Parametric macromodelling of linear high‐frequency systems using multiple frequency scaling and sequential sampling

Abstract

This letter presents an enhanced parametric macromodeling scheme for linear high-frequency systems based on the use of multiple frequency scaling coefficients and a sequential sampling algorithm to fully automate the entire modeling process. The proposed method is applied on a ring resonator bandpass filter example and compared with another state-ofthe-art macromodeling method to show its improved modeling capability and reduced setup time.Introduction: Design activities of electromagnetic (EM) systems such as design space exploration, optimization, sensitivity analysis, etc., often require a substantial number of computationally expensive EM simulations. The development of parametric macromodels acting as accurate and efficient surrogate models for complex EM systems is an active field of research [1,2, 3, 4]. These models tend to be good approximations of the EM system behavior, characterized by frequency and additional design parameters (such as geometrical or substrate features) and can be used to speed-up the design process. Robust interpolation-based parametric macromodeling methods have been proposed over the recent years, based on the parameterization of a set of frequency-dependent rational models called root macromodels [1], [4]. In [4], interpolation of root macromodels at the input-output level, based on two scaling coefficients was presented : one of the coefficients is a multiplicative factor at the input/output level of the system (amplitude scaling) and the other coefficient is a compression or expansion term for the Laplace variable s (frequency scaling). The approach of [4] results in high modeling capability and robustness.In this letter, the parametric macromodeling method proposed in [4] is generalized by using multiple frequency scaling coefficients for all partial fractions of the root macromodels. This allows to model the behavior of the partial fractions of the root macromodels independently, in order to achieve a more flexible modeling capability. The proposed method is compared with the approach described in [4] to show its enhanced modeling capability and reduced CPU setup time.

Scalable macromodelling methodology for the efficient design of microwave filters

“…Then, for each N -box region Ω l a set of amplitude and frequency scaling coefficients is computed and an interpolation process of FRFs and scaling coefficients is used to generate a scalable macromodel R Ω l (s, g) [15,16,24]. The Mean Absolute Error (MAE) measure or the L1-norm per port is used to assess the accuracy of the model in every N -box region of the design space at the corresponding validation points…”

“…These modelling methods [15, 16] are based on the use of interpolation of transfer functions and scaling coefficients. Recently, a scalable macromodelling approach has been proposed in [30] to enhance the modelling capability of [15, 16] by using multiple frequency scaling coefficients. In this paper, we use the scalable macromodelling technique [30] and combine it with the sequential sampling method [17].…”

“…Recently, a scalable macromodelling approach has been proposed in [30] to enhance the modelling capability of [15, 16] by using multiple frequency scaling coefficients. In this paper, we use the scalable macromodelling technique [30] and combine it with the sequential sampling method [17]. This is an important step that allows automating the generation of scalable macromodels and reducing the efforts needed by designers to use scalable macromodels as a design tool.…”

“…The corresponding main modelling steps are recalled briefly in what follows. The reader can refer to [15, 16, 30] for more detailed explanations. N ‐dimensional hyper‐rectangular ( N ‐box) regions are used as a building block for the design space.…”

“…Then, for each N ‐box region Ω l a set of amplitude and frequency scaling coefficients is computed and an interpolation process of FRFs and scaling coefficients is used to generate a scalable macromodel [15, 16, 30]. The mean absolute error (MAE) measure or the L 1‐norm per port is used to assess the accuracy of the model in every N ‐box region of the design space at the corresponding validation points where H u , v ( s , g ) and R u , v ( s , g ) denote the EM simulation response and scalable macromodel response, respectively.…”