Spread Spectrum technology in the context of EMI reduction is a method of distributing or spreading the energy concentrated in a narrow band of frequency over a wider band thereby effectively reducing the peak energy levels. This is done in many ways but the basic concept is some form of frequency modulation of a periodic signal.

This is not a new concept and the basic principle is described briefly below

If a sinusoidal signal of frequency f_{c} is frequency modulated by a sinusoidal signal of frequency f_{m}(modulation rate) by a maximum amount Δf the resulting spectrum of the modulated signal is comprised of the carrier frequency and sidebands spaced at intervals of f_{m} over the frequency band Δf

Mathematically, the instantaneous frequency of the modulated carrier can be represented as

f(t) = f_{c} + k_{f} * m(t) Equation 2.1

(m(t) is the modulating waveform and k_{f} is the frequency sensitivity (Hz/V) )

m(t) = A_{m}cos(2πf_{m}t) Equation 2.2

f(t) = f_{c} + k_{f}*Amcos(2πf_{m}t)Equation 2.3

(Replacing Δf = k_{f}*A_{m})

f(t) = f_{c} + Δf*cos(2πf_{m}t)Equation 2.4

The instantaneous angle of this modulated wave is given by

Θ(t) = Equation 3.1

Θ(t) = Equation 3.2

We define the ratio of the maximum frequency deviation (Δf)to the modulation rate fm as the Modulation Index β.

β = Equation 3.3

Θ(t) = 2πf_{c} *t + β*sin(2πf_{m}t) Equation 3.4

From equation 3.2 we see that β represents the maximum phase deviation of the FM wave from that of the carrier phase angle.

The FM wave can be represented as

s(t) = Acsin{Θ(t)} Equation 5.1

s(t) = Acsin{2π f_{c} * t + β*sin(2π f_{m}t)] Equation 5.2

This can be evaluated as the Bessel series

s(t) = A_{c}[J0(β)sin(2π f_{c}t) Equation 6.1

+ J1(β){sin(2π f_{c} + 2π f_{m})t - sin(2π f_{c} - 2π f_{m})t}

+ J2(β){sin(2π f_{c} + 2*2π f_{m})t - sin(2π f_{c} – 2*2π f_{m})t}

+ J3(β){sin(2π f_{c} + 3*2π f_{m})t - sin(2π f_{c} - 3*2π f_{m})t}

+ J4(β){sin(2π f_{c} + 4*2π f_{m})t - sin(2π f_{c} – 4*2π f_{m})t}

+ … etc.]