This reverse model is realized by swapping some of the inputs/outputs in the analysis model, and training the neural networks accordingly. Since the analysis and synthesis processes for these systems have “one-to-one mapping” relations with each other, a forward model is defined for the analysis process for all these types of the planar transmission lines on the other hand, a reverse model is also considered for the synthesis of the same lines. In this work, the multiplayer perceptron (MLP) and radial basis function (RBF) neural networks in their simplest forms are employed in function approximation for highly nonlinear and complex analysis and synthesis of the most commonly used planar RF/microwave transmission lines, that is, microstrip lines, coupled microstrip lines, and basic and shielded coplanar-waveguides. Thus it has been verified that this neural Smith chart can be exploited for the whole classical transmission line theory including impedance matching. Applications of the Neural Smith chart are given by the numerous examples with the proved accuracy. This can also be considered as solving the simultaneous nonlinear equation set for (ℓ, Z0) parameters of the required impedance transformations ZOUT(ω) = ROUT (ω) + XOUT (ω) from the given complex termination ZS = RS + jXS. Furthermore, the neural unit element (NUE) is defined by the two independent neural networks as problems in the forward and reverse directions to be incorporated into the analysis and design algorithms of the unit element (UE). Activation of the hidden layers of the modules are performed by the tangential-sigmoid type of function while the output layers are activated linearly. Briefly, the outputs of these ANN modules are the standing waves and the impedance transformation, which are the characteristic features of the transmission line circuits. The ANN architecture is also simple, which consists of the two simple multilayer perceptron (MLP) modules with the common inputs which are the termination ZS = RS + jXS, line operation bandwidth B between the defined fmin, fmax and the dielectric ε. Data ensembles for the training and testing processes are obtained from the systematically selected locations on the Smith chart with the adaptive radius sampling algorithm. Thus, relative to the similar works in the existing literature, this article provides the continuous Smith chart domain to facilitate the “Smith chart” methodology in solving the highly nonlinear transformation equations between the rectangular impedance and polar reflection planes for an infinite number of passive impedance to be used in design tasks of the microwave circuits. ![]() ![]() ![]() In this article, briefly the Smith chart is mapped with an artificial neural network (ANN) covering its whole details to be exploited CAD of the microwave circuitry.
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