with Geometric Circuit Language

Introduction

Thevenin and Norton equivalent circuits are powerful tools for simplifying complex electronic circuits. They replace a given network of voltage sources, current sources, and resistors with an equivalent, simpler circuit. In this blog post, we will explain the concepts of Thevenin and Norton equivalent circuits using the geometric language of electronic circuits.

Thevenin Equivalent Circuit

The Thevenin equivalent circuit consists of an equivalent voltage source (Vth) in series with an equivalent resistance (Rth). To find the Thevenin equivalent circuit of a given network, follow these steps:

Remove the load resistor (RL) from the original circuit.
Calculate Vth, the open-circuit voltage across the terminals where RL was connected.
Calculate Rth by short-circuiting all voltage sources and open-circuiting all current sources, and then finding the equivalent resistance across the terminals.
Reconnect the load resistor RL to the Thevenin equivalent circuit.
Using the geometric language, we can represent a simple example of a Thevenin equivalent circuit as follows:

Original Circuit:
(0,0) (1,0) V 10;
(1,0) (2,0) R 2;
(2,0) (3,0) R 4;
(3,0) (4,0) RL;

Thevenin Equivalent Circuit:
(0,0) (1,0) Vth;
(1,0) (2,0) Rth;
(2,0) (3,0) RL;

Norton Equivalent Circuit

The Norton equivalent circuit consists of an equivalent current source (In) in parallel with an equivalent resistance (Rn). To find the Norton equivalent circuit of a given network, follow these steps:

Remove the load resistor (RL) from the original circuit.
Calculate In, the short-circuit current across the terminals where RL was connected.
Calculate Rn, which is the same as the Rth calculated in the Thevenin equivalent circuit.
Reconnect the load resistor RL to the Norton equivalent circuit.
Using the geometric language, we can represent a simple example of a Norton equivalent circuit as follows:

Original Circuit:
(0,0) (1,0) V 10;
(1,0) (2,0) R 2;
(2,0) (3,0) R 4;
(3,0) (4,0) RL;

Norton Equivalent Circuit:
(0,0) (1,0) In;
(1,0) (1,1) Rn;
(1,1) (1,2) RL;
(1,0) (1,1) -;
(1,1) (1,2) -;

Conclusion

Thevenin and Norton equivalent circuits are essential techniques for simplifying and analyzing complex electronic circuits. Using the geometric language of electronic circuits, we can easily represent and understand these concepts. This compact notation helps to visualize the circuit components and their connections, making it easier to analyze and design electronic circuits.