Abstract:

Radiofrequency (RF) and microwave design techniques are commonly based on the scattering (S) parameters approach. Classic undergraduate and graduate text books such as the ones by D. Pozar [1] or G. Gonzalez [2] rely on this theory, which is indeed a high frequency version of linear circuit theory and network analysis or, more accurately, its adaptation for propagating voltage and current waves.

S-parameters are not only relevant for circuit analysis [3], characterization and design purposes, but also useful to describe a circuit in a phenomenological way. While the teaching potential of this approach is clear as, essentially, most of the characterization schemes for RF circuits are based on them, S-parameters fail when working with non-linear circuit and devices.

Some alternatives as large signal S-parameters or multi-frequency S-parameters, are then needed to deal e.g. with mixer design or large signal device operation. Among the potential characterization schemes for non-linear systems, highlight the so-called X-parameters [4] due to their ability to include non-linear performance while being completely compatible with the linear S-parameters, i.e., the X-parameters of a linear device coincides with its S-parameters.

The fact of keeping some of the properties of their linear version, is a relevant advantage from the perspective of Bachelor or Master level students who are still developing their RF abilities. In this context, X-parameters are extremely useful to comprehend the importance of the non-linear modelling, while still allowing S-parameters to be the battle horse for circuit design.

In this work, we propose a simple teaching experiment, based on the simulation, fabrication and characterization of the X-parameters of a non-linear circuit based on a RF commercial diode. Employing a Keysight PNA-X [5], which should only be used under the supervision of experts, the students can explore the convergence of S- and X-parameters for low power signals (and the corresponding divergence for large input power), while exploring the file system and mathematical complexity of the X-parameters.

References:
[1] D. M. Pozar. Microwave and RF Wireless Systems. John Wiley & Sons. 4th Ed. 2013. ISBN: 978-0-471-32282-5.
[2] G. González. Microwave Transistor Amplifiers: Analysis and Design. 2nd Ed. 1996. ISBN: 978-0132543354
[3] PathWave Advanced Design System (ADS) – Keysight. https://www.keysight.com /es/en/products/software/pathwave-design-software/pathwave-advanced-design-system.html
[4] D. Root, J. Horn, J. Verspecht, and M. Marcu, X-Parameters Char- acterization, Modelling and Design of Nonlinear RF and Microwave Components, Cambridge, Ed. Cambridge University Press, 1st Ed. 2013. ISBN: 978-0521193238
[5] Keysight. PNA-X Networks Analyzers https://www.keysight.com /es/en/products/network-analyzers/pna-network-analyzers/pna-x-network-analyzers.html. [Online].

Keywords:

Engineering teaching, X-parameters, non-linear devices.