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

Steve - Yes, I agree.  Y and Z parameters do not require a common
reference node to be correct.  As you and Joel Phillips (in a private
note) have pointed out, the Z and Y matrices may be singular under
certain conditions which prevent inversion.  But S parameters should be
ok.

It is not necessary to know the number of reference nodes while doing
the math to convert between S, Z and Y.  But eventually, when you get
to a circuit simulator, you have to make some choices.  In fact, I
believe the choices may have already been made when the number of
reference nodes were chosen for the circuit model.  To simulate and
interpret the results correctly the person doing the simulation needs
to know something about the assumptions that went into building the
model, or else he/she may obtain incorrect results.

I'll quit now so that I don't contribute yet another ...long... note on
this thread.  But I believe that this is an important issue that we
need to understand.  I (for one) don't understand the validity and
limitations of using S parameter models for SI simulations,
particularly where SSN and crosstalk (generated by impedance in the
return path) are concerned.

regards,
Larry Smith
Sun Microsystems

> Delivered-To: si-list@xxxxxxxxxxxxx
> Date: Mon, 28 Apr 2003 10:05:00 -0700
> From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
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> Subject: [SI-LIST] Re: N-port model limitations in simulators
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> 
> Hi Larry -- As others have pointed out, there's nothing special about Y 
> or Z or any other parametric representation which requires that all 
> reference nodes be at the same potential.  Network theory transcends 
> your decision as to what variables you want to use to characterize your 
> circuit.  In the case of voltage variables (including incident and 
> reflected voltage in the case of scattering parameters) it only asks 
> that they be referenced against known voltages.  S parameters are 
> friendly in some ways, for example because they never go infinite 
> (except at their poles), and also because you can buid circuits which 
> measure them at high frequency.  (Try designing a 50GHz ideal voltage 
> source...)  However, mathematically they are no more general than any 
> other linear combination of voltage and current.
> 
> I don't have Brian Young's book handy, but it sounds like he's stating, 
> perhaps implicitly, a property of admittance matrices -- that if there's 
> no current path from a port node to its reference node, then the matrix 
> will be singular.  Since it's singular, you can't invert it to compute 
> impedance parameters (because they don't exist -- they're infinite). 
> However, you can still convert it into its scattering parameters.  As a 
> one-port example, take an open circuit, conductance g=0.  You can't 
> invert it to get its impedance, but its reflection, which is one-port 
> scattering parameters, is 1.
> 
> I'm guessing that in Brian's book, choosing the datum node allowed all 
> port variables to have a path to their reference nodes (which in this 
> case are the same node) which makes the matrix nonsingular.  Anyway, 
> that's just conjecture since I don't have specifics.  The main point is 
> that this issue of matrix invertibility is not related to the question 
> of a single reference node vs. multiple reference nodes.  Other posters 
> have said the same thing in different ways.
> 
> I will be posting on Ray's original question soon.
> 
>    -- Steve
> 
> -------------------------------------------
> Steven D. Corey, Ph.D.
> Time Domain Analysis Systems, Inc.
> "The Interconnect Modeling Company."
> http://www.tdasystems.com
> 
> email: steven.corey@xxxxxxxxxxxxxx
> phone: (503) 246-2272
> fax:   (503) 246-2282
> -------------------------------------------
> 
> 
> Larry Smith wrote:
> 
> > Zangkun - For S Parameters, there are incoming and outgoing waves at
> > each port.  Each port has two terminals.  Voltage for the positive and
> > negative waves are measured (or inferred) across the terminals of each
> > port and there is an equal and and opposite current in each terminal
> > (return current).  The beauty of S parameters is that we do not need a
> > common reference point.  Voltages measured between ports are not unique
> > and not defined.  
> > 
> > However, For the Y and Z parameters, I believe we need a common
> > reference point in order for voltage to be defined.  If there is no
> > common reference point, then what do we measure the voltage on port 1
> > with respect to?  If there is a reference point for each terminal, we
> > don't get unique voltages.  If ports 2, 3, ... have a different
> > reference levels than port 1, I don't think the equations work.  Sure,
> > you can do the math and convert S to Z or Y matrices, but how do you
> > interpret the voltages if there is not a common reference node.  How do
> > you hook it up in a circuit simulator?
> > 
> > This gets back to the basic question that Ray asked several days ago
> > about the number of terminals for the black boxes used in circuit
> > simulators.  I think that N port boxes for Y and Z parameters have to
> > have N+1 terminals in order for the voltage to be defined at each
> > port.  Is this right or am I missing something here??
> > 
> > regards,
> > Larry Smith
> > Sun Microsystems
> > 
> > 
> >>Delivered-To: si-list@xxxxxxxxxxxxx
> >>Date: Sat, 26 Apr 2003 08:04:57 +0800
> >>From: Zhangkun <zhang_kun@xxxxxxxxxx>
> >>Subject: [SI-LIST] Re: N-port model limitations in simulators
> >>To: Larry.Smith@xxxxxxx, si-list@xxxxxxxxxxxxx, arpad.muranyi@xxxxxxxxx
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> >>
> >>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>
> >>To: <si-list@xxxxxxxxxxxxx>; <arpad.muranyi@xxxxxxxxx>
> >>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
> >>>
> >>>
> >>>>From: "Muranyi, Arpad" <arpad.muranyi@xxxxxxxxx>
> >>>>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".
> >>>>
> >>>>Arpad 
> >>>>-----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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