PCB Crosstalk Simulation Toolkit
Overview
The simulation primitive elements in the library "pcb" enable simulation
of the PCB track elements described in this paper.
The PCB track is represented by a lumped equivalent circuit, after the paper by Ladd & Costache, IEEE Trans. on Circuits & Systems, Vol 39 No 6 June 1992. The transmission lines formed by PCB track can be broken up into electrically short segments, such that the segment length is less than or equal to onetenth of the wavelength of interest. Then, the distributed parameters of each segment can be replaced by a series inductor or shunt capacitor, as may be seen in the drawing '2cm'. The crosstalk effects modelled, include electrostatic and electromagnetic coupling between the tracks. Also, since the current in each segment can be measured, the current distribution along the line can be simulated. This means that the electric field emanating from the track can also be estimated, at various distances from the board. The base module has been chosen to be two such lumped (1cm) segments, representing a 2 cm length of two parallel tracks. Two forms of this are supplied. One is '2cm', which has a third (ground) conductor midway between the transmitting track and the receiving track. The other is '2seg', which omits the third conductor. The examples, '10seg' and '10cm', represent a 10cm section of parallel track, made up of five 2cm segments. They differ in that '10seg' is a twotrack test circuit, while '10cm' is a threetrack circuit. The tracks are 2.5mm wide, and have (w / h) set at 1.58 such that the characteristic impedance is 58 ohms. The tracks are set 7.5mm apart, from inside edge to inside edge, on a glass epoxy PCB, with a dielectric constant of 4.7. The circuit values have been calculated from distributed parameter data, obtainable either from the PCB manufacturer, or from finiteelement analysis. The drawing 'via' is a plated through hole, assumed to be solid copper, of height 1.588mm, and radius 0.1mm. The equations for calculating the five terms of the LR series representing the hole are on the drawing. The via is for use with 2cm, for grounding the central conductor at the appropriate intervals which, for optimum crosstalk suppression, are:
Dvia < 1 / (4 * fMAX * sqrt(Ue)) MODEL PARAMETERS The lumped model parameters for the PCB tracks are derived from the distributed parameters by multiplying by the line length and dividing by the number of segments. The perunitlength parameters for tracks of the above dimensions and spacing are as follows:
Parameters For Three Track TopologyFrom the above, the value of inductors L1, in the transmitting line:
L1 = (L11 / 100) / 2 = 3.637 / 2 nH (as there are 2 per cm) = 1.8185nH For all inductors L2, in the receiving line:
L2 = (L22 / 100) / 2 = 3.637 / 2 nH (as there are 2 per cm) = 1.8185nH And for inductors L3, in the ground conductor:
L3 = (L33 / 100) / 2 = 4.052 / 2 nH = 2.026nH The inductive coupling coefficients, from each line to the ground conductor, are given by:
kij = Lij / (sqrt(Lii * Ljj))
Thus, K13 = L13 / sqrt(L11 * L33) = 42.2e9 / sqrt(363.7e9 * 405.2e9) = 42.2e9 / 383.8896e9 = 0.109927 And
K23 = L23 / sqrt(L22 * L33) = 42.2e9 / sqrt(363.7e9 * 405.2e9) = 42.2e9 / 383.8896e9 = 0.109927 Since there is only one capacitor per 1cm segment, the capacitor values are:
C1 = C10 / 100 = 0.919pF C12 = C12 / 100 = 0.00185 pF C13 = C13 / 100 = 0.043 pF C2 = C20 / 100 = 0.919 pF C23 = C23 / 100 = 0.043 pF C3 = C30 / 100 = 0.795 pF Parameters for Two Track Topology (No Gnd Line)With just two tracks, the values all need to be recalculated from the figures in the first column:
L1 = (L11 / 100) / 2 = (374.2 / 200) nH = 1.871 nH L2 = (L22 / 100) / 2 = (374.2 / 200) nH = 1.871 nH The only inductive coupling is now from L1 > L2, so
K12 = L12 / sqrt(L11 * L22) = 13.22e9 / sqrt(374.2e9 * 374.2e9) = 13.22e9 / 374.2e9 = 0.0353287 THe new capacitances are:
C1 = C10 / 100 = 0.953pF C12 = C12 / 100 = 0.00459 pF C2 = C20 / 100 = 0.953 pF
SimulationThere are two meaningful analyses which may be performed on the circuit as it stands. AC AnalysisThe frequency range of interest is from 5 MHz to 1 GHz, and the resolution should be set to around 200 points per decade. Driving with a 1 volt AC source provides a reference level to which the output crosstalk can be related. It is instructive to plot the voltages at both ends of all tracks, but the only important waveforms are at the near and far ends of the receiving track. The response shows a rising characteristic, with two points of inflection. The first is situated at approximately 600MHz for the nearend response, while the second occurs at around 930 MHz. The farend curve rises more steeply, the first inflection point being at around 420 MHz, and the second at 800 MHz. Note that the curves for twotrack topology will show more crosstalk than those for threetrack. A special drawing, '10cm2via' simulates the case where the ground conductor is only provided with a via at each end. An analysis of this circuit shows a large resonance peak at around 800MHz, this being the frequency for which 10cm is a quarter wavelength. Taking the propagation velocity as 3.16e10 cm/sec:
3.16e10 = f * 40 f = 790 MHz Transient AnalysisThe timedomain measurements are made on the near end of the receiving track. The analysis is set up to sweep 0 to 80n in 10ps steps. The transmitting track is driven by a rectangular pulse, defined by
pwl 0 0 1n 0 6n 1 40n 1 46n 0 80n 0 The results show two pulses in the nearend waveform, both 5ns wide, coincident with the rising and falling edges. The magnitudes are about 400800uV for the positive pulse, and 500650uV for the negative one.
IMPORTANT NOTE:To speed up the analysis, you should not include the parameter TMAX in the specification of the .TRAN line Also, the use of ".options method=gear" will remove the spurious oscillations. Although this is a wellknown standard precaution for LC simulations, it does no harm to mention it.
