[ibis-interconn] Re: Mixed mode matrix definition
- From: <radek_biernacki@xxxxxxxxxxx>
- To: <ibis-interconn@xxxxxxxxxxxxx>
- Date: Fri, 2 May 2008 18:55:33 -0600
Hi Bob,
I did say:
"It is likely that the prevailing data will preserve this relationship (because
of the measurement setups), but it seems unnecessary to restrict this."
The "actual terminations" are in a broad sense of what is connected to the
black box represented by the data. During simulation the reference impedance is
a "model parameter" of the data regardless of the actual terminations. And,
regardless of how the data is set up together with the reference impedances the
external behavior of the black box remains the same.
Insisting on the reference impedances to be the actual terminations used during
the extraction process (whether hardware measurements or simulated data) is one
option and we need to make sure that it is what we want.
Just a food for thought!
Radek
-----Original Message-----
From: ibis-interconn-bounce@xxxxxxxxxxxxx
[mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of Bob Ross
Sent: Friday, May 02, 2008 4:59 PM
To: ibis-interconn@xxxxxxxxxxxxx
Subject: [ibis-interconn] Re: Mixed mode matrix definition
Hi Radek, Vladimir and All:
Just to briefly summarize, the discussion so far is based on
normalized n-port data with respect to corresponding "reference"
impedances. I would document in Touchstone the symmetrical
diagonal arbitrary ordering method in some final format to be
determined for MM and generalized representations and also would
just default to the SE [Reference] values subject to the reference
impedance constrain Ri = Rj for any MM pair and Rd = 2Ri and Rc = Ri/2.
Optinal syntax extentions such as a new mixed mode reference or
optional columns with the MM specification can be added with
syntax to be determined for any general reference impedance case.
However, unless there are some specific practical applications,
this might just be a theoretical extension where the tool would
have pre or post process the data into some other format.
So far we are assuming
Vd = V1 - V2
Vc = 0.5*(V1 + V2)
Id = 0.5*(I1 - I2)
Ic = I1 + I2
While the Sigrity syntax proposal seems to assume that other
expressions could be defined - e.g.,
Vp = aV1 - bV2
Vq = cV1 + dV2)
Ip = aI1 - bI2
Iq = cI1 + dI2
even more general, I would want to find out if there will ever
be a need to support this.
This could be a far in the future extension, if needed, along with
complex references.
---
Radek, could you elaborate regarding the difference between actual
terminations (I assume used for physical extraction) that might not
conformed to the default reference impedances. In other words,
would the physical MM extraction be done directly with Rc and Rd
termination that could be of any value?
The theoretical n-port data in S-parameter MM data would still be
extracted assuming all other ports terminated by their reference
impedances. So, I would consider the MM extraction with Rc and Rd
"load" values as if they were "reference" impedance values for
the purpose of consistent MM normalization. So I would consider
the load impedance to be the reference impedance for MM.
So why would we need a MM "load" impedance to be different from
a "reference" impedance for the purposes of expressing MM and
generalized data?
Bob
radek_biernacki@xxxxxxxxxxx wrote:
> Hi Vladimir,
>
> We should differentiate between the reference impedances and the actual
> terminations (loadings).
>
> Yes, I refer to (1) as the starting point definition. The other is the
> corresponding definition of the incident and the reflected waves with the
> respective reference impedances. All I am saying is that we may allow Rd to
> be different from 4*Rc, similarly to allowing the corresponding port
> reference impedances in the SE format to be different from one another. Of
> course, when Rd=4*Rc we get all the nice interpretation that you are talking
> about.
>
> Radek
>
>
> -----Original Message-----
> From: ibis-interconn-bounce@xxxxxxxxxxxxx
> [mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of Dmitriev-Zdorov,
> Vladimir
> Sent: Friday, May 02, 2008 1:55 PM
> To: ibis-interconn@xxxxxxxxxxxxx
> Subject: [ibis-interconn] Re: Mixed mode matrix definition
>
> Hi Radek,
>
> Yes, such transformations are theoretically possible, but isn't the
> overall issue then too complicated?
>
> Another thing. In your previous mail you said:
>
>>It looks like all we should to stick to are the mixed mode current and
>
> voltage definitions with respect to those for the single-ended ports.
>
> Such voltage/current relations are:
>
> Vd = V1 - V2 (1)
> Vc = 0.5*(V1 + V2)
>
> Id = 0.5*(I1 - I2)
> Ic = I1 + I2
>
> Now, assume that the ports are terminated with their normalizing
> impedances. Then, we can define the differential normalizing impedance
> as:
>
> Rd = -Vd/Id = -2*(V1 - V2)/(I1 - I2). (2)
>
> If the SE ports 1 and 2 have identical normalizing impedances R0 then Rd
> becomes 2 * R0 since V1 = -R0*I1 and V2 = -R0*I2. Similar, with common
> mode for which we'll get Rc = 0.5 * R0.
>
> However, if SE port impedances are different, then the very relations
> (1) make no sense. Trying to apply the same approach we'll get the ratio
> in (2) that depends on currents and voltages.
>
> That's why I think that if we agree with (1) as basic relations, we
> inevitably have
>
> Rd = 2*R0 and Rc = 0.5*R0. (3)
>
> Therefore my opinion is that we should either stick to both (1) and (3)
> or use more general extensions of both. I don't see how we can always
> follow (1) but not (3). At least, this could be confusing.
>
> Vladimir
>
>
>
>
> -----Original Message-----
> From: ibis-interconn-bounce@xxxxxxxxxxxxx
> [mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of
> radek_biernacki@xxxxxxxxxxx
> Sent: Friday, May 02, 2008 1:16 PM
> To: ibis-interconn@xxxxxxxxxxxxx
> Subject: [ibis-interconn] Re: Mixed mode matrix definition
>
> Hi Vladimir,
>
> One possible way: given your Smm data for Zref_mm=[1,2,3,4] you can
> renormalize the matrix to (Smm)' defined for Zref_mm=[1,4,2,8], for
> example. The mathematics for such a renormalization is the same as for
> single-ended S parameters. Then, following the "standard" manipulation
> you get (Sse)' for Zref[2,2,4,4]. Then, if you like it, you may generate
> (Sse)'' for Zref=[0.1, 1, 50, 100).
>
> Radek
>
> -----Original Message-----
> From: ibis-interconn-bounce@xxxxxxxxxxxxx
> [mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of
> Dmitriev-Zdorov, Vladimir
> Sent: Friday, May 02, 2008 11:56 AM
> To: ibis-interconn@xxxxxxxxxxxxx
> Subject: [ibis-interconn] Re: Mixed mode matrix definition
>
> Hi Radek,
>
> Can you show the example of using arbitrary normalizing values?
> Let us have 4x4 MM matrix and vector components ordered as
>
> [D1,2 C1,2 D3,4 C3,4].
>
> The reference impedances are:
>
> Rc1,2 = 1
> Rd1,2 = 2
> Rc3,4 = 3
> Rd3,4 = 4
>
> How then you will find the standard S-parameter matrix?
> I.e. the one that corresponds to vectors [X1 X2 X3 X4].
>
> [My preference would be always using similar values for the same pair]
>
> Vladimir
>
>
> -----Original Message-----
> From: ibis-interconn-bounce@xxxxxxxxxxxxx
> [mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of
> radek_biernacki@xxxxxxxxxxx
> Sent: Friday, May 02, 2008 12:00 PM
> To: ibis-interconn@xxxxxxxxxxxxx
> Subject: [ibis-interconn] Re: Mixed mode matrix definition
>
> Hi Bob,
>
> It looks like all we should to stick to are the mixed mode current and
> voltage definitions with respect to those for the single-ended ports.
>
> Thus, as we allow _any_ reference (real) impedances for the single-ended
> ports we should also allow _any_ reference impedances for the mixed mode
> waves, without requiring Rc=Rd/4. As for the standard S parameters which
> can be recalculated to a different set of reference impedances
> (including those with equal reference impedances for specified pairs of
> ports), the same applies to the mixed mode parameters - they can be
> recalculated to those with the ratio of 4 for the paired quantities. It
> is likely that the prevailing data will preserve this relationship
> (because of the measurement setups), but it seems unnecessary to
> restrict this.
>
> Radek
>
> -----Original Message-----
> From: ibis-interconn-bounce@xxxxxxxxxxxxx
> [mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of Bob Ross
> Sent: Friday, May 02, 2008 10:17 AM
> To: ibis-interconn@xxxxxxxxxxxxx
> Subject: [ibis-interconn] Re: Mixed mode matrix definition
>
> Hi All:
>
> I agree with the comments below and with making the Ci,j index
> ordering the same as Di,j. But we could flag that as a Warning
> in case it is different and still process it. The reason for
> the Warning it that the user may have intended to specify Dj,i.
>
> Furthermore I am assuming that the normalized S-parameter MM data
> is represented with the (real only) reference impedance constraint:
>
> Ri = Rj, Rdi,j = 2Ri, Rci,j = Ri/2. (1)
>
> This leads to the complete set of vector relationships:
>
> Aci,j = 1/sqrt(2) * ( Ai + Aj)
> Adi,j = 1/sqrt(2) * ( Ai - Aj)
> Bci,j = 1/sqrt(2) * ( Bi + Bj)
> Bdi,j = 1/sqrt(2) * ( Bi - Bj)
>
> A different normalizaton assumption might be:
>
> Ri = Rj = Rdi,j = Rci,j (2)
>
> This is described in the Ferrero and Pirola paper that Vladimir
> referenced and this changes the vector relationships to
> (their eq. 20):
>
> Aci,j = (3Ai + Bi - 3Aj - Bj) / 4, etc.
>
> Should we require the contraints in (1) to document MM and generalized
> data in Touchstone?
>
> What is the minimal set of reference impedance constraints needed
> for normalized S-parameter MM pairs?
>
> ------
>
> Symmetry:
> Assume for SE data is symmetrical (Xi,j = Xj,i). Assume the
> reference impedances satisfy (1) for S-parameter normalization.
>
> Is the MM and generalized format also be symmetrical about the
> diagonal?
>
> I assume yes.
>
> In other words, if [Matrix Format] <Upper | Lower> is used for
> SE data, it would also be used for the MM or generalized format.
>
> For a 6-port example:
>
> D2,4 fixed, sequential re-mapping in a fixed D, C, X
> order
> D5,6
> C2,4
> C5,6
> X1
> X3
>
> the generalized matrix is this
>
> Xd2d4,d2d4 Xd2d4,d5d6 . Xd2d4,c2c4 Xd2d4,c5c6 . Xd2d4,1 Xd2d4,2
> Xd5d6,d2d4 Xd5d6,d5d6 . Xd5d6,c2c4 Xd5d6,c5c6 . Xd5d6,1 Xd5d6,2
> ....................................................................
> Xc2c4,d2d4 Xc2c4,d5d6 . Xc2c4,c2c4 Xc2c4,c5c6 . Xc2c4,1 Xc2c4,2
> Xc5c6,d2d4 Xc5c6,d5d6 . Xd5c6,c2c4 Xc5c6,c5c6 . Xc5c6,1 Xc5c6,2
> ....................................................................
> X1,d2d4 X1,d5d6 . X1,c2c4 X1,c5c6 . X1,1 X1,2
> X2,d2d4 X2,d5d6 . X2,c2c4 X2,c5c6 . X2,1 X2,2
>
> Symmetry about the diagonal implies some non-intuitive (at least to me)
> relationships exist.
>
> For example
>
> X2,c5c6 = Xc5c6,2
>
> Xc2c4,d5d6 = Xd5d6,c2c4. etc.
>
> Does the symmetry relationship still exist with a different reference
> impedance assumption, such as with (2)?
>
> What is the minimal set of reference impedance constraints needed
> for SE and MM pairs for normalized S-parameter to preserve generalized
> symmetry?
>
> Bob
>
>
> radek_biernacki@xxxxxxxxxxx wrote:
>
>>Hi Bob/Vladimir/All,
>>
>>While there are some advantages of grouping all SE ports either at the
>
> beginning or at the end of the list, and have DD, DC, CD and CC
> structure for the MM ports (like case 5), I am for the second case of
> fully arbitrary arrangement (subject to Vladimir's comments) of the
> MM/SE ports.
>
>>As the common mode quantities do not depend on which node in the pair
>
> is "+" and which is "-", the meaning of C5,6 and C6,5 is the same. Yet,
> I agree, for clarity we may restrict this order to be the same as for
> the corresponding Dx,y.
>
>>Radek
>>
>>
>>-----Original Message-----
>>From: ibis-interconn-bounce@xxxxxxxxxxxxx
>
> [mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of
> Dmitriev-Zdorov, Vladimir
>
>>Sent: Thursday, May 01, 2008 2:19 PM
>>To: ibis-interconn@xxxxxxxxxxxxx
>>Subject: [ibis-interconn] Re: Mixed mode matrix definition
>>
>>Hi Bob,
>>
>>You put very important questions. I think all the ordering types
>
> listed
>
>>below should be definitely allowed. I don't see why we need any
>
> further
>
>>restriction on that. The only requirements are:
>>
>>- Input and output vectors (like A and B) are similarly ordered
>>- Each SE component in the vector appears only once, each C/D pair of
>
> MM
>
>>components appears once and each port may participate in only one MM
>>pair or not participate at all
>>- Indexes are built from port numbers use in standard mode
>>
>>As a result, the standard mode matrix can be uniquely restored from
>
> the
>
>>given matrix and given mapping
>>
>>It seems as all 5 examples satisfy these requirement.
>>
>>
>>
>>
>>Regarding your second question:
>>
>> >Would C5,6 and C6,5 be considered equivalent?
>>
>>Since mixed mode pair is produced by the relations:
>>
>>Ac5,6 = 1/sqrt(2) * ( A5 + A6)
>>Ad5,6 = 1/sqrt(2) * ( A5 - A6)
>>
>>It follows that at least D5,6 and D6,5 are not equivalent.
>>
>>Therefore, the order of indexes in each pair matters. I think we
>
> should
>
>>not allow - for clarity - the modes C5,6 and D6,5 present at the same
>>time. Of course, they are still convertible, because D5,6 = -D6,5, but
>>still, the data should be consistent. The first index stands for the
>>'positive' and the second for 'negative' in defining the differential
>>pair.
>>
>>Vladimir
>>
>>
>>-----Original Message-----
>>From: ibis-interconn-bounce@xxxxxxxxxxxxx
>>[mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of Bob Ross
>>Sent: Thursday, May 01, 2008 11:57 AM
>>To: ibis-interconn@xxxxxxxxxxxxx
>>Subject: [ibis-interconn] Re: Mixed mode matrix definition
>>
>>Hi Vladimir and All:
>>
>>I agree with your position to constrain the format per your
>>arguments and also per your other comments in item 8 that you
>>sent out earlier. This also appears consistent with Tao Su's
>>proposal.
>>
>>Also this conforms to practice in application notes and also allows
>>easily supporting generalized formats with both mixed-mode (MM)
>>and single-ended (SE) formulations. Any other MM ordering
>>should be done outside of the Touchstone format, such shown the
>>one shown in your Agilent example below.
>>
>>----
>>
>>As a practical matter, can we allow some arbitrary ordering?
>>For example using your mapping notation for a 6-port ...
>>
>>1. Arbitrary mixing of SE and MM data for generalized formats:
>>
>> X1 keeps SE locations fixed
>> D2,4 symmetrical DD and CC blocks
>> D3,5
>> C2,4
>> C3,5
>> X6
>>
>> X6 arbitrary repositioning of SE data
>> X1 and different port association definitions
>> D4,3
>> C4,3
>> D2,5
>> C2,5
>>
>> X1 keeps SE locations fixed
>> D2,3 moves MM ports into corresponding SE locations
>> C2,3 with arbitrary D, C sequencing and possible
>
> in-place
>
>> X4 teble entry calculations
>> C5,6
>> D5,6
>>
>> X1 keeps SE locations fixed
>> D2,4 moves MM ports into corresponding SE locations
>> X3
>> C2,4
>> D5,6
>> C5,6
>>
>> D2,4 fixed, sequential re-mapping in a fixed D, C, X
>
> order
>
>> D5,6
>> C2,4
>> C5,6
>> X1
>> X3
>>
>>2. C index ordering convention:
>>
>> Would C5,6 and C6,5 be considered equivalent?
>>
>> I assume the D entry depends on the stated order.
>>
>>----
>>
>>I would prefer allowing arbitrary ordering since the table itself
>>has the necessary information to identify the stored entries and
>
> locate
>
>>the position of the associated data within the Touchstone set of data.
>>
>>E.g., Sd2,4_x1 or Sx1_c2,4 only exits in some of the above formats and
>>its
>>corresponding complex data at each frequency can be extracted from the
>>file
>>with a mapping to position program.
>>
>>Bob
>>
>>Dmitriev-Zdorov, Vladimir wrote:
>>
>>
>>>Hello,
>>>
>>>I noticed that there have been several proposals - mostly in example
>>>touchstone form - that assumed the S-matrix as being asymmetrical,
>>
>>even
>>
>>
>>>for reciprocal multiports.
>>>
>>>For example, here is the definition of matrix components from Agilent:
>>>
>>>! S11 = SDD11
>>>! S12 = SDD12
>>>! S13 = SDD21
>>>! S14 = SDD22
>>>! S21 = SDC11
>>>! S22 = SDC12
>>>! S23 = SDC21
>>>! S24 = SDC22
>>>! S31 = SCD11
>>>! S32 = SCD12
>>>! S33 = SCD21
>>>! S34 = SCD22
>>>! S41 = SCC11
>>>! S42 = SCC12
>>>! S43 = SCC21
>>>! S44 = SCC22
>>>!
>>>
>>>
>>>As we see, the diagonal matrix components, such as S22 and S33 are
>>>allowed to define conversion from differential to common mode that
>>>assumes the incident and reflected wave vectors are permuted in a
>>>different way. Also, the matrix is non-symmetrical. For example, S13 =
>>>SDD21 but S31 = SCD11.
>>>
>>>In brief, the matrix specified above (Sx) does not satisfy definition
>>
>>of
>>
>>
>>>the S-parameter matrix. It can be thought as a 'true' S-parameter
>>
>>matrix
>>
>>
>>>multiplied on the permutation matrix from right or left only: Sx =
>>
>>S*P.
>>
>>
>>>The matrix S is symmetrical for all realistic interconnects but Sx is
>>>not.
>>>
>>>It would be logical not to allow such permuted matrix in the
>>
>>Touchstone
>>
>>
>>>file. It is a way easier to define and properly use the matrix S than
>>>matrix Sx. In general, there is no other way of defining Sx are
>>
>>listing
>>
>>
>>>all its components that total to NxN. For large matrices, counting
>>>hundreds of ports, such definition becomes impractical.
>>>
>>>Even in case of extreme need for allowing such matrices, there is a
>>>better way to define the ordering, that requires only 2*N instead of
>>
>>NxN
>>
>>
>>>components. But of course, it would be much better to work with
>>
>>standard
>>
>>
>>>ones only.
>>>
>>>Vladimir
>>>
>>>
>>
>>
>
>
--
Bob Ross
Teraspeed Consulting Group LLC Teraspeed Labs
121 North River Drive 13610 SW Harness Lane
Narragansett, RI 02882 Beaverton, OR 97008
401-284-1827 503-430-1065
http://www.teraspeed.com 503-246-8048 Direct
bob@xxxxxxxxxxxxx
Teraspeed is a registered service mark of Teraspeed Consulting Group LLC
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