## [SI-LIST] s parameters and transient simulation

• From: Geoff Stokes <gstokes@xxxxxxxxx>
• To: "'si-list@xxxxxxxxxxxxx'" <si-list@xxxxxxxxxxxxx>
• Date: Mon, 8 Dec 2003 16:45:17 -0000

```Hi Ray

With reference to your posting earlier this year regarding n-ports etc.,
here is a thought on simulation of interconnects at high frequencies where
the concept of common voltage reference nodes seems to become a bad recipe,
thinking particularly of RF modelling of IC packages.

As Khalil and Steer (paper cited below) have pointed out, the voltage
between two points is undefined in general.  This is an aspect of field
theory which becomes relevant when the frequency is high enough that the
phase delay between two points in a structure is a significant proportion of
the wavelength.  The significant proportion of course depends upon the
application, so we can't define a specific threshold frequency even for a
specific mechanical dimension.  In analog or mixed-mode circuit designs,
relatively small values of couplings or impedance may be significant, but
such values might be ignored in a purely digital circuit.  In addition, for
a correct DC simulation of the operating point and power supply currents,
together with broad band accuracy, the effect of internal inductance and
frequency dependent resistance
(both arising from skin effect and providing several percent effects) will
need to be included.

In an earlier posting, Ege Engin wrote this helpful comment:

"If an S parameter matrix is implemented in a circuit simulator, it
actually divides the rest of the circuit (all the other linear and
non-linear elements) into groups, that are only coupled to each other by
means of this S parameter matrix (due to the fact that an S parameter
matrix represents a distributed circuit). Since the voltage drops
between the local reference nodes in various groups are undefined, they
can be connected to each other in an arbitrary manner."

I would just add that in practice, from the s-parameters obtained by
electromagnetic simulation or measurement, we have to formulate a polynomial
or lumped-element solution to feed into the nodal transient circuit
simulator (Spice or Spectre).  Ege Engin's final sentence would then apply
to the interconnection of the extracted n-port model with the chip
schematic.
In Khalil and Steer, "Circuit Theory for Spatially Distributed Microwave
Circuits" (IEEE Transactions on Microwave Theory and Techniques, Vol. 46 No.
10, October 1998), we find:

"The essence of the problem is that a global reference node cannot
reasonably be defined for two spatially separated nodes when the
electromagnetic field is transient or alternating.  In this situation, the
electric field is nonconservative and the voltage between any two points is
dependent on the path of integration and, hence, voltage is undefined.  This
includes the situation of two separated points on an ideal conductor."

So we see that each port requires its own separate local return pin in order
to describe the distributed structure with sufficient accuracy over the
required frequency range.  Two or more ports can only use a common ground if
they are physically close enough to one another (for the specific case).

Finally, we make the arbitrary (?) decision to join the local ground(s) to
the common ground and hope it's OK.  From the network theory it seems OK,
but is a little hard to swallow.

Best wishes,

Geoff

______________________________________________

Geoff Stokes
Applications Engineer, Signal Management Group

Zetex plc
Tel direct:  +44-161-622-4857   Switchboard: +44-161-622-4444
Fax:  +44-161-622-4469
http://www.zetex.com <http://www.zetex.com/>
e-mail:  gstokes@xxxxxxxxx

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