[SI-LIST] Re: why do I need mixed mode S parameters?
- From: "Sobrany RF Mr (PG/R - Electronic Eng)" <R.Sobrany@xxxxxxxxxxxx>
- To: si-list <si-list@xxxxxxxxxxxxx>
- Date: Fri, 17 Sep 2004 13:26:49 +0100
Mixed mode S parameters are what you get when you combine the method of
analysis of differential circuits developed by Middlebrook with modern
single-ended S parameter theory. A balanced circuit conveys two types of
signals, differential mode and common mode. A complete theory of operation of
balanced circuits in terms of voltages and currents and four gains was
presented by Middlebrook in his book on differential amplifiers in the early
1960s. The first two of the four gains of a balanced circuit are just gains
(but are losses if less than 1) for the differential mode signal and common
mode signal and the other two are the mode conversion gains which give a
measure of the conversion of the common mode signal to a differential mode
signal and a differential mode signal to a common mode signal.
Mixed mode S parameters describe the operation of a balanced circuit in terms
of S parameters rather than voltages or currents. The single-ended S parameter
S21 term is a measure of the gain of a single ended circuits whilst the four
Sxx21 terms of mixed mode S parameters correspond to the four gains from the
Middlebrook theory of operation.
It is possible to test a balanced circuit by directly applying a pure
differential mode and pure common mode stimulus to it and measuring the emitted
differential mode and common mode signals. This will allow a direct measure of
the four gains. A VNA which applies and measures such signals is termed a pure
mode VNA and produces a direct measurement of the mixed mode S parameters. A
balanced circuit can also be tested by applying two independent single ended
signals and measuring the two independent single ended signals and the four
gains can be calculated from the voltages and currents of these signals. Using
a 4-port VNA on a differential circuit will supply and measure single ended
signals and produce a 4x4 single ended S parameter matrix and the mixed mode S
parameter matrix can be calculated from this.
Mixed mode S parameter theory was officially developed during the mid 1990s by
Bockelman and Eistenstadt although allegedly it was developed in the early
1970s by a certain UK government department but government policy prevented
publication.
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