### T-π Network Simulation and Thevenin- Norton Equivalent Circuit Values From Laplace Description Using Pspice Software

#### Abstract

*From the conversion methods of T-π (star-delta) for impedances circuits, the behavioral modeling of Pspice simulation program is used to obtain equivalent circuits using LAPLACE option. The conversions are verified for two types of circuits by obtaining AC values of voltages and currents at various nodes and branches using Pspice computer simulations. There are many ways of expressing Thevenin/Norton equivalent circuit parameters such as (a) as real numbers for pure resistive circuits with DC current and voltage sources, (b) as complex numbers (both polar and rectangular forms) for AC energy sources, (c) and as LAPLACE transforms in laplace domain, for linear circuits in both AC and DC forms. If these equivalent circuit parameters are known in the form of Laplace transforms, by knowing any two of the three parameters, the other parameter can be determined as a function of frequency using Pspice. Two port Z, Y parameters, in addition to representing passive networks, can also be used to represent an active small signal or passive electronics circuitr by hybrid equations at the input and the output from the non-linear model of non linear active device. These representations, models, and tables can be utilised by the computer analysis applications Spice and Pspice to provide circuit models with two ports for electrical circuit simulation and analysis, and then construct Thevenin/Norton equivalent circuits after linearization. The SPICE analogue behavioural option, which was included in the Pspice version, is useful for modelling two-port linear circuits. DC networks with pure resistances and voltage- and current-controlled dependent sources can be modelled effectively using tools like the current generator (VALUE option). The LAPLACE option is another choice that is used to simply specify the two ports with parameter values provided in rectangular, Cartesian, and polar form. Rectangular complex impedances and admittances, voltage and current gains of transfer functions, and two ports can be properly modelled using the third model for dependent sources using FREQ option of analogue behavioural modelling of Pspice Lite. A common emitter circuit from fictitious data to represent non-linear model is cascaded with passive circuit, and the AC response to circuit is determined and verified. The method and procedure described here would be useful for currently available circuit simulation programs like OrCAD are not necessarily at low frequencies. A combination of these like the Laplacian analog behavioural model with FREQ option to represent a two port circuit would also yield results, which can be verified with designed circuits by practical and experimental results. *

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