[SI-LIST] Re: passive but not reciprocal network
- From: Scott McMorrow <scott@xxxxxxxxxxxxx>
- To: Al Neves <al@xxxxxxxxxxxxxxxxx>
- Date: Mon, 25 Nov 2013 11:43:23 -0500
Let me point out a few additional things about causality of measurements
and EM simulation.
Most of our "concepts of causality" are based on the assumption that there
cannot be a pulse or step response at the receiver prior to T=0. However,
T=0 at the receiver is generally either not well defined, or assumed to be
the point at which the first wavefront on the interconnect propagates from
the transmitter to the receiver in the dielectric medium. Using the T=0
definition of causality, it is the fastest propagation path in the
interconnect measurement or full wave model that defines where T=0 at the
receiver is. The fastest propagation path is often a direct line of sight
path through the board, but it need not be.
There are many cases in measurements and full wave EM extractions where the
path that you think you are measuring is not the only path that is being
measured. For example, take two SMA connectors and place them on two ends
of a straight trace, and make a measurement. What you are measuring is a
2-port s-parameter that is the result of multiple propagation paths. The
primary and dominant path will be along the trace. If we are able to make
a "perfect" measurement then we will "see" just that trace. However,
measurements are never perfect. There are leakage paths in the test
equipment, cables and connectors, however small. These represent causal
propagation between the two ports, but are measurement artifacts. Two
cables placed against one another such that there is some slight coupling
will be seen as non-causal noise. When transformed to the time domain it
will be seen as non-causal noise. This noise should be reduced to
extremely low levels in the measurements, and should be filtered in
modeling.
There are additional modes of propagation that may "appear" non-causal, but
in fact are absolutely causal. For example, that SMA connector launch may
have vias that penetrate the planes of the PCB. Some signal energy will be
lost to excitation of the planar cavities. That planar energy will be
picked up at the far end SMA-via, and will be included in the measurement.
The propagation path is real, it is causal, and it will contribute out of
phase noise to the received primary signal. The s-parameters produced from
these measurements, or electromagnetic extraction, are valid and
informative, with the caveat that you "meant" to measure the via excitation
of the cavities. If this was not the case, then it represents an error.
Now take the same trace, and rather than keep it straight, place the two
SMAs directly adjacent to each other, and loop the trace around the board
with the same length. All of the previous propagation paths exist, yet now
the SMA-via to SMA-via planar cavity path is shorter. Significantly shorter
than the path across the trace. S-parameters produced from these
measurements, or electromagnetic extraction, are valid and informative.
Yet, they appear to be non-causal. The step or impulse response created
from this s-parameter will have some "noise" or "lift off" prior to what
appears to be T=0. Depending on how well the vias are shielding by ground,
the amount of noise, and resonance peaked noise, can be quite high. If
that "noise" were filtered out of the impulse response, or removed by some
causality correction algorithm, the result is now "non-real." In some
cases this might just be poor design of the measurement platform. In other
cases, it may reflect the reality of the actual design. An example of the
later would be traces on a backplane that travel between two adjacent
connectors that are 700 mil apart, but require a minimum trace length of 2
inches. The cavity wave will most definitely arrive before the primary
signal wave does.
--
Scott McMorrow
Teraspeed Consulting Group LLC
16 Stormy Brook Rd
Falmouth, ME 04105
(401) 284-1827 Business
http://www.teraspeed.com
Teraspeed® is the registered service mark of
Teraspeed Consulting Group LLC
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