Exploiting the Response Surface Method for Optimizing Reconfigurable RF-MEMS Devices for Future Applications Beyond 5G, 6G, and Super-IoT


Much of the current research in the fields of electronics, telecommunications and distributed sensing networks falls within broad application paradigms, among which the Internet of Things (IoT)1Internet of Everything (IoE)2 and 5G3.4 unquestionably dominate. In the longer term, a decade from now, the Super-IoT, equivalently referred to as the Touch Internet (IT), together with 6G, will mark an unprecedented leap beyond mainstream application designs and Quality of Experience (QoE) made available to the end user5,6,7. Simple to imagine, 6G will require remarkable performance in terms of data transmission capacities. Taking as a benchmark the 5G currently being rolled out, the move to so-called Beyond-5G and then to 6G, will mark a 1000-fold increase in data rates, from the (already significant) 1 Gbps of 5G, to 1 Tbps6. In addition to the enormous transmission/reception needs, other technical challenges will have to be met, such as very low end-to-end (E2E) latency, going from 5 ms for 5G to 1 ms for 6G, as well as with very high reliability of the transmissions, these characteristics being crucial for safety-critical applications, including Vehicle-To-Vehicle (V2V) and Massive Machine-Type Communications (MMTC)8as well as remote surgery9, are certainly valuable examples. From a technology perspective, the specifications mentioned above will require frequency ranges well above 6 GHz, thus including millimeter waves (30–100 GHz), as well as the sub-THz range (100–300 GHz), necessary to transform small/small cellstenmassive-MIMO (Multiple-Input-Multiple-Output) and Large Intelligence Surface (LIS)11 antenna technologies in reality.

Given the scenario described so far, current and future network and communication paradigms will heavily capitalize on high-performance, frequency-agile, and broadband hardware (HW) components. To this end, the present contribution deals with passive radiofrequency (RF) components of low complexity, and in particular with the MEMS (MicroElectroMechanical-Systems) technology for their realization, well known in the literature under the acronym RF-MEMS.12. During more than two decades of research, a wide variety of highly miniaturized RF-MEMS passives with outstanding characteristics, in terms of RF performance and wide frequency operability, have been demonstrated, such as ohmic and capacitive micro-relays13.14multi-state phase shifters15tunable filters16switch matrices17.18etc

Unlike other consolidated technologies, MEMS still exhibit complex multi-physics behavior, in which typical electrical and electronic properties of materials are coupled to mixed mechanical and electromechanical domains. In particular, in the case here at stake of RF-MEMS, the structural/mechanical field is coupled to electrostatics and electromagnetics.19. This translates into an articulated and diverse set of degrees of freedom (DoF) available to the designer, in order to optimize the electromechanical and RF characteristics of the studied RF-MEMS device, often revealing a non-negligible number of trade-offs across the domain. physics mentioned. The approaches and techniques available to handle such complex optimization problems are diverse and effective. Typically, very good accuracy of simulated results comes from commercial tools based on Finite Element Method (FEM) analysis.20, the ANSYS (www.ansys.com) and COMSOL (www.comsol.com) environments being the most used. The main disadvantages of FEM are that the computational complexity of the model and the analysis time can be considerable, especially if a fine mesh is used to achieve greater accuracy and/or if the model geometry is complex. Moreover, the available FEM tools are not suitable to simulate the whole multi-physics behavior of RF-MEMS. Therefore, it may be necessary to use different environments, for example one for the electromechanical coupling, another for the RF properties, which makes the overall optimization of the design in the loop more tedious. In light of these considerations, there are multi-domain simulation approaches based on simplified/compact analytical models, as well as equivalent lumped element networks.21.22, which allow rapid simulation and DoF evaluation of RF-MEMS, at the cost of reduced accuracy and usability. In fact, best practice is often to use both tools, i.e. simplified models in the rough design evaluation phase, looking for example the sensitivity of available DoFs, and FEM tools for fine tuning.

We have chosen as the target device for this study an RF passive component which is quite critical for MIMO and 6G applications mentioned above, i.e. a multi-state RF power attenuator. A few design concepts, entirely realized in RF-MEMS technology, have already been presented and discussed by some of the authors, demonstrating good characteristics up to 110 GHz, and thus providing an experimental database to be used as a reference for the new methodology. predictive discussed in the following pages.

In such a framework, we propose an innovative design optimization approach, orthogonal to the classical methodologies in use, which allowed us to predict the results of physical simulations without the need to perform them each time a parameter is varied. We based our approach on a response surface method (RSM), which is a common statistical methodology, in which the observed system is viewed as a black box, with the controllable factors as inputs and the returns of interest as outputs. In the specific case here at play, the inputs are related to the DoFs geometry and material parameters of the studied RF-MEMS design concept. On the other hand, since the device of interest is an RF power attenuator (as mentioned in more detail below), the outputs of interest are the broadcast parameters (S-parameters), with particular emphasis on the transmission (S21), providing indications of the level of attenuation achieved, and the voltage standing wave ratio (VSWR), which is related to the amount of reflected power, i.e. dependent on the parameter S11. RSM allows the construction of empirical equations that capture the behavior of the system in the considered range of the factorial space. Unlike physical models, such equations can be applied regardless of the values ​​of the factors, as long as these are interpolated into the observed data ranges. Keeping this in mind, the great advantage of RSM is the general understanding of the evolution of yields, even in a wide range, using few simulations carried out at certain strategic points.

In order to confirm the RSM method, we test it by simulating points inside the range considered but not used to build the empirical model, and, as additional proof, against values ​​obtained by experimental measurements of a device. physical. By building an RSM model on a small set of simulations, we prove its reliability in predicting with good accuracy the S21 and VSWR parameters, given the characteristics of the device geometry.

The paper is organized as follows. The second section discusses the design concepts of the RF-MEMS step attenuator, first reporting the technology and operating principles, then the 3D FEM model of the multi-DoFs device (target of subsequent analysis based on on RSM), as well as its validation. against experimental datasets. The third section reports the development of the RSM optimization method based on FEM datasets as inputs, as well as its validation and confirmation against additional FEM simulations and experimental data. In the last section, finally, collects some conclusive considerations.


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