T-π, π-T Network Conversion for Three Identical Impedances and Equivalent Thevenin Networks Using Pspice Software

K Bharath Kumar

Abstract

Conversion methods of T-π (star-delta) π-T for impedances circuits, the behavioural modeling of Pspice simulation program is used to obtain equivalent circuits for two types of passive equivalents consisting of three impedance/resistance in two configurations using LAPLACE option of analog behavioural modelling. 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. Two port Z, Y, H, G parameters, in addition to representing passive networks, can also be used to represent an active small signal or passive electronic circuitby hybrid equations at the input /output from the non-linear model of nonlinear active device.The analog behavioural option which is added in Pspice version of SPICE is effectively used in modelling the two port linear circuits. There are useful models like current generator (VALUE option) which can be used to model DC networks with pure resistances and voltage/current controlled dependent sources. The LAPLACE option is used to conveniently describe the two ports with parameter values given in rectangular or Cartesian and polar form. The third model for dependent sources with FREQ option, of analog behavioural modelling of Pspice Lite can be used effectively to model rectangular complex impedances and admittances and voltage and current gains of transfer functions and two ports. A common emitter circuit from fictitious data to represent non-linear model is cascaded with a circuit using passive elements, 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 at both low and high frequencies. Various combinations 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. A passive network consisting of resistors and impedances can be represented by their equivalent in either T-π (star-delta) model according to circuit theory principles. From the conversion methods of T-π (star-delta) for resistive/impedances circuits, the behavioural modeling of Pspice simulation program, in which various mathematical equations (DC/AC resistance* DC /AC currents= DC /AC voltage) could be represented by non-linear voltage/current dependent sources, is used to obtain equivalent circuits using DC/AC option. The resistors or conductances or immittances are represented by their linear voltage/current relationship. The spice voltage sources are used with zero value to measure currents in the circuit equivalents of resistors. A non-linear Spice BJT model (built-in) is used with proper DC bias with the T-π (star-delta) connection in examples. The conversions’ equivalence are verified for two types of circuits by obtaining DC values of voltages and currents at various nodes and branches using Pspice computer simulations. The method can be used to replace linear and non-linear circuitry by their respective star-delta equivalents in DC bias point calculation and simulation. Now, the Thevenin equivalents for the Network eamples till the Base terminal of non-linear BJT are determined.

T-π, π-T Network Conversion for Three Identical Impedances and Equivalent Thevenin Networks Using Pspice Software

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