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

• From: Zhangkun <zhang_kun@xxxxxxxxxx>
• Date: Sat, 26 Apr 2003 08:04:57 +0800

```Dear Larry

I do not agree with you that "If you cannot define a common reference for the N
terminals, then you cannot convert the S parameters to Y or Z
parameters."

S parameter is defined by the voltage, current and impedance. Y and Z are also
defined by the voltage, current. From S parameter to Y or Z parameter, matrix
transfer is ok.

Best Regards
Zhangkun
2003.04.26

----- Original Message -----
From: "Larry Smith" <Larry.Smith@xxxxxxx>
Sent: Saturday, April 26, 2003 2:31 AM
Subject: [SI-LIST] Re: N-port model limitations in simulators

>
> 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 He then cites some historical references.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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