# The node voltage method of circuit analysis

### Nodal analysis tutorial

Basic case1[ edit ] Basic example circuit with one unknown voltage, V1. We've picked a reference node to be node three, down here. Let's do that right here. So let's solve for V1. Each of the m voltage sources in the circuit is associated with a dependent variable. That's the Node Voltage Method, and we're going to go through the rest of this, we've done the first two steps. EN to remaining nodes.

Whoever thought this up was pretty bright and I'm really glad that they wrote it down and shared it with us. This resistor's going to be R1, and we'll give it a value of 4kohms. We'll call this R2, and we'll give it a value of 2kohms.

### Nodal analysis with voltage source

The siemens S is the unit of conductance , having replaced the mho unit. This analysis looks strange because it involves replacing voltage sources with equivalent current sources. These coefficients fall on a diagonal. The circuit on the right leaves no question where the nodes are. What I want to do first is just write down what are the steps of this method? Before we start talking about what this method is, we're going to talk about a new term called a node voltage. The right-hand side of the equations is the associated current source, 0. If the voltage is already known, it is not necessary to assign a variable. This is no coincidence, for the 0. A common node E0 is chosen as a reference point. Example of Node Voltage Method Example: Set up the equations and solve for the node voltages using the numerical values in the above figure.

The last current is Is, minus Is. The equation obtained at node c, equation 3 is not independent of previous two equations 1 and 2; in fact, it may be obtained by adding the equations obtained at nodes a and b.

And here's Step Three. The currents of the two nodes are combined in a single equation, and a new equation for the voltages is formed. So this was step three.

These coefficients fall on a diagonal.

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