By Dipak L. Sengupta
Utilized Electromagnetics and Electromagnetic Compatibility offers with Radio Frequency Interference (RFI), that's the reception of undesired radio signs originating from electronic electronics and digital apparatus. With trendy fast improvement of radio conversation, those undesired indications in addition to signs as a result of normal phenomena akin to lightning, sparking, and others have gotten more and more vital within the basic sector of Electro Magnetic Compatibility (EMC). EMC should be outlined because the potential of a few digital apparatus or procedure to be operated at wanted degrees of functionality in a given electromagnetic atmosphere with out producing EM emissions unacceptable to different platforms working within the region.
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Extra resources for Applied electromagnetics and electromagnetic compatibility
Orthogonal functions are the solutions of a particular type of differential equation. The origin of orthogonal functions is described next. The emphasis now shifts from solving the PDE to understanding the general properties of the solutions. 4 Sturm-Liouville Differential Equation Orthogonal functions are the solutions of Sturm-Liouville differential equation (S-LDE) with proper boundary conditions. The S-LDE represents most of the useful second order differential equations of physics and engineering.
If the method of separation of variables cannot be applied, we may use Green’s function method, integral transform technique, or computational methods. The method of separation of variables utilizes the orthogonality of functions to determine the expansion coefficients in a Fourier series expansion. 3 Orthogonality Condition 37 this useful property, the orthogonal functions can be employed to expand any arbitrary continuous function or piecewise continuous function; that is, they serve as basis functions in the expansion of arbitrary functions.
36), the coefficient c j is called projection of a function. 4 where the function 5x x 2 x 4 f (x) = − − and the normalized basis function u(x) = √2 sin ( x) are plot6 2 3 ted over the interval (0, 1). 41) 0 and is given by the area under the curves as shown in the figure. 2012. The notation ( f, u) is called the inner product of two functions, analogous to the dot product of vectors. 5. 40) should include a weight function w(x). 4 Projection of the function f (x) on the basis function u(x). 40 Analytical Methods and Orthogonal Functions situation.