Correlation Transverse Wave Formulation (CTWF) for Modeling of Stochastic Electromagnetic Fields

In this work we apply the Correlation Transver se Wave Formulation (CTWF) method for direct computation of the auto- and cros s correlation functions (ACFs and CCFs) of stationary stochastic electromagnetic fields. These ACFs and CCFs are com puted from the Johns matrices, i.e. the discrete- time TWF Green's functions and are directly related to the EMI power spectra. Radiated EMI is represented by stoc hastic EM fields. For efficient EMI compliant design and optimization of circuits and systems the si mulation methodologies based on the field autocorrelation and cross correlation spectral densities are required. Semi-ana lytic numerical methods based on Green's function formalism already were presented in (Russer and Russer, 2011a, 2015). The Transmission Line Matrix (TLM) method is an e fficient time-and space discrete numerical method for modeling of complex electromagnetic structures (R usser and Russer, 2011b, 2014). Introducing network models allows the application of correlation matrix met hods for the modeling of stochastic fields. This can be done either by method of moments as discussed in (Russer and Russer, 2015) or by applying network oriented space discretising methods for EM field computation as for example the TLM method (Russer et al., 2016). Mode matching is the superposition of modal field solu tions. If an electromagnetic structure is subdivided into substructures and complete sets of modal field solutions are known for the sub-domains, these modal solutions form a complete basis and allow to expand the field solutions into these basis functions. Choosing modal functions as the basis functions ensure s that these functions are already solutions within the respective regions and we need only to care that the boundar y conditions are fulfilled. The mode matching method is potentially exact if we allow infi nite series expansions. Considering the modal basis functions as the basis of a function space, Hilbert space methods, in particular the method of moments (Harrington, 1968), can be applied. Baudrand and Baj on introduced Hilbert space methods to transform integral formulations of electromagnetic field pr oblems into algebraic ones (Baudrand, 2001). An extension of this method has been given in the transve rse wave formulation (Wane et al., 2003). Now, we extend the Transverse Wave Formulation method to compute auto- and cross correlation functions of stationary stochastic electromagnetic fields. References Baudrand, H.: Introduction au Calcul des Elements de Circuits Passifs en Hyperfreequences, Cépaduès- Éditions, Toulouse, 2001. Harrington, R. F.: Field Computation by Mom ent Methods„ IEEE Press, San Francisco, 1968. Russer, J. A. and Russer, P.: Stochastic electrom agnetic fields, in: German Microwave Conference (GeMIC), pp. 1-4, 2011a. Russer, J. A. and Russer, P.: Modeling of Noisy EM Field Propagation Using Correlation Information, in IEEE Transactions on Microwave Theory and Techniques, 2015. Russer, J. A., Cangellaris, A., and Ru sser, P.: Correlation Transmission Line Matrix (CTLM) Modeling of Stochastic Electromagnetic Fields, in: Proceeding o f: IEEE International Microwave Symposium, IMS, San Francisco, CA, USA, 2016. Russer, P. and Russer, J.: Transmission Line Matrix (TLM) and network methods applied to electromagnetic field computation, in: Micr owave Symposium Digest (MTT), 2011 IEEE MTT-S International, pp. 1-4, IEEE, doi:10.1109/MWSYM.201 1.5972622, 2011b.      «

In this work we apply the Correlation Transver se Wave Formulation (CTWF) method for direct computation of the auto- and cros s correlation functions (ACFs and CCFs) of stationary stochastic electromagnetic fields. These ACFs and CCFs are com puted from the Johns matrices, i.e. the discrete- time TWF Green's functions and are directly related to the EMI power spectra. Radiated EMI is represented by stoc hastic EM fields. For efficient EMI c...     »