WEBVTT

Slide 1:
Hello. I'm going to discuss matrix parameters in Touchstone.

Slide 2:
Agenda is to discuss goals, and Touchstone format differences that are designated as V1.0, 1.1, 2.0 and 2.1.
The per-port reference impedances are designated as resistances.
Shown are n-port matrices S, Y, and Z and conversions and 2-port matrices H, G and their conversons,
Finally a conclusion is presented.

Slide 3:
Regarding goals, we are preparing a new Touchstone Version 2.1 document.

I'll discuss some of its contents.  I'll show some conversion mathematics when we have different per-port
reference impedance.  A new TSCHK2.1 parse should handle the conversion mathematics.

Note that the reference impedance is designated as resistances because complex references are not supported.

Slide 4:
The Touchstone Version 2.1 document will contain 4 formats.

The first two are designated as Version 1.0 and 1.1.

These formats are not keyword based, they're based on strict formatting rules.

Version 1.0 the original Version supports only a single port reference resistance in the option line beginning 
with #, the R value, and that other possible entries.

Version 1.1 adds per-port reference resistances that have to be positioned at the end of the option line with
the syntax at the end of the options line the R and then a list of resistor values.

Now, S-parameter matrix are defined based on the option line resistance entries and are the same as before.

All other matrices are normalized regardless of the option line entries.

As an example, R, if R = 50 ohms, then Z11 might be 1 in a Version 1.0 Touchstone file if the measured value
is Z11 equals 50 ohms.

Per-port reference resistances are already supported by several EDA tools, but they may have different formats.

Slide 5:
The last two formats in the Version 2.1 document are designated as Version 2.0 and 2.1.

A keyword, [Version] 2.1, is added and permitted, but all other matrix data is identical.

S-parameter matrices remain unchanged from the Version 1.0 and 1.1 formats and are based on reference resistance
entries.

The Y, Z, H, and G parameters are un-normalized and are sensitive to the reference resistance values, as if
measured directly in ohms or siemens (which you may be familiar with as the the unit for mhos).

In Version 2.0 and 2.1, a [Reference] keyword exists that lists reference resistances on a per-port basis.

The advantage of the Version 2.0 and 2.1 formats is that the reference values can wrap for easier readability.
This is unlike in Version 1.1 where all reference values are on a single line.

Slide 6:
TSCHK2.0 supports conVersions between Version 1.0 and 2.0.

The help menu shows canonical, canonical -v2, and canonical -v1.

I would have preferred "conversion" but "canonical" is what is used. 

The canonical -v2 flag upgrades a Version 1.0 file to a Version 2.0 by adding keywords for [Number of Ports],
[Number of Frequencies], and other keywords that are extracted from the Version 1.0 file from through its
strict formatting rules.

All Version 1.0 files can be upgraded to Version 2.0.

The canonical -v1 flag can downgrade a Version 2.0 file to a 1.0 file, if possible. Some keywords in Version 2.0
are not supported in the Version 1.0 syntax.

A TSCHK2.1 parser should be expanded to support Version 1.1 and 2.1 conVersions.

That's what we will be specifying.

Slide 7:
Regarding the conversion mathematics, I'm using this notation.

If there's no superscript, we're describing normalized parameters, as might occur in Version 1.0 and 1.1 formats.

If a superscript "U" exists, it's for un-normalized data, as would exist in Version 2.0 and 2.1 formats.

And except for Version 1.0, all formats can support per-port reference resistors along with a R single reference
resistance.

Slide 8
The formulas for a general N-port Z matrix conversion or based on lecture notes by Jose Schutt-Aine given in the
reference below, in the uploaded course and slides 28-29.

The formulas are restated using the notation in this presentation.

k is a square diagonal matrix whose elements are square root of r1 through rn, where these are the reference
resistors of these ports, and this is based on power wave per-port normalization between incident and reflected
waves for S-parameters, b = Sa.

The Z matrix conversion from S-parameters is based on this formula, as shown

I is the unit matrix.

And so (I + S) * inverse of (I - S) converts to Z matrix if the reference resistance is 1.
The general formula shows that the un-normalized Z matrix has the k matrix (aa square matrix) that
pre- and post-multiplies the first formula and produces k * Z * k.

And it turns out that the multiplication by the diagonal matrix k produces, on a term by term basis, 
Z un-normalized I,J equals Z normalized I, J times the square root of ri rj reference resistances.

Slide 9:
The multiplication is demonstrated here.

The last two terms are shown that the j-th column times the j-th column of the Z matrix to produce kj times the
j-th column terms.  Actually all the terms are shown.

So, the first column k1 and the last column kn are shown.

And then the pre-multiplication by the i-th value produces the i-th row changes, and I also show the first row
and n-th row changes, but of interest is the ki * zi,j * kj term equal to zi,j * square root of ri * rj.

This is the conversion formula to change normalized to un-normalized Z parameter data.

Slide 10:
So, the Z conversion formulas are summarized showing the ri*rj scaling, square root of those actually, and the 
same for the Y conversions.

Note in 1.0 and 2.0, only a single reference impedance is used, and this assumes ri equals rj.

Secondly, Version 2.0 cannot be down converted to 1.0 if ri is not equal rj. This will be upgraded in the new
TSCHK2.1 parser, where if ri is not equal to rj, the Touchstone file can be converted to a Version 1.1 format.

Slide 11:
Finally, the two port H-parameters can be converted with reference resistances that don't need the square root,
and the off diagonal terms are not converted, because they represent gains, and therefore, there's no scaling.

Slide 12:
The same applies for the G-parameters.

The off-diagonal terms do not need to be converted, but the diagonal terms need to be converted using the
reference resistances directly.

Slide 13:
So, in conclusion.

I've described differences in formats Version 1.0, 1.1, 2.0, 2.1, for an upcoming Touchstone 2.1 document.

The main difference is that Version 1.1 contains a new option line syntax that supports per-port reference resistances.

I've shown briefly transformations between normalized and un-normalized matrix data, for different per-port reference
resistances  This presentation is targeted for a TSCHK2.1 parser developer, but it's also shown for the audience here
for general interest

Are there any questions?
