SCTE IPS Template, Rev 2

The fundamental output at a particular channel is given by:y fund (t) = k 1 (w c ) V pk cos(w c t + θ c – φ 1 (w c )) {A.11 }The total output of the Cross Modulation term at the channel carrier (denoted by ‘w c ’), due to thesum of the cross modulation contributions from all the other modulated channel carriers (denotedby ‘w nc ’), is given by:y xmod (t) = (3/4) [V pk ] 3 k 3 (w i ) cos(w mod t) {cos(w c t + θ c ) [Σ n cos(φ 3 (w nc ))] +where:+ sin(w c t + θ c ) [Σ n sin(φ 3 (w nc ))]} {A.12}w i ≡ w c ± w mod , the frequency of the sideband{A.13}Notice that, the added relationship of the third order phase exists as a function of frequency atthe channel carriers. Therefore the cross modulation signal is composed of two signals, each inquadrature with the other, causing the effect of amplitude and phase modulation. Thismodulation is, in effect, ordinary QAM, where the ‘in-phase’ signal (I) and the ‘quadrature’signal (Q) are combined so to give a signal which is both amplitude and phase modulated; and insuch a manner as to be able to resolve the I and Q components separately, when demodulated.Combining both components {y fund (t) and y xmod (t)} and a simplification of terms, gives anexpression for the total output at the particular carrier of interest:y c (t) = k 1 (w c ) V pk [1 + b cos(ϕ) cos(w mod t)] cos[w c t + θ c - φ 1 + b sin(ϕ) cos(w mod t)]{A.14}where:b = (3/4) [V pk ] 2 √ε [k 3 (w i ) / k 1 (w c )]ϕ = - ψ + φ 1ψ = tan -1 [Σ n sin(φ 3 (w nc )) / Σ n cos(φ 3 (w nc ))]ε = n + 2 Σ q = 1 to (n-1) Σ p = (1+q) to n cos[φ 3 (w qc ) - φ 3 (w pc )]{A.15}{A.16}{A.17}{A.18}20