. The amplitude and frequency remains constant after the modulation process. Mathematical analysis: Let message signal: And carrier signal:

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**PM (cont’d) After phase modulation, with**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION PM (cont’d) After phase modulation, with the instantaneous voltage will be where = Modulation index of phase modulation K = a constant and called deviation sensitivities of the phase = phase angle of carrier signal .It is changed in accordance with the amplitude of the message signal

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**FREQUENCY MODULATION(FM)**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION FREQUENCY MODULATION(FM) A process where the frequency of the carrier wave varies with the magnitude variations of the modulating or audio signal. The amplitude of the carrier wave is kept constant.

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**FM(cont’d) Mathematical analysis: Let message signal:**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION FM(cont’d) Mathematical analysis: Let message signal: And carrier signal:

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION FM (cont’d) During the process of frequency modulations the frequency of carrier signal is changed in accordance with the instantaneous amplitude of the message signal .Therefore the frequency of carrier after modulation is written as To find the instantaneous phase angle of modulated signal, integrate equation above w.r.t. t

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**FM(cont’d) Thus, we get the FM wave as: Where**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION FM(cont’d) Thus, we get the FM wave as: Where Known as the modulation index for the FM

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION FM(cont’d) Frequency deviation: ∆f is the relative displacement of carrier frequency (Hz) w.r.t its unmodulated value. Given as: Where K is the deviation sensitivity in Hz/V

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION FM(cont’d) The peak to peak frequency deviation (2Δf) is called the carrier swing. Therefore: The modulation index is

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**Example 3.1 An FM modulator with Determine**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Example 3.1 An FM modulator with Deviation sensitivity, K1=5kHz/V Modulating signal Vm(t)=2cos(2π2000t) Determine The peak frequency deviation(Δf) : Ans:10kHz. The modulation index (m) : 5 (unitless) Hint:

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**Angle-modulated wave in the frequency domain.**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Angle-modulated wave in the frequency domain.

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**Example 3.2 A PM modulator with Determine**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Example 3.2 A PM modulator with Deviation sensitivity, K=2.5rad/V Modulating signal Vm(t)=2cos(2π2000t) Determine The peak phase deviation(m) : Ans: 5 rad Hint: Peak phase shift for modulated wave is the modulation index itself.

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Phase and frequency modulation of a sine-wave carrier by a sine-wave signal: (a) unmodulated carrier; (b) modulating signal; (c) frequency-modulated wave; (d) phase-modulated wave

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**FM&PM (Bessel function)**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION FM&PM (Bessel function) Thus, for general equation:

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**Bessel function EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION Bessel function

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**Representation of frequency spectrum**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Representation of frequency spectrum

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION Bessel Functions of the First Kind, Jn(m) for some value of modulation index

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**Example 3.2 An FM modulator with**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Example 3.2 An FM modulator with m=1 Modulating signal Vm(t)=Vmsin(2π1000t) Unmodulated carrier V c(t)=10sin(2π500kt) Determine Number of sets of significant side frequencies (Ans: 1 carrier + 3 sets sides freq.) Their amplitudes Draw the frequency spectrum Hint: (i), (ii), (iii) use table of Bessel functions of the First Kind, Jnm

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**Solution (ii) Their amplitude J0=0.77(10) ; Carrier**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Solution (ii) Their amplitude J0=0.77(10) ; Carrier J1=0.44(10), ; 1st sideband pairs J2=0.11(10) ; 2nd sideband pairs J3=0.02(10) ; 3rd side band pairs

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**(iii) Draw the frequency spectrum.**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Solution (cont’d) (iii) Draw the frequency spectrum. 6kHz

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**Angle Modulation Part 2 FM Bandwidth Power distribution of FM**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Angle Modulation Part 2 FM Bandwidth Power distribution of FM Generation & Detection of FM Application of FM

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION FM Bandwidth Theoretically, the generation and transmission of FM requires infinite bandwidth. Practically, FM system have finite bandwidth and they perform well. The value of modulation index determine the number of sidebands that have the significant relative amplitudes If n is the number of sideband pairs, and line of frequency spectrum are spaced by fm, thus the actual minimum bandwidth using Bessel table: With n = number of significant sidebands = modulating signal frequency

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION FM Bandwidth (cont’d) Carson’s rule also can be used to estimate the bandwidth regardless of modulation index

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**Example 3.3 An FM modulator has the following information; Determine**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Example 3.3 An FM modulator has the following information; Determine Actual minimum bandwidth from the B.F table : Ans=60kHz. Approximate minimum bandwidth using Carson’s rule. Plot the output frequency spectrum for the Bessel approximation Hint:

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**Solution Given; Actual minimum bandwidth from the B.F table.**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Solution Given; Actual minimum bandwidth from the B.F table. m=10kHz/10kHz=1, from B.F table, B=2(3x10kHz)=60kHz. (b) Approximate minimum bandwidth using Carson’s rule.

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**(c) Plot the output frequency spectrum for the Bessel approximation**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION (c) Plot the output frequency spectrum for the Bessel approximation

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION Deviation Ratio (DR) The worse case modulation index which produces the widest output frequency spectrum. Where ∆f(max) = max. peak frequency deviation fm(max) = max. modulating signal frequency

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION Example 3.4 An FM broadcast-band transmitter has a maximum frequency deviation of 75kHz and a maximum modulating signal frequency of 15kHz. Determine the deviation ratio bandwidth. Solution The deviation ratio (i.e the worst case modulation index). From the B.F table, a modulation index of 5 gives 8 significant sidebands. Then B=2(8x15kHz)=240kHz.

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**EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION FM Power Distribution As seen in Bessel function table, it shows that as the sideband relative amplitude increases, the carrier amplitude,J0 decreases. This is because, in FM, the total transmitted power is always constant and the total average power is equal to the unmodulated carrier power, that is the amplitude of the FM remains constant whether it is modulated or not. The total power in angle-modulated wave is equal to the power of the un-modulated wave.

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**FM Power Distribution (cont’d)**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION FM Power Distribution (cont’d) In effect, in FM, the total power that is originally in the carrier is redistributed between all components of the spectrum, in an amount determined by the modulation index, mf, and the corresponding Bessel functions. At certain value of modulation index, the carrier component goes to zero, where in this condition, the power is carried by the sidebands only.

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**Average Power EKT 231 : COMMUNICATION SYSTEM**

CHAPTER 3 : ANGLE MODULATION Average Power The average power in unmodulated carrier The total power in the angle modulated carrier. The modulated carrier power is the sum of the powers of the carrier and the side frequency components as follow; Vc=peak unmodulated carrier voltage (volts), Vn= sidebands voltage (volts), Pc=Carrier power, R=Resisitive load (ohms)

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**Example 3.5 An FM modulator has the following information; Determine;**

EKT 231 : COMMUNICATION SYSTEM CHAPTER 3 : ANGLE MODULATION Example 3.5 An FM modulator has the following information; Determine; The unmodulated carrier power for the FM modulator (Assume RL=50Ω) The total power in the angle modulated wave.

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