Analysis of EM scattering in Waveguide Filter using Neural Network
This paper discusses the application of Neural Network (NN) technique in the modeling of a typical electromagnetic (EM) field scattering problem in a waveguide filter structure [1]. The structure under consideration is a rectangular waveguide with four dielectric circular rod inserted symmetrically. The Neural Network takes into consideration the geometrical and material parameters of the EM model of the structure and the reflection coefficient values for different frequencies in the frequency band of interest. The Neural Network is trained off line using training data sets generated by the image theory. The work is to find out an acceptable Neural Network model of the waveguide structure having four dielectric post, verification using Method of moment by simulation and the corresponding filter structure practically implemented in hardware for verification.
Designing Stepped Impedance Microstrip Low-Pass Filters Using Artificial Neural Network at 1.8 GHz
In this paper a design technique for a Stepped impedance Micro strip Low-pass filters is presented by using the artificial neural network (ANN) modeling method. Required dimensions of the micro strip filter layout are used to get the input-output relationships in the ANN model. This paper presents the design and analysis of Stepped impedance Micro strip Low-pass filters at cut-off frequency 1.8 GHz which gives insertion loss (S21) of-3 dB at cut-off point. Subsequently an artificial neural network model is developed to find out the Magnitude variation of scattering parameters (S-parameters) of Micro strip Low-pass filters at 1.8 GHz for different dimensions. After developing the ANN model of micro strip low-pass filter, it is computationally more efficient in the design and it has been displayed to be as accurate as an Electromagnetic simulator. The simulation is performed using the commercial software IE3D 14.1 and MATLAB programming language GUI Tools are used for ANN Training.
UNIVERSAL LOCALLY COMPACT SCATTERED SPACES
If δ is an ordinal, we denote by C(δ) the class of all cardinal sequences of length δ of locally compact scattered (in short: LCS) spaces. If λ is an infinite cardinal, we write Cλ(δ) = {s ∈ C(δ) : s(0) = λ = min[s(ζ) : ζ < δ]}. An LCS space X is called Cλ(δ)-universal if SEQ(X) ∈ Cλ(δ), and for each sequence s ∈ Cλ(δ) there is an open subspace Y of X with SEQ(Y ) = s. We show that • there is a Cω(ω1)-universal LCS space, • under CH there is a Cω(δ)-universal LCS space for every ordinal δ < ω2, • under GCH for every infinite cardinal λ and every ordinal δ < ω2, there is a Cλ(δ)-universal LCS space, • there may exist a Cω(ω2)-universal LCS space. As a consequence, we obtain that it is consistent that 2 = ω2 and Cω(ω2) is large as possible, i.e. Cω(ω2) = {s ∈ 2{ω, ω1, ω2} : s(0) = ω}. 2000 Mathematics Subject Classification. 54A25, 06E05, 54G12, 03E35.