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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