## S-, h-, T-, Y-, Z-, ABCD- Parameter Conversions^{1}, I felt it was my duty to publish it for
public access. The paper is available on the IEEE website by subscribers only. Other have published the full paper
without permission of author Frickey. None that I found also include the correction paper^{2}
published a year later that address some of the technicalities of the S- and T-parameter translations when complex
impedance reference planes are used. In order to avoid those sticky issues, I have reproduced only the sets of
translations that are unaffected. Many thanks to Mr. Frickey for his unique work.One of the most sought-after sets of conversion is from s-parameters to T-parameters, and then back to s-parameters. This is because matrix multiplications can be performed directly on T-parameters in order to calculate cascaded component responses. That is, s-parameters matrices cannot be multiplied in series to obtain cascaded s-parameters, but T-parameters can be. So, convert your component s-parameters to T-parameters, multiply matrices, then convert the result back to s-parameters.
All of the parameter equations make use of complex values for all numbers of impedance and the resulting matrix parameters, i.e., Z = R ± jX. Z _{01} and Z_{02} are the complex impedances of ports
1 and 2, respectively; similarly, Z*_{01} and Z*_{02}
are the complex conjugates of the respective impedances.The values R _{01}
and R_{02} are the real parts of port impedances Z_{01} and Z_{02}.If you do not already know, here is the meaning of each type of parameter matrix: S (scattering), Y (admittance), Z (impedance), h (hybrid), ABCD (chain), and T (chain scattering or chain transfer). These are all I have, so please do not write to ask if I have others.
Conversions Between S, Z, Y, h, ABCD, and T Parameters which are Valid for Complex Source and Load Impedances. By Dean A. Frickey, Member, IEEE 2. IEEE Transactions on Microwave Theory and Techniques. Vol 43, No 4. April 1995. A correction was printed by Roger B. Marks and Dylan F. Williams. 3. I _{1} formula corrected to use V_{2}
rather than V_{1}. Thanks to Christoph T. for noticing.
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