Numerical and Compact Modelling of Squeeze-Film Damping in RF MEMS Resonators

Oscillatory gas flow in squeeze-film dampers is studied at frequencies where the length of the acoustic wave is comparable with the damper dimensions. Damping and spring forces are calculated both numerically and analytically from the linearized 2D Navier-Stokes equations. In addition to the low frequency region of inertialess gas, where the use of the Reynolds equation is limited, the new model considers several additional phenomena. These are the inertia of the gas,the transition from isothermal to adiabatic conditions, and the gap resonances at frequencies where the acoustic wavelength is comparable to the gap height. Velocity and temperature slip conditions are considered to make the model valid in micromechanical structures where the gap heights are of the order of a micrometer. An approximate compact model is derived combining the low frequency model and the gap resonance model. The accuracy of the compact model is studied by comparing its response to the numerical results calculated with the finite element method. The agreement is very good in a wide frequency band when the ratio of the damper width and the gap height is greater than 10. The numerical study and the compact model are directly applicable in predicting the damping and the resonance frequency shift due to air in RF MEMS resonators having narrow air gap widths and operating at frequencies where the wavelengths become comparable to the damper dimensions

Trade-off Between Optimal Efficiency and Envelope Correlation Coefficient for Antenna Clusters

This paper introduces a theory for assessing and optimizing the multiple-input-multiple-output performance of multi-port cluster antennas in terms of efficiency, channel correlation, and power distribution. A method based on a convex optimization of feeding coefficients is extended with additional constraints allowing the user to control a ratio between the power radiated by the clusters. The formulation of the problem makes it possible to simultaneously optimize total efficiency and channel correlation with a fixed ratio between power radiated by the clusters, thus examining a trade-off between these parameters. It is shown that channel correlation, total efficiency, and allocation of radiated power are mutually conflicting parameters. The trade-offs are shown and discussed. The theory is demonstrated on a four-element antenna array and on a mobile terminal antenna.Comment: 10 pages, 12 figure

Laajakaistaisten sovituspiirien hyödyntämisestä älypuhelimien antennien suunnittelussa

Transferring the growing amount of data calls for wider bandwidths in new wireless standards. For the mobile antennas, which have to be squeezed to a very limited space, this poses quite a challenge for impedance matching, if efficiency is not to be sacrificed. Earlier, wideband matching was studied as a rather theoretical problem, but this work takes a practical viewpoint to produce readily applicable results. The goal is to utilize circuit elements to improve the performance of handset antennas. Because the number of matching elements is to minimized in practical designs, this work focuses particularly on three-element matching circuits. The presented efficient procedure for determining the available bandwidth with a certain matching topology, i.e., the bandwidth estimator, enable accounting for the matching circuit from the beginning of the antenna design process. Furthermore, evaluating the potential of different radiating structures becomes feasible. In mobile systems, the desired frequency band consists of two passbands, and therefore finding methods for dual-band matching is reasonable. This work presents how any two matching circuits designed separately for frequencies f1 and f2 can be converted into a dual-band matching circuit operating both at f1 and f2. In addition, simple design equations for dual-band matching are given. A dual-band matching can be realized also with two radiating elements. This widens the study to illustrate how bandwidth estimators can be used to design matching circuits for multiple ports. Moreover, it is shown that bandwidth estimator analysis offers a suitable starting point for practical design - the simulations and measurements are in good agreement. Finally, the work introduces other ways to improve antenna performance with aid of circuit elements and bandwidth estimators.Älypuhelimilla siirrettävän datamäärän kasvu näkyy uusissa standardeissa yhä laajempina taajuuskaistoina. Pieneen tilaan mahdutettujen antennien impedanssisovittaminen tulee tällöin hyvin haastavaksi, jos hyötysuhteesta ei suostuta tinkimään. Aiemmin laajakaistasovitusta on tutkittu varsin teoreettisista lähtökohdista, mutta tässä pyritään käytännönläheisiin ja helposti sovellettaviin tuloksiin. Tavoitteena on matkapuhelinantennien suorituskyvyn parantaminen. Tarkastelu keskittyy kolmen elementin sovituspiireihin, koska käytännön ratkaisuissa piirielementtien määrä pyritään pitämään pienenä. Esitetty tehokas menetelmä antennirakenteella saavutettavan kaistanleveyden määrittämiseen (ns. kaistanleveysestimaatti) mahdollistaa sovituspiirin vaikutuksen huomioimisen antennirakenteen suunnittelussa jo alusta alkaen. Myös erilaisten vaihtoehtoisten rakenteiden vertailu helpottuu. Koska matkapuhelintaajuudet koostuvat kahdesta erillisestä taajuusalueesta, on mielekästä tarkastella myös kaksikaistaista sovittamista. Työssä esitetään, kuinka kaksi eri taajuuskaistoille suunniteltua sovituspiiriä voidaan muuntaa yhdeksi sovituspiiriksi, joka antaa sovituksen molemmilla alkuperäisillä taajuuskaistoilla. Kaksikaistaiseen sovitukseen esitetään myös erilliset mitoituskaavat. Kaksikaistainen sovitus on mahdollista toteuttaa myös kahdella erillisellä elementillä ja siksi työssä havainnollistetaan, kuinka kaistanleveysestimaatteja voidaan hyödyntää sovituspiirien suunnittelussa moniporttitapauksessa. Samalla osoitetaan, että ideaalisilla piirimalleilla lasketut tulokset soveltuvat hyvin käytännön antennien suunnittelun lähtökohdaksi. Lopuksi käydään vielä läpi muita mahdollisia tapoja, joilla piirielementtejä sekä kaistanleveysestimaatteja voisi tulevaisuudessa hyödyntää antennien suorituskyvyn parantamisessa

Time-Domain Model of Dispersive Transmission Line

OF THE MASTER'S THESIS Author: Anu Lehtovuori Name of the thesis: Time-domain model of dispersive transmission line Date: May 31, 2000 Number of pages: 61 Department: Electrical and Communications Engineering Professorship: Circuit Theory Supervisor: Prof. Martti Valtonen The simulation of lossy and dispersive transmission lines has become an essential part of the design process. On the other hand, their accurate and e#cient simulation in the time domain is still a problem

Adjusting radiation pattern of small antennas

The antenna clusters have been used to control the impedance properties of the antenna, but they have potential also in radiation pattern reconfigurability. We demonstrate the benefits of multi-feed antennas using a mobile antenna as an example.Peer reviewe

On Realized Gain-Optimal Feeding Coefficients of Antenna Arrays

Funding Information: ACKNOWLEDGMENT This work was supported by the Business Finland through ENTRY100GHz CELTIC-NEXT project. Publisher Copyright: © 2023 European Association for Antennas and Propagation.The feeding coefficients maximizing the realized gain are often solved from an eigenvalue problem. We derive an alternative method for obtaining the optimal feed coefficients in this paper and show that it gives the same solution. The derived method obtains the coefficients from a direct equation. We compare the realized gain obtained with the optimal feeding coefficients to the case where the elements are progressively phased. The examples show that with optimal feeding coefficients the realized gain can be improved in cases where the mutual coupling is high, edge-element effect is strong, or the embedded element patterns are unequal. Also, an example demonstrates that circularly polarized realized gain can be improved in dual polarized array by feeding the elements with optimal coefficients.Peer reviewe

Base station antenna array with calibration structure

The introduction of 5G technologies is pushing research in mobile communications to millimeter waves. However, sub-6 GHz frequency range as a part of the 5G standard provides excellent wave propagation properties and more capacity due to new usable frequency ranges. This paper introduces a design for picocell base station 2x2 antenna array with integrated signal injection network for transceiver calibration. Operation frequency range is from 2 to 6 GHz. The antenna array with calibration board has better than -6.3 dB active reflection coefficient and efficiency higher than -3 dB. Calibration network provides 29 dB coupling.Peer reviewe