Nbfm Presentation

1

Angle Modulation
Angle modulation is the process in which the instantaneous angle of the carrier signal is changed according to the instantaneous amplitude of modulating or message signal. Carrier Signal,

The instantane ous frequency is f i ( t ) = lim f ∆ t ( t )
∆t → 0

1 d θ i (t ) 2π dt For an unmodulate d carrier, θ i ( t ) is =

θ i ( t ) = 2π f c t + φ c , where φ c is constant

There are two ways of varying the angle of the carrier: By varying the frequency, ωc – Frequency Modulation. By varying the phase, φc – Phase Modulation

2

Frequency modulation is a type of angle modulation in which the instantaneous frequency fi(t) of the carrier signal c(t) is varied linearly with the message signal, m(t).
Carrier Signal

Modulating Signal Modulated Signal

FM modulated signal s(t) is a nonlinear function of the modulating signal m(t), thus it is known as nonlinear modulation process. FM is more difficult than amplitude modulation (AM).
3

let m(t) = A m cos ( 2 πf m t) f i (t) = f c + k f A m cos ( 2 πf m t) = f c + ∆f cos ( 2 πf m t) ∆f = k f A m :frequency deviation t 0

θ i (t) = 2π ∫ f i (τ)dτ = 2πfct + Modulation index β= ∆f fm ∆f sin ( 2πf m t) fm

θi (t) = 2πfct + β sin ( 2πf m t) s(t) = Ac cos[2πfct + β sin ( 2πf m t)]

Depending on β, FM are of 2 types: Narrowband FM : β < 1 radian Wideband FM : β > 1 radian

4

s(t) = Ac cos[2πf c t + β sin ( 2πf m t)] = Ac cos ( 2πf c t) cos[β sin ( 2πf m t)] − Ac sin ( 2πf c t) sin[β sin ( 2πf m t)] Because β is small, cos[β sin ( 2πf m t)] ≈ 1 and sin[β sin ( 2πf m t)] ≈ β sin ( 2πf m t) ∴ s(t) ≈ Ac cos ( 2πf c t) − βAc sin ( 2πf c t) sin ( 2πf m t)

A narrowband FM wave consist of a carrier, an upper side-frequency component and a lower side-frequency component.

5

+

6

s(t) ≈ Ac cos ( 2πf c t) − βAc sin ( 2πf c t) sin ( 2πf m t)
The modulated narrowband FM signal s(t) differs from the ideal response in two fundamental ways: The envelope contains a residual