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# Angle modulation

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### Angle modulation

1. 1. Angle Modulation BYMuhammad Uzair Rasheed 2009-CPE-03 UCE&T BZU MULTAN
2. 2. Contents Properties of Angle (exponential) Modulation Types  Phase Modulation  Frequency Modulation
3. 3. Properties Angle Modulation: A non-linear process:- – Modulated wave does not look like message wave – Amplitude of an exponentially modulated wave is constant Therefore, regardless of message signal the average transmitted power is 1 2 P Ac 2 – It is less sensitive to noise
4. 4. Basic Concept First introduced in 1931A sinusoidal carrier signal is defined as: c(t ) Ac cos [ c t c (t )]For un-modulated carrier signal the total instantaneous angle is: c (t ) ct c (t )Thus one can express c(t) as: c(t ) Ac cos c (t ) Ac Re [e j c (t ) ] Thus: • Varying the frequency fc Frequency modulation • Varying the phase c Phase modulation
5. 5. Basic Concept - Cont’d.  In angle modulation: Amplitude is constant, but angle varies (increases linearly) with time c(t) (red) Frequency-modulated Unmodulated angle carrier Unmodulated 47 /2 carrier 35 /2 Phase-modulatedAmplitude 23 /2 angle Ac 11 /2 Slope = - /2 c/ t t Initial phase c 0 1 2 3 4 (ms) t=0 t 2 m(t) 0 -1
6. 6. Phase Modulation (PM)PM is defined If c (t ) K p m(t ) K p 1800Thus c(t ) PM Ac cos [ c t K p m(t )]Where Kp is known as the phase modulation index Instantaneous phase i (t ) K p m(t ) i(tAc ) Instantaneous frequency c(t) c(t) d c (t ) c(t) i (t ) c c (t ) dt Rotating Phasor diagram
7. 7. Frequency Modulation (FM)The instantaneous frequency is; i (t ) c K f m(t )Where Kf is known as the frequency modulation index. Instantaneous phaseNote that c (t ) K f m (t ) tIntegrating i (t ) c c (t ) c (t ) ct K f m(t ) dt 0 0 tSubstituting c(t) in c(t) results in: c(t ) FM Ac cos[ ct K f m(t ) dt ] 0
8. 8. Bandwidth of Angle modulation• For FM:- 1 BFM 2k f m p 8 B 2 BFM 2 f 2B k f mpFrequency deviation= f 2 k f mp
9. 9. • Deviation Ratio:- f B • Carson’s Rule:- BFM 2B 1 Note : Deviation ratio is also called modulation index
10. 10. • For PM:- k f mp Where, mp m t max Now, k pmp BPM 2 B 2
11. 11. THANKS