Section: New Results

Frequency approximation and OMUX design

Participants : Laurent Baratchart, Jean-Paul Marmorat, Fabien Seyfert, Damien Pacaud [ Thales Alenia Space, Toulouse ] .

An OMUX (Output MUltipleXor) can be modeled in the frequency domain through scattering matrices of filters, like those described in section 4.3 , connected in parallel onto a common guide. The problem of designing an OMUX with specified performance in a given frequency range naturally translates into a set of constraints on the values of the scattering matrices and of the phase shift introduced by the guide in the considered bandwidth.

An OMUX simulator on a Matlab platform was designed last year and checked against a number of designs proposed by Thales Alenia Space (a.k.a. TAS). Under the terms of a contract with TAS (2007), it has been used to design a dedicated software to optimize OMUXes whose second release to TAS has taken place this year.

The software proceeds by adding channels recursively, applying to the new channel the above short-circuit and reflection-in-the bandwidth rules. This yields an initial guess for the global “optimizer” which seems to regularly outperform those currently used by TAS. More extensive tests are being conducted. A natural sequel should consist of the study of the so-called “manifold-peaks” that may impede a design based on ideal assumptions of losslesness.

A new problem was brought in by Damien Pacaud (TAS) concerning a de-embedding problem one encounters while tuning T-junction diplexers. Let S be the measured scattering matrix of a diplexer composed of a junction with response T and two filtering devices with response A and B as plotted on figure 12 . The de-embedding question is the following: given S and T , is it possible to derive A and B ? Although the question may appear classical very little seems to be known about it in the literature and among measurements specialists.

Figure 12. Diplexer made of a junction T and two filtering devices A and B

Using algebraic elimination techniques we derived the following interesting relation:

which shows that the reflexion term S_{1, 1} can be deduced, from the remaining measurements (independently from A and B ). As a consequence of this redundancy we showed that de-embedding problem, in its current statement, is ill posed. Even if additional loss-less conditions are made, the following statement holds: for every phase parameter of the transmission A_{1, 2} there exists a unique set of measurements A and B that are compatible with S and T . Moreover closed form expressions exists for the derivation A and B .

In order to overcome the ill posed character of the de-embedding problem we currently study approaches where several measuring campaigns are made, for example while varying the short circuit position of the junction T . Generalisation of our preliminary results to general multiplexers are also of great interest.