# [SI-LIST] Re: N-port model limitations in simulators

• From: Larry Smith <Larry.Smith@xxxxxxx>
• Date: Fri, 25 Apr 2003 11:31:20 -0700 (PDT)

Arpad - Yes, we throw around the word "port" a lot but not everybody
understands the meaning of the word in the same way.

In Pozar's book (page 216 of 1990 edition), he says

"The term port was introduced by H.A.Wheeler in the 1950's to
replace the less descriptive and more cumbersome phrase
'two-terminal pair'."

He then cites some historical references.

Ray Anderson and I have been kicking this discussion around a lot
lately.  For the measurement and definition of S parameters, we believe
that a port has two terminals.  V+ and v- (the forward and reverse
traveling waves) are measured between these two terminals.  The current
into the port goes into one of the terminals and returns back out the
other terminal.

The confusion comes when we convert S parameters to Y or Z parameters.
Brian Young has a nice diagram on page 154 of his book.  He shows a
black box with N ports, each with a voltage and a current.  The black
box has a single wire connected to a ground symbol, so the box has N+1
terminals.  I believe all voltages for this box are measured with
respect to the ground symbol terminal.  The current on the N terminals
are defined as going into the box.  No doubt the ground terminal
carries what ever current it has to in order for the total current into
the box to sum to zero (Kirchhoff).  On page 155, he talks about the Z
matrix being the inverse of the Y matrix and he makes the comment, "If
a datum node has not been defined, then the matrix inverse does not
exist."

I believe this is the source of the confusion.  For S parameters, each
port has two terminals, leading to 2N terminals for N ports.  For Y and
Z parameters, I believe there must be N+1 terminals for for N ports.
Pozar lists a bunch of conversions between S, Y, Z and ABCD parameters
on page 235.  I believe these conversions require the use of matrix
inversion and Brian's comment about a "datum node" applies to all of
these conversions.  If you cannot define a common reference for the N
terminals, then you cannot convert the S parameters to Y or Z
parameters.

If you follow this line of reasoning far enough, I believe you find
that an electrical circuit with a single reference node has a unique S
parameter representation.  But a set of S parameters (matrix of
magnitudes and phases for each port) does not have a unique circuit.
You can convert the S parameters to Y or Z parameters (for a black box
with a single reference node), but there are many circuits that could
be built that will have exactly the same port characteristics.

There are incredibly important implications for this as we try to
convert S parameter data into a black box that is to be used in a
circuit simulator.

regards,
Larry Smith
Sun Microsystems

> To: <si-list@xxxxxxxxxxxxx>
>
> I would like someone to give us a definition of "port".
>
> The reason I am asking for this is because I think there
> is an important detail that makes things confusing in these
> responses.  Is a port just one node, *assuming* a universal,
> global reference (as in SPICE node 0)?  Or does a port
> consist of two nodes, neither one of which is GND (node 0)
> between which the measurements are done with respect to
> each other?  The first one could also be called single=20
> ended, and the second one differential.  There may be far
> reaching implications depending on how we define "port".
>
> -----Original Message-----
> From: Marek Schmidt-Szalowski
> [mailto:marek.schmidt-szalowski@xxxxxxxxxxx]
> Sent: Friday, April 25, 2003 2:02 AM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: N-port model limitations in simulators
>
>
>
> Dear All,
>
> 1. N-port scattering parameters do not say anything about
>    voltages between ground terminals of different ports.  In
>    particular, they do not say whether you have a common ground
>    terminal or not.  Thus, in my eyes, S-parameters give only a
>    *partial* description of a multiport device. =20
>
> 2. Although both twoports and fourpoles have four terminals there
>    is no general one-to-one relationship between twoports and
>    fourpoles.  In case of a twoport we define 2 voltages and 2
>    (balanced) currents.  In case of a fourpole we define 4
>    voltages and 4 currents (only 3 voltages and 3 currents are
>    independent).  Thus, the fourpole formalism gives more
>    information on the device than twoport S-parameters.  In
>    particular, it is possible to define a common terminal by
>    zeroing one of the voltages.
>
> 3. Generally speaking, there is no global ground node in a
>    distributed circuit. A good microwave circuit simulator
>    defines a local ground node for each cluster of lumped
>    components.  Some simulators automatically connect the local
>    ground nodes one with each other.  Otherwise, you must connect
>    them explicitly.  You must do it cautiously or simulation
>    results will be completely wrong.
>
> 4. There are cases when the partial description of fourpole
>    offered by twoport S-parameters is not enough for a circuit
>    simulation.  Imagine a lumped twoport A (obviously having a
>    well-defined ground node) to which you connect a distributed
>    twoport B, e.g. long coaxial cable.  In this case twoport B
>    does not divide the circuit in two parts with local ground
>    nodes.  The current at both ports of the cable are in general
>    no longer balanced.  For instance the current though the inner
>    connector can be much larger then in the outer one.  However,
>    S-parameters fail to describe this kind of behavior.
>
>    Assume, that you have a lossless cable whose length is 1
>    lambda.  If you replace it with a 10 times longer cable you
>    will have still the same S-parameters but twoport A will see a
>    completely different connection between its ports.=20
>
>    Or remove the outer connector and leave the inner one.=20
>    S-matrix is now {{1,0},{0,1}}, thus no transmission.  However,
>    if twoport A gives an alternative return-current path it will
>    see some transmission.=20
>
> 5. If you simulator implements only a common-ground-node
>    S-parameter component but also a four-terminal transformer you
>    may still simulate generic S-parameters (S-parameter with
>    local ground nodes).  In order to de-couple the ground nodes
>    use an S-parameter component you have and connect a 1:1
>    transformer to one of its ports.
>
> 6. The above issues are mere consequences of a circuit theory.=20
>    The type of propagation mode (TEM, waveguide etc.) is here
>    irrelevant.
>
> with kind regards,
> Marek
>
>
> M.Schmidt-Szalowski
> Philips Semiconductors
>
>
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