Thevenin and Norton Resistance Using Time Domain Analyses Using Spice Simulations

Abstract

Thevenin and Norton equivalent circuits are of interest to circuit simulation designers and researchers. For the Thevenin resistance and Norton conductance determination of a network with available circuit theorems, the substitution network theorem (applied to OrCAD, SPICE, and Pspice AD simulation project) is shown to be suitable with the SPICE/ Pspice circuit simulation software. Instead of the DC option, the transient analyses option of SPICE is used to determine Thevenin/Norton conductance/resistance to pure resistive and active circuits, using polynomial sources for voltage to current division. The procedure can be extended to personal computer software like Pspice, OrCAD, and MicroCAP. The described application procedure can also be applied to active circuits with HEMT, and BJTs represented by their small signal/linear models. The results can also be verified by the Superposition theorem and individual resistances could also be replaced by the Analog behavioral modeling (VALUE) option available in the OrCAD simulation program. By using temperature dependent models for resistors to look up tables for use in electronics circuits for THEVENIN and NORTON equivalents can be obtained. For tutorial interest. the substitution theorem variants can also be used to determine Thevenin/Norton immittance; for the Thevenin resistance determination the equation with arbitrary value of k’ {I branch * Runknown + k’ *Thevenin voltage = 1/2 * Thevenin voltage}, can be used to know R unknown which should be substituted at the termination in series with k’* Thevenin voltage. The terminating value for Norton conductance GNOR/k’ with independent current source k1 *Isc can be obtained with the following equation {Isc/2 = k1*Isc + GNOR*Vbranch/k’}. The individual Thevenin/Norton resistances could also be employed as substitutes for larger circuits, for time domain and DC analyses and verification.