[ibis-interconn] Re: Mixed mode matrix definition
- From: <radek_biernacki@xxxxxxxxxxx>
- To: <ibis-interconn@xxxxxxxxxxxxx>
- Date: Fri, 9 May 2008 14:23:49 -0600
Hi Bob,
I agree with your position. I assume that the diagonal format means the same
ordering of incident and reflected waves in the respective vectors.
I'd support an additional set of MM port reference impedances under a separate
keyword. The default scenario should apply if one is specified and the other is
not. This will also imply specific requirements for the data (Ri = Rj for the
SE case, or Rd = 4*Rc for the MM case). The default should extend to the case
where no [Reference] keyword is specified - then the option line R should be
treated as SE.
The default scenario is relevant if both MM and SE matrices are present in the
file. I think we may re-evaluate our position on whether to allow MM only data
in one file.
Vladimir,
Sorry I overlooked your request for the re-normalization formulas. They are the
same as for the SE parameters. One simple way to express them is via the S -> Z
-> S transformations. Given the S1 matrix and the R1 vector we express the
matrix S2, renormalized with respect to the vector R2, as:
Z = diag(sqrt(R1j))*(1-S1)^(-1)*(1+S1)*diag(sqrt(R1j))
S2 = diag(sqrt(1/R2j))*(Z-diag(R2j))*(Z+diag(R2j))^(-1)*diag(sqrt(R2j))
Here the Z matrix is in terms of the MM voltage and current quantities.
Radek
-----Original Message-----
From: ibis-interconn-bounce@xxxxxxxxxxxxx
[mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of Bob Ross
Sent: Tuesday, May 06, 2008 2:25 PM
To: ibis-interconn@xxxxxxxxxxxxx
Subject: [ibis-interconn] Re: Mixed mode matrix definition
Hi All:
Thank you Vladimir and Radek for technical discussion, and others for
the technical contributions. This has been very helpful.
My position is
- Support adding MM or generalized MM/SE syntax
- Restrict ourselves to a "diagonal" format that we have been discussing
with explicit association of D and C entries to the SE ports and
with arbitrary re-mapped positions
- Assume the SE set of reference impedances and the Rdiff = 2R and
Rcomm = R/2 as the default relationships. Also, whether stated
explicitly or not, this appears to be the common assumption.
- [Matrix Format] would apply for both SE and generalized formats
if they are in the same file.
- Possibly consider supporting an independent set of generalized MM
reference impedances that are different from the default above
- The MM vector relationships might be more complicated
- However, the data could also be converted from/to an arbitrary
MM referece impedance set to/from a set with the default
reference impedances.
We are open to more discussion and technical consdierations.. We
also have some choices regarding the exact syntax of this addition.
Bob
Dmitriev-Zdorov, Vladimir wrote:
>
> Hi Radek,
>
> > All I am saying is that we may allow Rd to be different from 4*Rc
>
> I have no objections about allowing more general situations as long as
> it does not considerably complicates the syntax and the
> parsing/transforming tools.
>
> > 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.
>
> Although I believe I know the relations, we need to explicitly specify
> them in the accompanying document (white paper). Can you provide these?
>
> Thanks,
> Vladimir
>
>
> -----Original Message-----
> From: ibis-interconn-bounce@xxxxxxxxxxxxx on behalf of
> radek_biernacki@xxxxxxxxxxx
> Sent: Fri 5/2/2008 3:36 PM
> To: ibis-interconn@xxxxxxxxxxxxx
> Subject: [ibis-interconn] Re: Mixed mode matrix definition
>
> 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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--
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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