# NEXT and FEXT crosstalk calculations

For a lossless line:

The characteristic impedance is given by Zo=sqrt(L/C) and the velocity of propagation by Vp=1/(sqrt(L*C))

Where L and C are, respectively, the line's inductance and capacitance per metre length.

A transmission line is formed by two identical parallel tracks in a printed circuit board, as depicted in the attached figure. The line has a length of 50 mm and all line terminations are of 70 . The line can be assumed to be lossless.

a) Use equations (1) and (2) to calculate the magnitude of the NEXT and FEXT voltages generated in the victim conductor when the source voltage, Vin, in the aggressor conductor is a voltage step of 2 V with a rise time of 100 ps.

[Note that the Vs voltage at the input to the aggressor conductor is

Vs=Vin(Rin/Rin+Zo)]. Please see attached drawing.

Equations:

NEXT

The crosstalk voltage appearing at the near end of the victim circuit due to a changing voltage Vs(t) in the aggressor circuit is given by:

Vne=Kne[Vs(t)-Vs(t-2td)]............(1a)

Kne=1/4td(C*Zo+L/Zo)...............(1b)

Kne is the near end coupling coefficient and C and L are the per unit length mutual capacitance and inductance respectively and td is the time taken for the aggressor signal to travel down the line.

FEXT

The crosstalk voltage generated at the far end of the victim circuit due to a changing voltage Vs(t) in the aggressor circuit is given by:

Vfe=Kfe*l*d/dt[Vs(t-td)]...............(2a)

where l is the length of the line

Kfe=1/2(C*Zo-L/Zo.....................(2b)

b) Sketch the NEXT and FEXT waveforms.

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#### Solution Preview

Please see the 2 attachments for the solution.

- Near End Cross Talk NEXT voltage analysis

The NEXT voltage is given by 1a.

1a.

where is given by 1b.

1b.

However, since the characteristic impedance of the transmission line is given by the square root of the ratio of unit length line inductance and unit length line capacitance we can write and the velocity of propagation of signals along the line given by which on substitution into 1b yields the alternative simplified form for given by equation1c as shown below.

1c.

We can evaluate these ratios since we are given the unit length mutual inductance between the lines as and the unit length line inductance as so

In addition as we are given the unit length mutual capacitance between the lines as and the unit length line capacitance as so we can evaluate the ratio

Then

Also we need to evaluate using the parameter values given where

Then

Since

And

We can also work out the velocity ...

#### Solution Summary

The expert examines NEXT and FEXT crosstalk calculations.