Anu Lehtovuori

Applying the Problem-Based Learning Approach to Teach Elementary Circuit Analysis

Problem-based learning (PBL) is a motivating, problem-centered teaching method. The methodology and its application to education in elementary circuit analysis is discussed in detail. Because of administrative constraints, the implemented course does not strictly adhere to the PBL methodology in the sense that the course curriculum is strictly defined. Also, the PBL students take the same exam as the students in the traditional form of the course. The learning experience in the two course forms is compared via a questionnaire response and exam results. This comparison of the two groups seems to indicate that the PBL method is a better way of imparting education in circuit analysis, or even technology in general. The PBL students appear to grasp better the details and the overall picture of the issues taught. In addition to the subject matter, the PBL course students learn social skills through interaction in small groups, how to identify and define a problem, and how to look for and filter out relevant information. Presentation skills are also practiced

Numerical and compact modelling of squeeze-film damping in RF MEMS resonators

Oscillatory gas flow in squeeze-film dampers is studied up to frequencies where the length of the acoustic wave is comparable with the dimensions of the air gap. 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 air gap height. Velocity and temperature slip conditions are considered to make the model valid in micromechanical structures where the air 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 flow channel dimensions.

Enhanced multivariate steady-state time-domain method

Highly nonlinear circuits are very demanding to simulate, especially when they are excited with two separate frequencies as is the case with, e.g., RF circuits and SC filters. Frequency-domain methods, e.g. harmonic balance (HB), that can handle two-tone signals are more suitable for sine wave excitations and weakly nonlinear circuits. Multivariate steady-state time-domain (MSSTD) analysis is efficient also for signals with sharp edges and strongly nonlinear circuits. The computation of this method has been improved to make the MSSTD analysis faster than before. New features are initial guess, i.e. quick MSSTD (QMSSTD), and new preconditioners for the generalized minimum residual (GMRES) method of the MSSTD analysis, both of which are implemented into the APLAC circuit simulator achieving remarkable speed-up.

GMRES preconditioners for multivariate steady-state time-domain method (RF simulation)

Envelope methods play an important part in current RF simulation. We focus on an envelope method called the multivariate steady-state method (MSSTD). The method solves the steady state of a circuit especially in the case when signals at two very different frequencies are present, and harmonic balance is inefficient due to the shape of the signals. Different preconditioners for the iterative matrix solving method (GMRES) have been tested. Simulation results show that the preconditioner consisting of larger diagonal blocks decreases the number of iteration cycles needed and also the simulation time. However, other types of preconditioners should be studied to find a more robust and reliable solver for this type of problem and therefore one new approach has been proposed.