[SI-LIST] Re: N-port model limitations in simulators
- From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Mon, 28 Apr 2003 10:36:24 -0700
List members -- I apologize in advance for the long post -- I'm even
including a mini-outline. You've been forewarned...
I. Reference nodes for modeling
II. Reference nodes for measurement
III. Global datum node in SPICE
Ray, et. al. -- Having independent reference nodes for each port doesn't
necessarily make your model any more accurate, since it adds no
information into the simulation. There's no loss of mathematical
generality in tying the reference nodes together, since if you want to
offset a certain voltage by a certain amount, you can do that easily
enough with an ideal voltage source. Once a system matrix is built, the
relationships between the reference nodes are folded into the system
matrix, never to be uniquely retrieved. This is why you don't choose
two nodes as reference nodes if you care about the voltage and current
relationship between them.
Taking the two port example like Ray did: If we allow the two reference
nodes to float against each other, it may be accurate if we happen to be
modeling something coupled by an ideal transformer. However, as Ray
suggested, what if the reference nodes are two nearby points on a ground
plane? Now placing one at 5V with respect to the other causes no
apparent discomfort to our model, whereas it would fry our circuit in
practice. In other words, decoupling reference nodes gives you enough
rope to hang yourself, and requires you to carry addition information
about the relationships between reference nodes if your model is to be
used accurately.
My general policy is to be very circumspect, and in fact very frugal, in
choosing reference nodes. You need to be certain that you truly don't
care how these nodes interact with each other. The ultimate in
frugality is to choose one node as reference node, which you can do
without losing any information about the device itself. This is also
the safest way, in that no outside information need be carried around
with the network regarding what is OK and not OK to do to the reference
nodes. This is because there is only one reference node, and all
relationships between all other nodes are explicit. This is what it
sounds like Brian Young is suggesting in his book, and what Arpad
alluded to some time back. This is what SPICE does -- every node but
one is a port, all ports are addressed against that single reference.
Addressing the questions Ray brought up in his original email:
1 Can't have a DC offset between the input and output ports
2 Common nodes that are physically separated can't be modeled as such
(connectors for example).
3 Can't be utilized to accurately model planes which are spatially large.
4 Can't be utilized for SSN simulations. (seems like return paths are
being ignored)
What I hear in each one of these is that there is some interest in
reasserting relationships between nodes which are being called reference
nodes. If this is the case, they should not have been reference nodes
in the first place, but should have been kept out as port nodes:
#1 To be as general as possible, there should be one reference node, and
the other three should be port nodes. Then you can place the voltage
offset across what used to be the two "reference" nodes. Your modeling
of the return path will have to be accurate, but it should have been
anyway. Having two reference nodes and two port nodes might be a
convenient approximation in this case, if you know enough information
about the AC coupling between the points, but it's not necessary, and
less accurate. Furthermore, the approximation can be accomplished using
the 2-port, 3-terminal SPICE-style multiport by using ideal voltage
sources. There's no need to offset the output reference node -- just
offset the output port node. (If you want an accompanying offset
"reference" node, you can create that as well.)
#2 Same as #1. The truth is that the return paths of the different
connector signal paths are related, even in cases where they don't share
a common ground plane. Having them all be reference nodes is
potentially inaccurate. But if the inaccuracy is OK, you can shift the
voltage source even though the multiport shares a common reference.
#3 If you truly only care about the voltage across each port at either
"end" of the plane, then sharing a common reference should be perfectly
acceptable. If you do care about the voltages between the reference
points, then one of them should not be a reference -- it should be a
port node, resulting in a 3-port, 4-terminal device. Then, if your
plane model is accurate (and I wouldn't argue that with the guys from
Sun), you will know explicitly what the fluctuations are between the two
points on the plane.
#4 Same as #3.
A quick word about two-port measurements. The same thing happens as
when you define multiple reference points in your circuit, and you don't
typically have the option of a single ground node when taking
measurements. Once you attach the two "ground" leads/sheaths to two
points in your circuit, you've stated that the relationship between them
doesn't matter to you. And your measurements will give you no
indication of the relationship. What you have to be aware of is that
you do have two physically distinct reference points. Even though they
can be subtracted in SPICE, absolute voltages between "distant" points
can't be measured without some type of de-embedding, since the
measurement setup inserts its own loading and return paths. So you
really are left with a two-port with different reference nodes.
However, it's important to remember that even though they aren't
necessarily at the same exact absolute voltage, neither can you in
general shift them at will in simulation without it becoming an
inaccurate representation of the circuit you measured. You are better
off doing simulations in which your results are independent of what the
voltage at the reference node is. If you do this, then everything is
self consistent whether the reference node is assumed to be at zero
volts or any other value.
Finally, even though this email is way too long already, I think it's
worth saying that SPICE's requirement of a global datum node is neither
mythical nor non-physical. It's actually the most general way of
representing a circuit in terms of voltage and current, since all
information is explicitly retained about the relationship between any
two points in the circuit. Where people commonly run into problems in
SI is when they fail to accurately model return paths, and instead just
assume that anything they call a "reference" node in their design is
equipotential with any other "reference" node in their design. So it's
not anything that's broken in SPICE, it's more of a "garbage in, garbage
out" issue.
-- 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
>>MIME-version: 1.0
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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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--
-------------------------------------------
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
-------------------------------------------
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