Crosstalk between two terminated lines (RT=,RS= Z0)

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An active line-1 and a passive line-2 are terminated by RS at near end, and are open at far end.

The voltages at both ends of active line are:

The voltages at both ends of passive line are:

where

An example waveform for a rising step input v01(t) with rise time tr=/2:

 

The pulse induced on passive line is called backward crosstalk or near-end crosstalk (NEXT).

Focusing on the first wave (n=1), the voltage on passive line is:

where is the crosstalk coefficient and rs is the normalized source resistance:

The amplitude of backward crosstalk saturates at the line lengh:

In the case of a parallel data transmission or a source synchronous clocking, transmission lines are identical. We will calculate the crosstalk between two identical lines.

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The voltages of line-1,2 will be derived from the voltages of even and odd mode. (Multiple reflection in terminated coupled-lines)

where

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For simplicity, we assume the conditions below:

(1) The far-end impedance is HiZ: RT= i.e. T+=T|=1

(2) The propagation speeds are equal between even and odd mode : +=|= (TEM mode)

Then the voltages on line-1,2 results in more simple form.

Active line:

Passive line:

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We will compute an waveform using these equations. For convenience, we express the reflection coefficients

with the crosstalk coefficient and the normalized resistance rS:

Assuming the input voltage v01(t) is a rising step with rise time tr=/2, and rS=1, =0.4, the waveform is:

The pulse induced on passive line is called backward crosstalk or near-end crosstalk (NEXT).

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For more intuitive understanding, we will simplify the equation above. We assume that the input voltage v01(t) is a rising step.

Using the identities

, the voltages on line-1,2 can be expressed in terms of the amplitude in n< t <m: v01(t-n)-v01(t-m),

Active line:

Passive line:

or, explicitly

Active line:

Passive line:

Note that the amplitude v2(l,t) is twice as large as v2(0,t) because of the total reflection (T+=T|=1).

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Noting ||<1, the amplitude attenuates exponentially with time. Then we will focus on the first wave (n=1) on passive line:

Noting 01, its polarity is the same as the input voltage. And the amplitude is almost proportional to the crosstalk coefficient .

Especially, when the source resistance matches the characteristic impedance:

, the first wave on passive line is:

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If the propagation time 2 is smaller than the rising time tr, the amplitude of crosstalk becomes small.

Conversely, the amplitude of backward crosstalk saturates at the line length:


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