Interview

Abstract

Jorge Ruiz-Cruz Dr Jorge Ruiz-Cruz from the Autonomous University of Madrid, Spain, talks to Electronics Letters about the paper ‘Analytical Expressions of the Q-Factor for the Complete Resonant Mode Spectrum of the Equilateral Triangular Waveguide Cavity’, page 944. Our field of research is the analysis and design of microwave and millimetre-wave passive devices, especially in waveguide technology. We work on numerical methods in the context of applied electromagnetics for engineering, with both quasi-analytical methods such as mode-matching or more generic techniques such as the finite element method. With these methods, we combine our expertise in the theoretical aspects of electromagnetic fields and microwave circuits with advanced optimisation methods. The result is the design of high-performance microwave devices such as filters, power dividers, multiplexers, polarisers, ortho-mode transducers, etc. We are particularly interested in developing different kinds of networks for radar systems and satellite communications using novel synthesis and manufacturing techniques. The work in our Letter is related to the numerical methods and microwave component research we have performed in recent years, especially with waveguide cavity filters for satellite communications. We have noticed that with the advance of new manufacturing technologies, there is a broad range of problems that were not addressed in the past because they were not practical, and now we can approach them since the fabrication of diverse geometries is not an issue anymore. In this way, a common geometry such as the equilateral triangular cavity can be used for other applications like the design of microwave filters or for checking numerical codes. Although the Q-factor of waveguide cavity resonators is a well-established concept in the microwave and millimetre-wave community (and in other related fields) the range of problems with a closed-form solution is very limited. For microwave and millimetre-wave practitioners, it is common to use the closed-form formulas found in the literature for rectangular or circular waveguide cavities, for diverse applications such as implementing filters or other circuits, as reference cases for checking numerical methods, or for calibration in measurement systems. With this work, we contribute a new closed-form expression not reported previously, since the equilateral triangle cavity had not been treated in detail, as have other canonical geometries, in the literature. The new analytical expressions provided for the equilateral triangular waveguide cavity in the paper are as simple as in the case of the rectangular waveguide cavity (the ones for the circular waveguide cavity are also simple, but they involve zeroes of Bessel functions). We have derived the closed-form expressions with works from other authors, who have presented the complete solution to the Helmholtz equation with homogeneous Neumann and Dirichlet boundary conditions in the specific geometry of an equilateral triangle. Starting with those solutions, we have been able to obtain very simple expressions for the Q-factor after a careful integration process. The analytical closed-form expressions that we have presented complement the classic cases (rectangular and circular waveguide resonators). They have potential use in microwave filters, validation of numerical solvers, or integration with microwave measurement systems. Cavities with larger volumes usually provide resonant modes with greater Q-factor. However, in this case, the spurious-free window is usually reduced. Filter designers must pursue a trade-off between these two parameters, so that a good out-of-band rejection and low insertion losses in the passband are achieved. To that end, resonant mode charts and Q-charts, like the ones provided in our Letter, are typically used to design the physical dimensions of the resonators, which can be used in microwaves up till the terahertz regime. This work has applications in several fields. In the area of filter design, we are developing several prototypes at different frequency bands in order to test the approach, along with a variety of topologies and manufacturing techniques. In the area of electromagnetic analysis, we plan to incorporate the closed-form expressions developed in this work not only for testing but also as part of in-house hybrid analysis techniques we are currently developing. Microwave and millimetre-wave engineering is continuously taking advantage of both new manufacturing facilities and enhanced computational capabilities. Regarding the former, technology is always changing the way we, engineers, think when a design is tackled, as new construction geometries and topologies are enabled with novel manufacturing methods. Therefore, problems that in the past might have been looked at as merely theoretical ones may now become of real practical interest. As for computational capabilities, no matter how high they reach, there will always be a need to develop efficient and accurate analysis methods to be included in microwave design tools. We strongly believe this contribution unites these two approaches and we will work on developing similar derivations and techniques.