Main content

Loop current method

The Loop Current Method is closely related to the Mesh Current Method. Use it for two special cases: non-planar circuits, and when a current source is shared between two meshes.

Introduction

The Loop Current Method is a small variation on the Mesh Current Method. It accounts for two special cases that are bothersome for the Mesh method. In this article we describe the special cases and show how to deal with them using the Loop method.

The Loop Current Method, just like the Mesh Current Method, is based on Kirchhoff's Voltage Law (KVL).

What we're building to

The two special cases are a non-planar circuit (one that can't be drawn without crossing wires) and a circuit with a current source shared between two meshes.

To analyze circuits like this, you include equations for some non-mesh loops. Make sure every loop includes a circuit element that is not part of any other loop. The steps in the Loop Current Method are otherwise the same as the Mesh Current Method.

Special case: non-planar circuit

The Mesh Current Method defines equations based on meshes. This works for circuits that are planar.

Planar vs. non-planar

A circuit is planar if it can be drawn on a flat surface without crossing wires. All the schematics you have seen up to now are planar. The schematic below on the left is planar. For planar circuits, we use the Mesh Current Method and write the equations based on meshes. This always works for planar circuits.
A non-planar circuit is shown below on the right. It has has to be drawn with at least one crossing wire, meaning it cannot be drawn flat. Since there is no way to redraw the circuit to avoid a crossing wire, the circuit on the right is non-planar.

When faced with a non-planar circuit, we must use the Loop Current Method (described below).

Another special case: current source shared by two meshes

A second special case comes up when you have a current source shared between two meshes. This is another time when you may want to include a non-mesh loop in the system of equations.

Both mesh

I

and mesh

II

go through the current source. It is possible (but irksome) to write and solve mesh equations for this configuration. (Try it and see what it's like. It is quite awkward to figure out the voltage at the node above the current source.)

This is a time when you might want to use a loop. You can drop one of the meshes and replace it with the loop that goes around both meshes, as shown here for loop

III

You then solve the system of equations exactly the same as the Mesh Current Method.

You may see loop

III

referred to as a supermesh.

Selecting loops

We can make a small adjustment to the Mesh Current Method to help us with the two special cases: We allow loops to participate in the equation-building step (not just meshes). This isn't a big deal. When selecting which loops to include:

Make sure every element is included in a loop or mesh. Every element needs to have a chance to influence the solution.
Make sure at least one element in each loop is not part of any other loop or mesh. This assures the loop equations are independent.

These rules generate just the right number of independent equations to solve the circuit.