components and the second term represents  the high

There is no rule for selecting the best level of resolution.

frequency components of the signal (Mallat 1998).

In general, the choice is based on a priori knowledge of

In the context of crosstalk analysis, the signal in the

the signal. In our simulations, decomposition levels 2 and

disturbed line may be decomposed accordingly to (6) and

3 lead to the best results. Notice that the analysis was

the detail coefficients are analysed to get some

done on a decimated version of the original signal

information about the source line of disturbance. The

generated by XFDTD simulator by a factor of 10 because

mean energy of the detail coefficients of the wavelet

it is unnecessary to take all samples.

decomposition provides a characterization of the source

of disturbance and can be used to estimate the distance

from the disturbed line to the source of disturbance.

,9 6,08/$7,21 5(68/76

In this section, we give examples which apply the

proposed approach based on a wavelet decomposition to

crosstalk analysis. The configuration used in the

simulation is that shown in figure 1 and the crosstalk were

generated by means of XFDTD simulation program. In

the first example, a trapezoidal source voltage with a rise

time W = 0.25 QV, a frequency I = 250 0+] and a duty

cycle δ = 0.5 was applied. A trapezoidal waveform with a

rise time W = 2.5 QV, a frequency I = 50 0+] and a duty

cycle δ = 0.5 is propagating down the disturbed line. In

(a)

addition, it is assumed that the source voltage and the

signal propagating down the disturbed line have the same

phase. The wavelet decomposition of the undisturbed

trapezoidal signal at level 2 using Daubechies wavelet of

order 2 (db2) leads to a set of detail coefficients that are

equal to zero except those corresponding to an abrupt

change of the signal (Figure 5).  For different tracks

separations, the detail coefficients of the disturbed signal

are shown in Figure 6. As seen, disturbance has

introduced nonzero detail coefficients that have a

magnitude comparable to the undisturbed signal. As the

separation between the coupled lines increases, the

magnitude of detail coefficients decreases.  Thus, by

analysing detail coefficients one can get an estimation of

the  distance  separating the  coupled  line.  As  a

(b)

characterization of the perturbation, the mean energy of

detail coefficients may be used. As shown in Figure 7, the

(

variation of the mean energy of the detail coefficients

follows a roughly linear curve and then, one can uses this

energy to estimate the distance from the disturbed line to

the source of disturbance.

)

c)

LJXUH  Detail coefficients of the disturbed

signal at level 2 using db2 wavelet for different

values of the separating distance V. (a) V = 1 PP.

(b) V = 5 PP. (c) V = 10 PP.

)LJXUH    Detail  coefficients

of

the

undisturbed signal at level 2.