Petrie Meyer

Bio: Petrie Meyer is an academic researcher from Stellenbosch University. The author has contributed to research in topics: Antenna (radio) & Waveguide filter. The author has an hindex of 15, co-authored 108 publications receiving 849 citations.

Creating accurate multivariate rational interpolation models of microwave circuits by using efficient adaptive sampling to minimize the number of computational electromagnetic analyses

Abstract: A fast and efficient adaptive sampling algorithm for multivariate rational interpolation models based on convergents of Thiele-type branched continued fractions (BCFs) is presented in this paper. We propose a variation of the standard BCF that uses approximation to establish a nonrectangular grid of support points. Starting with a low-order interpolant, the technique systematically increases the order by optimally choosing new support points in the areas of highest error until the required accuracy is achieved. In this way, accurate surrogate models are established by a small number of support points without any a priori knowledge of the data. The technique is evaluated on several passive microwave structures.

Design of a Ten-Way Conical Transmission Line Power Combiner

Abstract: Axially symmetric power combiners, such as radial line and conical line combiners, are very effective in combining the output signals from a large number of power amplifiers over a wide band with low losses. The main problem with radial lines is the behavior of the characteristic impedance against radial distance, which makes design of radial combiners difficult and normally optimization based. In this paper, a step-by-step design procedure is presented for the design of a conical line combiner. The design strategy relies on the transverse electromagnetic properties of the conical line to eliminate the need for complex full-wave optimization in the design process. Circuit models are instead employed and optimized to achieve a wide matched bandwidth. A ten-way prototype was developed at X-band, which displayed more than an octave matched bandwidth with low insertion loss

A robust integrated multibias parameter-extraction method for MESFET and HEMT models

Abstract: An integrated multibias extraction technique for MESFET and high electron-mobility transistor (HEMT) models is presented in this paper. The technique uses S-parameters measured at various bias points in the active region to construct one optimization problem, of which the vector of unknowns contains a set of bias-dependent elements for each bias point and one set of bias-independent elements. This problem is solved by an extremely robust decomposition-based optimizer, which splits the problem into n subproblems, n being the number of unknowns. The optimizer consistently converges to the same solution from a wide range of randomly chosen starting values. No assumptions are made concerning the layout of the device or the bias dependencies of the intrinsic model elements. It is shown that there is a convergence in the values of the model elements and a decrease in the extraction uncertainty as the number of bias points in the extraction is increased. Robustness tests using 100 extractions, each using a different set of random starting values, are performed on measured S-parameters of a MESFET and pseudomorphic HEMT device. Results indicate that the extracted parameters typically vary by less than 1%. Extractions with up to 48 bias points were performed successfully, leading to the simultaneous determination of 342 model elements.

Filter Parameter Extraction for Triple-Band Composite Split-Ring Resonators and Filters

Abstract: A configuration of composite resonators consisting of three split-ring resonators is proposed to obtain a triple-band response with two transmission zeros between the passbands. Two new topologies are presented to design triple-band filters with controllable responses. A systematic filter design approach is presented based on a filter coupling model. The model is established to enable triple-band filter design with controlled passbands. Two methods are proposed and compared for the extraction of filter parameters. Coupling between nonadjacent elements is considered in the model and shown to have a significant effect. By changing the orientation of the coupled composite resonators, it is possible to introduce additional transmission zeros. Two sixth-order filter examples illustrate the use of the coupling model with the filter design approach to design filters with specified responses. The limitations of this filter topology are discussed.

Design of Conical Transmission Line Power Combiners Using Tapered Line Matching Sections

Abstract: An axially symmetric power combiner, which utilizes a tapered conical impedance matching network to transform ten 50-Omega inputs to a central coaxial line over the X-band, is presented. The use of a conical line allows standard transverse electromagnetic design theory to be used, including tapered impedance matching networks. This, in turn, alleviates the problem of very low impedance levels at the common port of conical line combiners, which normally requires very high-precision manufacturing and assembly. The tapered conical line is joined to a tapered coaxial line for a completely smooth transmission line structure. Very few full-wave analyses are needed in the design process since circuit models are optimized to achieve a wide operating bandwidth. A ten-way prototype was developed at X-band with a 47% bandwidth, very low losses, and excellent agreement between simulated and measured results.

Space mapping: the state of the art

Abstract: We review the space-mapping (SM) technique and the SM-based surrogate (modeling) concept and their applications in engineering design optimization. For the first time, we present a mathematical motivation and place SM into the context of classical optimization. The aim of SM is to achieve a satisfactory solution with a minimal number of computationally expensive "fine" model evaluations. SM procedures iteratively update and optimize surrogates based on a fast physically based "coarse" model. Proposed approaches to SM-based optimization include the original algorithm, the Broyden-based aggressive SM algorithm, various trust-region approaches, neural SM, and implicit SM. Parameter extraction is an essential SM subproblem. It is used to align the surrogate (enhanced coarse model) with the fine model. Different approaches to enhance uniqueness are suggested, including the recent gradient parameter-extraction approach. Novel physical illustrations are presented, including the cheese-cutting and wedge-cutting problems. Significant practical applications are reviewed.

Calculation of Gauss quadrature rules.

Abstract: Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative ''weight'' function and another function better approximated by a polynomial, thus $\int_{a}^{b} g(t)dt = \int_{a}^{b} \omega (t)f(t)dt \approx \sum_{i=1}^{N} w_i f(t_i)$. Hopefully, the quadrature rule ${\{w_j, t_j\}}_{j=1}^{N}$ corresponding to the weight function $\omega$(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weight function are known or can be calculated.

Computational Electromagnetics for RF and Microwave Engineering

Abstract: The numerical approximation of Maxwell's equations, Computational Electromagnetics (CEM), has emerged as a crucial enabling technology for radio-frequency, microwave and wireless engineering. The three most popular 'full-wave' methods - the Finite Difference Time Domain Method, the Method of Moments and the Finite Element Method - are introduced in this book by way of one or two-dimensional problems. Commercial or public domain codes implementing these methods are then applied to complex, real-world engineering problems, and a careful analysis of the reliability of the results obtained is performed, along with a discussion of the many pitfalls which can result in inaccurate and misleading solutions. The book will empower readers to become discerning users of CEM software, with an understanding of the underlying methods, and confidence in the results obtained. It also introduces readers to the art of code development. Aimed at senior undergraduate/graduate students taking CEM courses and practising engineers in the industry.

Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling

Abstract: Simulated computer experiments have become a viable cost-effective alternative for controlled real-life experiments. However, the simulation of complex systems with multiple input and output parameters can be a very time-consuming process. Many of these high-fidelity simulators need minutes, hours or even days to perform one simulation. The goal of global surrogate modeling is to create an approximation model that mimics the original simulator, based on a limited number of expensive simulations, but can be evaluated much faster. The set of simulations performed to create this model is called the experimental design. Traditionally, one-shot designs such as the Latin hypercube and factorial design are used, and all simulations are performed before the first model is built. In order to reduce the number of simulations needed to achieve the desired accuracy, sequential design methods can be employed. These methods generate the samples for the experimental design one by one, without knowing the total number of samples in advance. In this paper, the authors perform an extensive study of new and state-of-the-art space-filling sequential design methods. It is shown that the new sequential methods proposed in this paper produce results comparable to the best one-shot experimental designs available right now.