I. The effect of inter-section crosstalk...
(1) The coupling between serpentine sections is a strong function of
(2) The coupling generated as the main signal passes through section N
is generated mostly from sections N-1 and N+1.
(3) Because the direction of flow on adjacent sections is always opposite,
the crosstalk from N to N-1, and from N to N+1, will be near-end
crosstalk (NEXT). It will have a positive polarity. The total crosstalk
generated as a step edge passes through section N will be a short burst
of NEXT preceeding the main wave (from section N+1), followed be a short
burst of NEXT following the main wave (from section N-1). The impulse
response of the whole mess resulting from the main signal traversing
section N will look like H = [A*exp(2Ts) + 1 + (-A)*exp(2Ts)]
(4) Each section does basically the same thing, so you get a total
system transfer function that looks like H raised to the power of N,
where N is the number of trombone section (actually N-1 is more accurate
because the sections at the end are missing some side partners).
(5) Overall, what this does is to advance the appearance of the
rising edge (reduce the total circuit delay).
II. The effect of right-angle bends...
(6) There is a tiny excess capacitance present at each right-angle bend.
Since a serpentine has so many of these, it may be worth taking them into
(7) This effect will increase the total circuit delay, and slightly reduce
the effective trace impedance.
III. The skin effect...
(8) The skin effect will disperse the rising edge at the output of the
(9) The effect is to increase the total circuit delay.
Overall, my impression is that effect I is the largest, with II and III
trailing not too far behind. If you want to predict serpentine accuracy
to within 1% or better, you will need all three corrections (plus
probably some more I don't know about yet). Alternately, you could
do what many people do and just build one, and then scale to fit.
A last note concerns the relation between the trombone section length
and signal quality. As long as the delay of each individual trombone
section is less than 1/10th the signal risetime, the crosstalk is fairly
well-behaved and has only the effect of lowering the overall delay.
As the delay of each individual trombone section approaches 1/2 of
a signal risetime, the frequency response of the crosstalk effect
develops nasty resonances in the passband of your signal, resonances
that will make hash out of the resultant waveform. My advice is
to use more sections, with a shorter delay each, as needed to conform
to the 1/10th risetime rule of thumb.
I would be very interested to see any experimental results measuring
delay versus trace separation. It's clear to me that if the lines
are separated too widely, we are just wasting space on the board.
On the other hand, if the traces are too close, the crosstalk
effect shrinks the effective trace delay. Somewhere in between
there is a value that will optimize the actual amount of
delay per square inch of board area.
Dr. Howard Johnson
At 01:00 PM 2/11/98 -0500, you wrote:
>Has anyone ever tried to simulate the effect of serpentine coupled lines in
>The scenario is 6 mil lines running through many slots of 2mm shielded
>connectors. With two tracks per channel, these data traces are serpentine,
>and couple closely every time they go around ground contacts, with 6 mils
>spacing and 8 mils spacing to ground.
>I was thinking of creating 3 distinct LRC tline models and cascading them,
>any thoughts on the accuracy of this?
>These data traces are routed to vias at most slots, so there will be
>capacitive coupling from the vias also. Has anyone found this situation to
>create significant crosstalk (>3%)?
>Thank you very much,
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Dr. Howard Johnson, Signal Consulting, Inc.
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