Crosstalk noise onto a floating line
An active line1 is terminated by resistances at both ends, and a passive line2 is floating.
The voltage on active line is the same in the case of a single line:
where
The voltage on passive line is proportional to that on active line:
where ξ is the crosstalk coefficient:
An example waveform for a rising step input v_{01}(t) with rise time tr=τ/2:

We will calculate the crosstalk voltage onto a floating line.
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We start from the general solutions in even and odd mode:
Transforming the variables of even and odd mode to those of each line:
we obtain the general solutions for each line:
where we have assumed that the propagation speeds are equal in even and odd mode.
For convenience, expressing (3),(4) in terms of Z_{0} and parameter ξ
,we have
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We are now ready to calculate the crosstalk noise onto a floating line.
Boundary conditions are:
then Laplace transformed boundary conditions are
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First, inserting the general solutions (1),(3') into the boundary conditions of line1:
Eliminating the pair of V_{a2},V_{b2}:
After some manipulation we obtain:
where τ is the propagation time from x=0 to x=l, and Γ_{S},Γ_{T} are reflection coefficients at source and termination end.
This result is the same in the case of a single line. (→Multiple reflection in a terminated line)
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Next, inserting the general solutions (2),(4') into the boundary conditions of line2:
Eliminating the pair of V_{b1},V_{b2} or V_{a1},V_{a2}:
We find that the voltage on passive line2 is proportional to that on active line1.
This parameter ξ indicates the ratio of amplitude between passive and active line, so it is called crosstalk coefficient.