SCTE IPS Template, Rev 2

Note that, our focus is on the mathematical terms associated with “Cross-Compression”. Theseterms then give an output expression, for any particular channel of interest, which includes theAM-XMOD component.Consider a device (or system) of the type that can be described by equation {A.1} and has, as itsinput, a signal described by equation {A.2}, including amplitude modulation of the type given insection 3.1. If we include the previously stated simplifications, an output expression for aparticular channel can then be written. If we exclude all second order terms, as well as allharmonic and inter-modulation terms, the expression is:y o (t) = k 1 A 1 (t) {1 + (3/2) (k 3 / k 1 ) {(1/2) [A 1 (t)] 2 + [A 2 (t)] 2 + [A 3 (t)] 2 +[A 4 (t)] 2 +…+ [A n (t)] 2 }} cos(w c t + θ c ) {A.4}where, ‘n’ is the number of channels present in the system (n ≥ 2 is implied).Note the ‘Self-Compression’ term, given by the expression “[A 1 (t)] 2 ”. The other squared termsrepresent the individual ‘Cross-Compression’ components. An expression for the amplitude ofthe particular channel, which includes the application of all simplifying assumptions (includingthat of synchronous modulation), is then given by:y o (t) = k 1 A 1 (t) {1 + (3/2) (k 3 / k 1 ) [V pk ] 2 (n-½) [μ m(w MOD , ϕ MOD , t)] 2 } cos(w c t + θ c ){A.5}The expression given in {A.5} contains simple amplitude modulation, hence the description as“AM-XMOD”. A useful expression for the value of the AM-XMOD can then be given as (for n>> 1): † AM-XMOD% (static case) ≡ (3/2) (k 3 / k 1 ) (n) [V pk ] 2 (100) {A.6}From the above expressions, it is apparent that any channel that is amplitude modulated willtransfer some of that energy of modulation to all the other channels present in the system, aspreviously stated. It follows from this derivation that, if all channels in the system aresynchronously modulated, then the total contribution of the AM-XMOD distortion at a particularchannel should be the exact sum of the AM-XMOD distortions contributed by each individualchannel. (This is represented by the ‘(n)’ term in {A.6}.)An important consequence of the above is that, any system that doubles the number of channels,would then double the level of the AM-XMOD distortion. Equivalently, a doubling of thenumber of channels in the system increases the AM-XMOD level by 6 dB. Anotherconsequence is that, if the number of devices in a system doubles, then the AM-XMODdistortion level of the system will also double; once again, this represents a 6 dB increase in theAM-XMOD energy at any particular channel of interest. (Note: this last statement is true only ifthe input levels to each device in the system remain unchanged.)† A complete derivation is given in the references.14