Calculate NEXT & FEXT Voltages for Lossless Line

[topcat123]

Homework Statement

A transmission line is formed by two identical parallel tracks in a printed
circuit board, as depicted in FIGURE 5. The line has a length of 50 mm
and all line terminations are of 70 Ω. The line can be assumed to be
lossless.
(a) Use equations (4) and (5) from the lesson 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.

(b) Sketch the NEXT and FEXT waveforms.

You may find the following relationship helpful in answering this
question:

For a lossless line:

The characteristic impedance is given by

Zo = squroot(L/C)

and the velocity of propagation by:

Vp = 1/squroot(LC)

where and are, respectively, the line's inductance and
capacitance per metre length.

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

Vs = Vin (Rin/(Rin+Zo)

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

Line inductance 400 nH per m
Line capacitance 80 pF per m
Mutual inductance 80 nH per m
Mutual capacitance 10 pF per m

Homework Equations

KNE = Vp/4(CmZo+Lm/o)

VNE = KNE [Vs(t) - Vs(t-2td)]VFE = KFE l(δ/δt)[Vs(t-td)]

KFE = 1/2(CmZo -(Lm/Zo))

The Attempt at a Solution

so far I have Zo = 70.71Ω
Vp = 176776695 m/s#
KNE = 0.08125

0.5Vin(t) = Vs(t)

td = l/Vp =282.8 ps

which gives
Vs(t)-Vs(t-2td)=0.5(Vin(t)-Vin(t-565.7 ps))

from then on I am stuck..

Any help would be appreciated.

 

[KataKoniK]

Hi there,

To calculate the NEXT and FEXT voltages, we can use the equations given in the problem statement:

KNE = Vp/4(CmZo+Lm/Zo)

VNE = KNE [Vs(t) - Vs(t-2td)]

VFE = KFE l(δ/δt)[Vs(t-td)]

KFE = 1/2(CmZo -(Lm/Zo))

First, let's calculate the characteristic impedance and velocity of propagation using the given values:

Zo = squroot(L/C) = squroot(400 nH/80 pF) = 70.71 Ω

Vp = 1/squroot(LC) = 1/squroot(400 nH * 80 pF) = 176,776,695 m/s

Next, we can calculate the NEXT and FEXT coefficients using the above equations:

KNE = Vp/4(CmZo+Lm/Zo) = 176,776,695/4(10 pF*70.71Ω+80 nH/70.71Ω) = 0.08125

KFE = 1/2(CmZo -(Lm/Zo)) = 1/2(10 pF*70.71Ω -(80 nH/70.71Ω)) = 0.035

Now, we can calculate the NEXT and FEXT voltages using the following equations:

VNE = KNE [Vs(t) - Vs(t-2td)] = 0.08125 [2 V - 2 V(t-565.7 ps)]

= 0.1625 V(t-565.7 ps)

VFE = KFE l(δ/δt)[Vs(t-td)] = 0.035 * (100 ps)^-1 * 2 V = 0.070 V

Therefore, the NEXT voltage is 0.1625 V(t-565.7 ps) and the FEXT voltage is 0.070 V.

To sketch the waveforms, we can plot the NEXT and FEXT voltages as a function of time. The NEXT voltage will have a step-like shape with a magnitude of 0.1625 V at t = 565.7 ps. The FEXT voltage will have a pulse-like shape with a magnitude of 0.070 V