crosstalk has a larger magnitude (0.4 V) and a longer

interferences. The paper is organized as follows. In

duration than the far-end crosstalk. As the length of the

section II, the crosstalk simulation is presented. In section

parallel lines increases, the crosstalk becomes more

III, we consider the problem of crosstalk analysis by

important and can results in many problems related to the

means of a wavelet decomposition. In section IV, we give

signal integrity.

some examples to illustrate the wavelet approach in

analysing crosstalk, and finally, conclusions are drawn in

section V.

line 2

ine 1

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Several simulation programs for crosstalk computation

have been developed (Weston 2001). To compute the

crosstalk by means of SPICE simulation program, a

numerical field solver program is required to obtain the

l

electrical parameters that characterize the line. In this

)

paper, the XFDTD simulation program has been used to

compute crosstalk. The XFDTD simulator uses the

method of finite difference time domain (FDTD) to solve

the time-dependent Maxwell' s equations (Pothecary and

Railton 1991, Xiao et al. 2001). The curl equations are

/

K

given by (Clayton 1999)

%

&

∇x( = -

& &

(1)

W

'  &

&

∇x+ =

+-

& &

(2)

ground

W

Z

V

where ( represents the electric field i& tensity vector,

n

LJXUH  Two parallel coupled tracks on a PCB.

*

% denotes the magnetic flux vector, + represents the

)

&

magnetic field intensity vector, ' represents the electric

&

flux density vector and - represents the current density

&

vector. Equations (1) and (2) are solved at each time step.

The three-dimensional simulation space is divided into

elementary cubical elements known as Yee cells. The

electric and magnetic fields are computed at points on a

grid composed of the Yee cells.

In order to examine the crosstalk phenomenon, two

parallel coupled tracks on a dielectric board characterized

by a permittivity ε with a ground plane on the opposite

side has been simulated (figure 1). In a typical situation, a

source voltage 9V(W) that has a resistor 5 is connected to a

load 5  via the first track and the ground. Two

LJXUH  Disturbed Signal.

terminations 5  and 5  are connected to the second

track at the near end and the far end. The circuit

associated to the source voltage is known as the generator

circuit and the circuit corresponding to the resistors 5

and 5  is named the receptor circuit. The generator

circuit will interact with the receptor circuit by generating

electromagnetic fields giving rise to an induced crosstalk

9 (W) and 9 (W) in the near-end and far-end terminations

of the receptor circuit. To illustrate the crosstalk

phenomenon, consider two parallel tracks on a PCB with

the following parameters: ε = 4.7, Z = 2 PP , V = 2 PP ,

/ = 10 FP and K = 1.5 PP. A trapezoidal source voltage

(figure 2) with equal rise time and fall time of 0.25 QV, a

frequency of 250 0+], a duty cycle δ = 0.5 and a source

resistor of 50 Ω was applied. The resistors 5 , 5  and

5 are equal to 50 Ω. The predicted near-end and far-end

)LJXUH  Near-end Crosstalk.

crosstalk using XFDTD simulator are shown in figure 3

and figure 4, respectively. As shown, the near-end