Understanding Mesh Circuits How to Use and Calculate Them

Microcontrollers and other digital systems concern mostly ones and zeros but when connections to the real word are needed it can get messy. Stuart writes about mesh analysis and how mesh circuits can be calculated and applied in practical scenarios.

- Stuart Ball

When working with microcontrollers and other digital systems, we don't usually have to be concerned about anything but ones and zeros, right? But sometimes our MCU has to connect to the real world, and that can be messy. Sometimes we have to use that algebra that we couldn't see the need for in high school to make sure that we get the inputs or outputs we want and do it without damaging anything in the process. And in some cases, mesh analysis is how we handle that. I want to show you a few simple mesh circuits, and how they may be calculated and applied in practical scenarios. If you went to EE school, you probably saw this material in a fundamentals of electrical engineering course.

SIMPLE MESH CIRCUIT

Figure 1 shows a simple mesh circuit of three resistors. For a review of resistors, see my article "Getting Started with Resistors" in Circuit Cellar issue 382. Let's say that we need to calculate the voltage across the 2K resistor R2. This is fairly simple to do using series/parallel resistor calculations. R2 is 2K, R3 is 3K, so the value of R2 and R3 in parallel is 1.2K.

The current through R1 plus the parallel combination of R2 and R3 is:

The voltage across the parallel combination of R2 and R3 is:

2.27ma x 1.2K = 2.73 v

So the current through R2 is 2.73V/2K = 1.36 ma.

This simple example illustrates some general principles of mesh circuits:

•The sum of the currents into a node (connection) is zero. The current flowing into the junction of R1, R2, and R3 has to equal the current flowing out. So the 2.27ma flowing in through R1 has to equal the two currents flowing out through R2 and R3. Note that in doing the calculations, you can (and usually do) assume that all currents are positive, flowing into the circuit. When you do the math, at least one will turn negative.