How Do NEXT and FEXT Impact Signal Integrity in PCB Transmission Lines?

[MrBondx]

Homework Statement

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 Ohms. The line can be assumed to be lossless.

a) Use the following equations:

VNE = KNE[Vs(t) - Vs(t - 2td)]
KNE = (Vp / 4)[(CM * Zo) + (LM / Zo)]

VFE = KFE * l * (d / dt)[Vs(t - td)], where l is the length of the line.
KFE = 1/2[(CM * Zo) - (LM / Zo)]

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)] .]

CM and LM are, respectively, the mutual capacitance and inductance per metre length.[ mentor note: no success adding image inline; so readers must click this thumbnail to see larger image ]

b) Sketch the NEXT and FEXT waveforms.

Homework Equations

[/b]

VNE = KNE[Vs(t) - Vs(t - 2td)]
KNE = (Vp / 4)[(CM * Zo) + (LM / Zo)]

VFE = KFE * l * (d / dt)[Vs(t - td)]
KFE = (1 / 2)[(CM * Zo) - (LM / Zo)]

The Attempt at a Solution

[/b]

Calculate for Zo and Vp

Zo = 70.71

Vp =176776695.3

Then plug in numbers to find KNE

KNE = 3124970032 ( number looks massive not sure if it's right)Getting stuck on finding VNE

Not sure if t = rise time. Is Vin = 2? How do I find td?

Thanks for your help in advance.

[ mentor note: excessive bold text corrected ]

 

[Asim Riaz]

Solution:a) Calculate Zo and Vp:Zo = 70.71 ΩVp = 1/√(L*C) = 1/√(50e-3*C) = 176776695.3 m/sCalculate KNE:KNE = (Vp / 4)[(CM * Zo) + (LM / Zo)] = (176776695.3 / 4)[(0.2 * 70.71) + (2e-3 / 70.71)] = 3124970032Calculate VNE:VNE = KNE[Vs(t) - Vs(t - 2td)]Let Vin = 2V, then Vs = Vin * (Rin / (Rin + Zo)) = 2V * (70 / (70 + 70.71)) = 1.9998VWhere td = rise time = 100ps = 0.0001s.At t = 0, Vs(t) = 1.9998VAt t = 2td, Vs(t - 2td) = 1.9998V since there is no change in voltage during the rise time (100ps).Therefore, VNE = KNE[Vs(t) - Vs(t - 2td)] = 3124970032 * (1.9998 - 1.9998) = 0VCalculate KFE:KFE = 1/2[(CM * Zo) - (LM / Zo)] = 0.5[(0.2 * 70.71) - (2e-3 / 70.71)] = 7124850.16Calculate VFE:VFE = KFE * l * (d / dt)[Vs(t - td)]Let l = 50e-3m, thenVFE = 7124850.16 * 50e-3 * (d/dt)[Vs(t - td)] = 7124850.16 * 50e-3 * (d/dt)[1.9998] = 7124850.16 * 50e-3 * 0 = 0Vb) Sketch