Modulation Technique:

Transcription

1 Modulation Tehnique: There are two basi failies of ontinuous-wave odulation tehniques: 1. Aplitude odulation, in whih the aplitude of a sinusoidal arrier is varied in aordane with an inoing essage signal. 2. Angle odulation, in whih the instantaneous frequeny or phase of the sinusoidal arriers varied in aordane with the essage signal.

2 In basi signal-proessing ters, in a ouniation syste, the transitter onsists of a odulator and the reeiver onsists of a deodulator as Message signal Modulator Modulated signal Reeived Signal Deodulator Estiate Signal Carrier wave Fig. 1 Coponents of Modulation syste The degradation in reeiver perforane due to hannel noise is deterined by the type of odulation used.

3 Fig. 2 AM and FM signals

4 Aplitude Modulation: Consider the sinusoidal arrier wave ( defined as ( = A os(2πf A is the arrier aplitude and f is the arrier frequeny. Let ( denote the baseband signal that arries the essage. The odulated signal is as s( = A [1 + k ( ] os(2πf a Where k a is a onstant alled the aplitude sensitivity, index of odulation, 0< k a <1.

5 Fig. 3 AM wave with k a ( <1 and k a ( >1

6 Aording to spetru analysis: A ka A S ( f ) = [ δ ( f f ) + δ ( f + f )] + [ M ( f f ) + M ( f + f )] 2 2 AM Exaple: Consider the essage ( =A os(2πf. Find the orresponding AM wave and spetru analysis.

7 Fig. 4 Spetru analysis of essage signal and AM wave

8 DSB-AM (Double Side Band AM): Consider the arrier wave is ( = A os(2πf The essage signal is (. Then, the odulated signal is s( = A ( os(2πf The representation of DSB-AM signal in frequeny doain is A A S ( f ) = M ( f f ) + M ( f + f ) 2 2

9 Fig. 5 DSB- AM

10 Assignent: SSB-AM (Single Side Band AM):

11 Angle Modulation: Let θ i ( denote the angle of a odulated sinusoidal arrier, assued nto be a funtion of the essage signal. Express the angle odulated wave is s( = A os[ θ ( ] i where A is the arrier aplitude. A oplete osillation ours whenever θ i ( hanges by 2π radians. θ i ( ay be varied in soe anner with the essage signal. There are two oonly used ethods, as Phase odulation and Frequeny odulation.

12 Phase Modulation (PM): ) ( 2 ) ( t k t f t p i + = π θ The Phase odulated signal s( is )] ( os[ 2 ) ( t k t f A t s p + = π Frequeny Modulation (FM): + = t f i d k t f t 0 ] ) ( [ 2 ) ( τ τ π θ The Phase odulated signal s( is ] ) ( 2 os[2 ) ( 0 + = t f d k t f A t s τ τ π π

13 FM Exaple: Consider the essage ( =A os(2πf. Find the orresponding FM wave.

14 Narrow Band FM: Consider the FM signal s( s( = A os[2π f t + β sin(2πf ] = A os( 2πf os[ β sin(2πf ] A sin(2πf sin[ β sin(2πf ] Assue β is sall, Hene, os[ β sin[ β sin(2πf ] 1 sin(2πf ] β sin(2πf s( A os(2πf A β sin(2πf sin(2πf

15 Assignent: Wide-Band FM

16 Bandwidth of FM signal: An approxiation for the transission bandwidth of an FM signal generated by a single-tone essage signal of frequeny f is as B T 2 f where f = k f A. + 2 f = 2 f (1 + 1 ) β

17 Another definition is alled deviation ratio D, defined as the frequeny deviation f to the highest odulation frequeny W. The deviation ratio D plays the sae role for nonsinusoidal odulation and β plays the sinusoidal odulation, B = 2( D + 1) T f

18 Exaple: A 20MHz arrier is frequeny odulated by a sinusoidal signal suh that the peak frequeny deviation is 100 KHz. Deterine the odulation index and approxiate bandwidth of the FM signal if the essage signal is (a) 1KHz, (b) 50KHz, () 500 KHz. The given ondition: f =100K, f =20M For sinusoidal odulation β = f /f

19 (a) With f =1000 Hz, β = 100K/1000 = 100 B = 2 f + 2 T f = 2 f f 1 (1 + β = 2 (1 + β ) = 202KHz (b) With f =50K Hz, β=2 B T = 300KHz () With f =500K Hz, β=0.2 BT 2 f = 1MHz )

20 Exaple, In North Aeria, the axiu value of frequeny deviation f is fixed at 75KHz for oerial FM broadasting by radio. If the odulation frequeny W=15KHz, whih is the axiu radio frequeny of interest in FM transission? Corresponding deviation ratio D 75K D = 15K = 5 The transission bandwidth of the FM signal is B T = 2 ( D + 1) 15K = 180KHz