Exploitation of response surface method for the optimization of RF-MEMS reconfigurable devices in view of future beyond-5G, 6G and super-IoT applications

Abstract

The emerging paradigms of the Beyond-5G, 6G and Super-IoT will demand for high-performance Radio Frequency (RF) passive components, and RF-MEMS technology, i.e. Microsystems-based RF passives, is a good candidate to meet such a challenge. As known, RF-MEMS have a complex behavior, that crosses different physical domains (mechanical; electrical; electromagnetic), making the whole design optimization and trimming phases particularly articulated and time consuming. In this work, we propose a novel design optimization approach based on the Response Surface Method (RSM) statistical methodology, focusing on a class of RF-MEMS-based programmable step power attenuators. The proposed method is validated both against physical simulations, performed with Finite Element Method (FEM) commercial software tools, as well as experimental measurements of physical devices. The case study here discussed features 3 DoFs (Degrees of Freedom), comprising both geometrical and material parameters, and aims to optimize the RF performances of the MEMS attenuator in terms of attenuation (S21 Scattering parameter) and reflection (VSWR-Voltage Standing Wave Ratio). When validated, the proposed RSM-based method allows avoiding physical FEM simulations, thus making the design optimization considerably faster and less complex, both in terms of time and computational load.

Figure 1

Cross-section of the RF-MEMS technology employed in this study. Image created with Microsoft Office 365 PowerPoint (www.office.com).

Figure 2

Microphotograph of the series (a) and shunt (c) RF-MEMS 1-bit attenuator samples, and corresponding equivalent lumped element circuits of the series (b) and shunt (d) design concepts. Images (b) and (d) created with Quite Universal Circuit Simulator (QUCS) 0.0.19 (http://qucs.sourceforge.net).

Figure 3

Comparison of the measured and simulated S-parameters characteristics of the 1-bit series (a,b) and shunt (c,d) RF-MEMS attenuators from 1 to 30 GHz. S21 (a) and VSWR (b) of the series attenuator, when the resistive load is inserted (switch OFF) and shorted (switch ON). S21 (c) and VSWR (d) of the shunt attenuator, when the resistive load is inserted (switch ON) and not inserted (switch OFF). Images created with Microsoft Office 365 Excel (www.office.com).

Figure 4

Ansys HFSS full-3D model of the 2-bit RF-MEMS attenuator (a). Close-up of the poly-silicon resistor/s in the series (b) and shunt (c) section of the composed attenuator. Images created with Ansys Electronics Desktop 2020 R2, HFSS (www.ansys.com/products/electronics).

Figure 5

Comparison of the measured and simulated S21 (a) and VSWR (b) of the 2-bit RF-MEMS attenuator in all the four implemented network configurations. Images created with Microsoft Office 365 Excel (www.office.com).

Figure 6

Contour plots (a–c) of the empirical model for the slope and the intercept (d–f) of the S21 curves in the linear zone, obtained from the physical simulations. The red points indicate where the physical simulations are performed. Image created with R v.4.0.4 using as Integrated Development Environment (IDE) R Studio v. 1.4.1104 (www.rstudio.com/products/rstudio) and GGPlot2 3.3.5 as graphic package (https://ggplot2.tidyverse.org). The graphs were then mounted in their final version using Affinity Designer v. 1.10 (https://affinity.serif.com/en-us).

Figure 7

Actual versus predicted plot of the S21 slope and intercept. In both cases, the points are slightly scattered on the diagonal line, indicating a good agreement between the RSM and the physical models. This was also confirmed by the value of R² close to 1. Image created with R v.4.0.4 using as Integrated Development Environment (IDE) R Studio v. 1.4.1104 (www.rstudio.com/products/rstudio) and GGPlot2 3.3.5 as graphic package (https://ggplot2.tidyverse.org). The graphs were then mounted in their final version using Affinity Designer v. 1.10 (https://affinity.serif.com/en-us).

Figure 8

Contour plots (a–c) of the empirical model for the slope and the intercept (d–f) of the VSWR curves in the linear zone, obtained from the physical simulations. The red points indicate where the physical simulations are performed. Image created with R v.4.0.4 using as Integrated Development Environment (IDE) R Studio v. 1.4.1104 (www.rstudio.com/products/rstudio) and GGPlot2 3.3.5 as graphic package (https://ggplot2.tidyverse.org). The graphs were then mounted in their final version using Affinity Designer v. 1.10 (https://affinity.serif.com/en-us).

Figure 9

Actual versus predicted plot of the VSWR slope and intercept. In both cases, the points are perfectly on the diagonal line, indicating perfect agreement between the RSM and the physical models. This was also confirmed by the value of R² equal to 1. Image created with R v.4.0.4 using as Integrated Development Environment (IDE) R Studio v. 1.4.1104 (www.rstudio.com/products/rstudio) and GGPlot2 3.3.5 as graphic package (https://ggplot2.tidyverse.org). The graphs were then mounted in their final version using Affinity Designer v. 1.10 (https://affinity.serif.com/en-us).