[ibis-interconn] Re: Mixed mode matrix definition
- From: "Dmitriev-Zdorov, Vladimir" <vladimir_dmitriev-zdorov@xxxxxxxxxx>
- To: <ibis-interconn@xxxxxxxxxxxxx>
- Date: Thu, 1 May 2008 15:19:22 -0600
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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