Crosstalk in a quasi-TEM mode (Forward crosstalk)

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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. And the propagation speeds in even and odd mode are not equal: u+≠u-. 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=τ/2: The narrow pulses added to the waveform in pure-TEM mode are called forward crosstalk or far-end crosstalk (FEXT). Focusing on the first wave (n=1), the voltage on passive line is: The forward crosstalk pulse width is (τ+-τ+) and its polarity is opposite to the input voltage. The amplitude of forward crosstalk pulse saturates at the line length:

We will calculate the crosstalk voltage in a quasi-TEM mode.

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For simplicity, we assume the boundary conditions below:

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

(2) The propagation speeds are not equal between even and odd mode : τ+≠τ- (quasi-TEM mode)

The voltages on line-1 and 2 are:

Active line:

Passive line:

where

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We will compute an waveform using these equations. Assuming the parameters Lm/L=0.4 and Cm/C=0.3, the characteristic impedances and the propagation speed in even and odd mode are:

Assuming the input voltage v01(t) is a rising step with rise time tr=τ/2, and RS=Z0, the waveform is:

Comparing this waveform with the case of pure-TEM mode, we find some narrow pulses added. These narrow pulses are called forward crosstalk or far-end crosstalk (FEXT).

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

This equation predicts a narrow pulse in the time τ-<t< τ+. Noting -(1-ΓS-)0, its polarity is opposite to the input voltage.

If the time difference (τ+-) is smaller than the rising time tr, the amplitude of pulse becomes small.

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

Note that this length is much longer than the saturation length of NEXT:(→Crosstalk between two terminated lines (RT=∞,RS= Z0))

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