[ibis-interconn] Re: Why is not the contents of Touchstone file not Transfer Functions
- From: Bob Ross <bob@xxxxxxxxxxxxx>
- To: "Dmitriev-Zdorov, Vladimir" <vladimir_dmitriev-zdorov@xxxxxxxxxx>
- Date: Thu, 16 Jul 2009 11:39:11 -0700
Hi Vladimir:
Good discussion, and you raise some specific cases where we could "legally"\
apply a name, a name with modifiers, or a different name.
I would have to re-read the Touchstone document just to look at
precise application of terminology. However, I think we did a
good job, and we also chose to maintain the original (generic)
terminology, as an accepted terminology without considering
whether it might be technically incorrect or incomplete in some
rigorous sense.
For me, the primary guidance for terminology is the technical
literature (books, technical papers, articles, vendor application
notes, etc.). Several terms are used, and X-parameters
and X-matrix are often used.
With respect to the sparse problem, the proposals document
index mapping from locations (of a reduced collection of complex-values)
to the full (or upper-half or lower-half) matrix indices which
happen to correspond to the implicit port numbers or just matrix
positions (for mixed mode order). So we are not even
concerned about the meaning of the entries.
Bob
Dmitriev-Zdorov, Vladimir wrote:
Hi Bob,
Mathematically, we can call S/Y/Z parameter matrices 'transfer functions' or
'transfer characteristics'. They all could be unambiguously derived once the
vector or excitations X and vector of responses Y are defined. Then, transfer
functions become matrices, with entries being either complex value functions of
frequency, or real value functions of time, or sampled dependences defined on
frequency or time. (Since function is a quite broad concept, a synonym for
'mapping' so that it maps one set to another. The set could be continuous or
discrete therefore sampled dependence also falls under definition of function).
No doubts that we all in this forum exactly understand every word when
discussing the structure and content of our data files. This is good but also
poses some danger.
From practical point of view we should select the terms easily understood by majority of
engineers and avoid those even legal expressions that could be misunderstood. Here, we
may use the words 'function' or 'transfer' function to denote only continuous functions
given analytically or assumed being continuous before they were sampled. In this sense,
the 'sampled transfer function' should be a legal term for the content of the Touchstone
files. But we can also call it 'sampled dependence'. As to terms "matrix and
vector", we may also need some convention here. For example, through the documents,
we should consistently apply the term 'sampled transfer function' or 'sampled dependence'
only to scalar complex dependence, or, to a single entry of the frequency-dependent
matrix (S/Y/Z or others). Then, the matrix should be called the 'matrix of sampled
dependences' for the case of sampled (Touchstone) and or 'matrix of transfer functions'
for analytical (e.g. pole-zero or other)
representations respectively. In general, a matrix may not necessarily be
square, and so is the matrix-value transfer function (if the # of excitations
and responses are different). However, here we are only dealing with square
matrices assuming that the size of input and output vectors is the same (or do
we need more generality here? I'm not sure, because square-ness follows from
definitions of S/Y/Z etc. parameters).
Some confusion is also associated with the word 'vector'. Most logically, the
only two vectors we should deal with here are the vector of input excitations
and the vector of responses, both sized to the number of ports. For
S-parameters, they are vector of incident and reflected waves (A and B).
We should avoid applying the word 'vector' to the collection of frequency
samples that e.g. describe S(1,1). We understand that the term 'vector' is of
course valid here, but let's not use it in this sense. Also, we should not call
vector the rows and columns of the matrix.
The word 'parameter' in our context should then be only associated with the
type of data we consider: S/Y/Z, ABCD, G, H, etc.
Even if we won't be able to always follow the convention, it would be desirable
to reduce the ambiguity as much as possible.
Vladimir
-----Original Message-----
From: ibis-interconn-bounce@xxxxxxxxxxxxx
[mailto:ibis-interconn-bounce@xxxxxxxxxxxxx] On Behalf Of Bob Ross
Sent: Wednesday, July 15, 2009 2:10 PM
To: Walter Katz
Cc: IBIS-Interconnect
Subject: [ibis-interconn] Re: Why is not the contents of Touchstone file not
Transfer Functions
Walter:
From a strict reading of the definition, you could draw the
conclusion that a particular Xij parameter over a frequency
range defines an input/output relationship, and therefore
could be designated as a "transfer function."
However, I am still not comfortable with "transfer function"
in the context of N-port parameter descriptions for many
reasons.
1. Common practice - I have not seen anyone else refer to the
N-port parameter Xij terms as "transfer functions," either at
a single frequency or as the collection of terms for that
particular Xij entry. We should stick with commonly used
terminology.
2. Single function - While the definition could be expanded to
a matrix input/output relationship, the language implies a single
output produced by a single input and seems to imply the functional
mathematical relationship. The Xij entry at one frequency is
the transfer function of j to i at that frequency only when
the other inputs of the matrix - all other ports are terminated.
From the matrix perpective, the output is a function of multiple
inputs. Also the functional relationship might imply a
collection of such Xij(f) for each frequency individually or
for the whole set of frequencies for the Xij term.
3. Transfer Function - this seems as a mathematical expression (referred
to as complex exponentials) as opposed to the specific data entries or
quanties on a per-frequency basis in the definition. I read that
to mean a mathematical function relatinship as opposed to
a collection of terms.
4. Filter design practice - I recall a distinction in (driving
point) impedance/admittances for the same terminal versus
a transfer function gain/(trans)impedance/(trans) admittance for
different physical terminals. That is the terminology conflict
in a related field.
------
Anyway, I think finding terms that are used in common practice for
S-parameters and N-port parameters entries and distinguishing whether
we are describing a specific entry at one frequency or a set of Xij
entries for all frequencies is better practice.
Bob
Walter Katz wrote:
All,
See http://cnx.org/content/m0028/latest/ for better graphics.
Is not the Touchstone file exactly this?
The ratio of the output and input amplitudes for Figure 1
<http://cnx.org/content/m0028/latest/#rc#rc>, known as the transfer
function or the frequency response, is given by
Vout
Vin
=
H(
f)
=
1
ⅈ2πfRC
+1
(1)
Implicit in using the transfer function is that the input is a complex
exponential, and the output is also a complex exponential having the
same frequency. The transfer function reveals how the circuit modifies
the input amplitude in creating the output amplitude. Thus, the transfer
function completely describes how the circuit processes the input
complex exponential to produce the output complex exponential. The
circuit's function is thus summarized by the transfer function. In fact,
circuits are often designed to meet transfer function specifications.
Because transfer functions are complex-valued, frequency-dependent
quantities, we can better appreciate a circuit's function by examining
the magnitude and phase of its transfer function (Figure 2
<http://cnx.org/content/m0028/latest/#magphase#magphase>).
Walter
Walter Katz
Chief Scientist
Signal Integrity Software, Inc.
wkatz@xxxxxxxxxx
303.449-2308
--
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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