# Methods to obtain a new Circuit whose Thevenin & Norton Equivalents are functions of two different Thevenin & Norton Circuits

Author: K. Bharath Kumar, Researcher

### Abstract

Thevenin and Norton equivalent of two different networks is obtained by using the Pspice simulation analysis program. The new networks have Thevenin(Norton) impedance which are product and numerical division of two different individual networks , Thevenin voltage (Norton current) which are numerical multiple and sum  of the given Thevenin voltage (Norton current) of  individual  two networks.

### I INTRODUCTION

SPICE/PSPICE methods to obtain Thevenin, Norton equivalent circuits for purely resistive and networks with R, L, C  elements , and dependent sources are described [1-4] by the author previously. In this idea, a circuit method which is implemented by Pspice software, to obtain the following equivalent circuits is described.

1. A Thevenin equivalent circuit whose, (i) open circuit voltage is the multiple of two open circuit voltages (two different circuits, a purely resistive with independent and dependent sources, and another consisting of resistive and independent sources),(ii) Thevenin impedance which is a negative multiple of two Thevenin impedances (two different circuits, again a purely resistive and independent/dependent sources, and another consisting of DC sources and resistive circuit elements).
2. A Norton equivalent circuit whose, (i) short circuit current is the sum of two short circuit currents(two different circuits, a purely resistive, and another consisting of AC elements),(ii) Norton admittance which is a division of two Norton impedances (two different circuits, again a purely resistive with dependent and independent sources, and another consisting of AC circuit elements with dependent and independent AC sources ).

### II THE CIRCUITS

Figure 1a. shows a circuit consisting of impedance elements and AC independent and dependent sources. Figure 1b. describes another pure resistive network consisting of DC sources.

#### Computation of  Equivalent Thevenin voltage  and equivalent Thevenin impedance for Figure 1a-1d:

The individual Thevenin open circuit voltages are obtained for Figures 1a&b using Spice/Pspice files TABLE I. They are multiplied and stored in a single voltage source. The individual Thevenin resistances are computed using Figures 1c &d. The two Thevenin resistances are multiplied and stored in a Spice model for resistor. A one ampere DC current source is used at the input of Figures 1c-d to obtain two Thevenin resistances.

#### TABLE I. SPICE/PSPICE FILE DESCRIPTION TO OBTAIN NEW THEVENIN CIRCUIT

V(18) in TABLE I  is the output voltage for new Thevenin equivalent circuit with 100 Ohm load.

### Computation of Equivalent Norton Current and equivalent Norton impedance for Figure 2a-d    :

The individual short circuit currents and Norton impedances are obtained for Figures 2a-b, and Figure 2c-d,  using Spice/Pspice files (TABLE II) . They are added and stored using  Pspice [5-10] with circuit commands.  The division of individual Norton impedances are obtained through the following technique which can be easily implemented by SPICE or PSpice circuit file. Figure 3 describes the technique using an operational amplifier, used as inverted amplifier with 1 ohm feedback, and Norton impedance  Zn2 as input impedance  and input voltage as  Norton impedance Zn1.

The output would yield the division of Rn1 and Rn2.  Again, the values of divisions which are equivalent to new Norton impedance in ingeneously stored using Pspice FREQ option.

Figure 3. A Opamp technique to obtain division of two impedances

The circuit in Figure 3 is implemented to obtain ratio of Norton Impedances. The two Norton short circuit currents are added and the ratio of impedances are stored by using Analog behavioural FREQ option of PSpice, to obtain new Norton equivalent.

#### TABLE II SPICE/PSPICE CIRCUIT FILE TO OBTAIN NEW NORTON CIRCUIT

The equivalent Norton circuit parameters of new circuit can be verified by the results presented in TABLE II.

### III CONCLUSION

SPICE/PSPICE Circuit simulation and analysis program has been used to obtain equivalents for a new circuit whose Thevenin parameters are

multiples of individual Thevenin parameters of two given circuits and have been verified. Similarly, SPICE/PSPICE Circuit program is used to obtain equivalents for a new Norton circuit whose Norton parameters are sum of individual Norton short circuit currents and numerical complex division of individual Norton impedances.

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