What is Spread Spectrum Technology?

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 fc is frequency modulated by a sinusoidal signal of frequency fm(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 fm over the frequency band Δf

Mathematically, the instantaneous frequency of the modulated carrier can be represented as
f(t) = fc + kf * m(t) Equation 2.1
(m(t) is the modulating waveform and kf is the frequency sensitivity (Hz/V) )
m(t) = Amcos(2πfmt) Equation 2.2
f(t) = fc + kf*Amcos(2πfmt)Equation 2.3
(Replacing Δf = kf*Am)
f(t) = fc + Δf*cos(2πfmt)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) = 2πfc *t + β*sin(2πfmt) 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 fc * t + β*sin(2π fmt)] Equation 5.2

This can be evaluated as the Bessel series
s(t) = Ac[J0(β)sin(2π fct) Equation 6.1
+ J1(β){sin(2π fc + 2π fm)t - sin(2π fc - 2π fm)t}
+ J2(β){sin(2π fc + 2*2π fm)t - sin(2π fc – 2*2π fm)t}
+ J3(β){sin(2π fc + 3*2π fm)t - sin(2π fc - 3*2π fm)t}
+ J4(β){sin(2π fc + 4*2π fm)t - sin(2π fc – 4*2π fm)t}
+ … etc.]