The ultra wideband transfer function representation of complex three-dimensional electromagnetic structures (2004)

the network-oriented ultra wideband transfer function representation of complex three-dimensional elec- tromagnetic structures is investigated. The transfer function is consisting of two parts: entire function and rational or pole function. The reduction of a rank of an ill-conditioned matrix is performed in accordance with the spectral crite- rion. System identification is carried out by the Matrix Pen- cil Method (MPM) and a criterion for the model order selec- tion is introduced. The presented method yields consider- able reduction of computational effort and allows to gener- ate compact models of electromagnetic systems. I. INTRODUCTION The need of novel and broadband circuitry in nowa- days applications, especially in mobile communication and vehicular sensing equipments, demands the availabil- ity of reliable and accurate modelling of complex elec- tromagnetic structures up to the millimetre wave range. The simulation of complex three-dimensional electro- magnetic structures is resulting in an enormous computa- tional effort and correspondingly large times for simula- tion. So the application of network-oriented modelling (1) in connection with system identification techniques al- lows reducing the computational effort and the computa- tional time by orders of magnitude. In network theory systematic approaches for one-port or multiport circuit analysis are based on the transfer function or impulse response representation of the circuit elements. This representation may be obtained through pole extraction from the numerical solution of the field problem for modelling electromagnetic structures. The transmission line matrix (TLM) method (2) or fi- nite-difference time-domain (FDTD) method (3) allows to provide the full-wave analysis of complex three- dimensional electromagnetic structures made of arbitrary materials. This is extremely important for ultra wideband (UWB) electromagnetic structures, because time-domain simulation allows to characterize the properties of these structures in a wide frequency band by computing the response to a single impulsive excitation. According to the singularity expansion method (4) the signal, scattered by the electromagnetic structure, can be decomposed into early-time and late-time parts. The early-time reaction is limited in time-domain and consists of the forced oscillations. This part can be represented by the entire function, which depends on the driving signal. The late-time response contains only natural oscillations and can be defined by the parameters of the electromag- netic structure. The subdivision of the total reaction into two parts and modeling of the structure by using only the late-time re- sponse leads to an incorrect transfer function representa- tion of the electromagnetic structure. First of all natural oscillations occur not only in the late-time response, but in the early-time part of the reaction too. To use this part of the total reaction for the network-oriented transfer function representation forced oscillations must be re- moved from the signal, scattered by the electromagnetic structure. It can be done by computing the ratio of the corresponding Fourier transforms of the time-domain waveforms of the scattered and input signals in frequency domain or by deconvolution of the scattered signal in time-domain. Moreover, the main portion of the total signal energy concentrates in the early-time reaction. The late-time response contains relatively low energy and so becomes substantially corrupted with noise. The deconvolution in time-domain can be done by the matrix inversion, but the matrix obtained in this way is ill-conditioned. The reduction of a rank of an ill- conditioned matrix is performed in accordance with the spectral criterion (7). This criterion needs to take into consideration only the spectral components of the driving signal, exceeding some threshold within the frequency bandwidth of the electromagnetic structure. The application of MPM to the estimation of transfer functions of complex 3-dimentional structures requires a strategy of choosing the order of the method. This strat- egy uses the analysis of the spectrum of the difference signal between original and reconstructed system impulse response. Another problem is the influence of the entire function on the accuracy of poles estimation. The method is applied to the electromagnetic full-wave simulation of a patch antenna. For the electromagnetic simulation the TLM method is used (2). Computational results with and without applying system identification are compared with measured data.