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:
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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+=ΓT-=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 a 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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Because of |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+. Because of -(1-ΓS-)＜0, its polarity is opposite to the input voltage.
If the time difference (τ+-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))
