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

• From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
• To: "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
• Date: Fri, 19 Dec 2003 10:44:36 -0800

```Hi Ege -- We may be getting hung up on nomenclature here.  What you are
calling an n-port in which the voltages between the reference nodes are
defined, is really a 2n-1 port in network theory.  If the voltages of
two nodes are defined with respect to each other, they can't both be
reference nodes.  Such a system has 2n-1 unknowns and 2n-1 equations are
required to describe it, which is what makes it a 2n-1 port.  You're
right -- arbitrarily setting nodal voltages to zero when they are
independent variables will affect the network's behavior.

You touched on this in describing an augmented system with 2n ports.
The 2n port results if you take none of the 2n nodes to be reference
nodes, and instead reference all of them against a yet-to-be-defined
reference node, for a total of 2n+1 nodes. This is what SPICE does when
you add elements (including subcircuits) to it -- it implicitly
references all of them against its global ground node.

-- Steve

Ege Engin wrote:
> Hello Steve,
> Common ground nodes are certainly not a bad recipe, if the multiport
> network represents a spatially distributed circuit such that no unique
> voltages between local reference nodes can be defined. I think this is
> the most common case.
>
> I can think of another case, where the common node approach fails. This
> issue was discussed some time ago in this list; quoted below was my post
> to the list:
>
> "As an exception, in some cases a network matrix (like the S parameter
> matrix or the impedance matrix Z) can be used to characterize a system
> whose reference nodes are close to each other, such that the voltage
> drops between the reference nodes are defined as well. In this case, the
> connections between the reference nodes cannot be done arbitrarily. A
> well-known example is an n-port Z matrix representing the partial
> inductances and resistances of an n-conductor interconnect. To implement
> this n-port Z matrix in a circuit simulator, n reference nodes have to
> be given explicitly (if all the reference nodes were connected to a
> common node, then one side of the interconnect would be
> short-circuited). If such a model does not exist in the circuit
> simulator, a possible workaround would be to create an equivalent
> 2n-port chain matrix with some math, and use this chain matrix in a
> model with a common reference node."
>
> Ege
>
> Steve Corey schrieb:
>
>>don't see where common ground nodes become a "bad recipe".
>>
>>When you take a measurement, you connect a reference conductor and a
>>signal conductor from your measurement system to the device.  By
>>connecting the reference conductor to a specific point, you're stating
>>that you don't care what the voltage is at that point -- you're only
>>interested in the difference between the reference conductor and the
>>signal conductor.  If you're taking two-port measurements, you can't
>>truly know how the voltages at the two signal nodes are varying with
>>respect to one another, since you don't know how the voltages at the two
>>ground reference nodes are varying with respect to each other.
>>
>>When you connect a receiver, be it digital or analog, to a port, you are
>>roughly making the same statement.  You don't care what any of the
>>voltages is with respect to some global ground, or some faraway port,
>>the local reference.   All these voltages are local -- theoretically,
>>the power rail, vin+, and vin- at the receiver could all be measured
>>against a single local "ground", and those are the same voltage
>>differences the device will see.
>>
>>When you drop a multiport network into SPICE, you have to be aware that
>>you're making the same assumptions.  Your simulation needs to be set up
>>-- the same way your circuit design is -- so that the behavior doesn't
>>depend on the difference between reference voltages of distant ports.
>>This is the same partitioning into "groups" that is outlined in the MTT
>>paper you referenced.  The paper does little more than to cast the logic
>>outlined above into modified nodal analysis (MNA) matrix notation which
>>casts all local references to zero volts by zeroing out their
>>rows/columns in the MNA matrix.
>>
>>The bottom line is, if you can't know the voltage between two faraway
>>points, you need to make sure that you don't care what it is -- by good
>>design, good measurement setup, good simulation setup.  It should be
>>reassuring that they all have to comply with the same set of limitations.
>>
>>   -- Steve
>>
>>-------------------------------------------
>>Steven D. Corey, Ph.D.
>>Time Domain Analysis Systems, Inc.
>>"The Interconnect Analysis Company."
>>http://www.tdasystems.com
>>
>>email: steven.corey@xxxxxxxxxxxxxx
>>phone: (503) 246-2272
>>fax:   (503) 246-2282
>>-------------------------------------------
>>
>>Geoff Stokes wrote:
>>
>>>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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>>
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--
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Analysis Company."
http://www.tdasystems.com

email: steven.corey@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax:   (503) 246-2282
-------------------------------------------

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