[ibis-interconn] IBIS Touchstone Generalized Mixed Mode Example
- From: Bob Ross <bob@xxxxxxxxxxxxx>
- To: ibis-interconn@xxxxxxxxxxxxx
- Date: Wed, 28 May 2008 17:54:53 -0700
Hi All:
In the Touchstone discussion this morning regarding mixed mode and
genralized representations, I mentioned a recent paper:
K. Jung + 7 other authors, "A New Characterization and Calibration
Method for 3-dB-coupled On-Wafer Measurements, IEEE Trans on
Microwave Theory and Techniques, Vol. 56, no. 5, pp. 1193-1200,
May 2008
The authors include a group from Cascade Microtech and also W. R.
Eisenstadt, who was an earlier referenced co-author. The specific
application is for a power splitter or balun probe.
In the paper, Fig 6. and equations (7) and (8) show the mapping of a
3-port from SE to generalized MM representation with port order
re-positioning.
I am using uppercase A, B for the vectors and lower case for the
subscripts d, c and also for "s". Here "s" stands for single-ended.
Single-Ended Ports
B1, A1 _______
1 ----| |
| |---- 3 A3, B3
2 ----|_______|
B2, A2
Generalized (and Mixed Mode) ports where "1", etc are the new
undefined port names and corresponding vectors.
Bd1, Ad1 _______
"1" ----| |
| |---- "2" As2
"1" ----|_______|
Bc1, Ac1
So the left side is defined as differential port 1, and the right side
is re-named port 2
The authors chose a format that re-postioned the generalized port data in
a manner that could be specified as:
port order entry (using dd, cc and ss instead of D, C, S)
1 dd(1,2)
2 ss(3) (could also have used s(3) or ss(3,3))
3 cc(1,2)
where the new differential set of S-parameters are presented in the
paper as:
Sdd11 Sds12 Sdc11
Ssd21 Sss22 Ssc21
Scd11 Scs12 Scc11
Or using the original single-ended port notation:
Sd(1,2)d(1,2) Sd(1,2)s(3) Sd(1,2)c(1,2)
Ss(3)d(1,2) Ss(3) Ss(3)c(1,2)
Sc(1,2)d(1,2) Sc(1,2)s(3) Sc(1,2)c(1,2)
And with the conversion relationships from SE port data:
(S11-S12-S21+S22)/2 (S13-S23)/sqrt2 (S11+S12-S21-S22)/2
(S31-S32)/sqrt2 S33 (S31+S32)/sqrt2
(S11-S12+S21-S22)/2 (S13+S23)/sqrt2 (S11+S12+S21+S22)/2
Note, this assumes that all SE ports have a common reference, are
are referenced the same impedance R, and the default Rd=2R and Rc=R/2
referemces for MM representation.
Also note that if the original SE n-port has symetrical data (Sxy=Syx),
then the new generalized format has symmetrical data. Otherwise the
data is not symmetrical (look closely at the signs of the conversion
terms).
----
Anyway, this demonstrates independent formatting capabilities
for SE-MM conversion and for re-positioning the port data.
(Actually the "re-positioning" could be managed by index book-keeping
rather than by actually moving the data - until the final set of
formatted data is needed.)
Bob
--
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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