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Methods of Analysis of Resistive Circuits

Node voltage with Current Sources

Analyzing a circuit containing n nodes will require n-1 KCL equations.

One way to obtain equations is to apply KCL to all nodes but one. The node where you dont apply the equations is called the reference node. (Often the bottom node).

The voltage at any node of the circuit, relative to the reference node is called a node voltage.

To write a set of node equations:

Express element currents as functions of the node voltages

Apply Kirchhoff's current law (KCL) at each of the nodes (except for the reference)

Although we want to express element currents as functions of the node voltages, we start by expressing element voltages

Once we know the node voltages or have expressions for node voltages we can apply Ohm's Law to find the currents

Node voltage with Current Sources and Voltage Sources

Supernode: two nodes connected by an independent or dependent voltage source.

Node voltage with Dependent Sources

When a circuit contains a dependent source the controlling current or voltage of that source must be expressed as a function of the node voltages.

Methods of Analysis of Resistive Circuits

Mesh Current method:

The mesh current method uses a new type of variable called the mesh current. The "mesh current" equations are a

set of simultaneous equations that represent a given electric circuit.

The unknown variables are the mesh currents .

When to use?

Circuits with resistors and independent voltage sources.

Circuits with resistors and independent current and voltage sources.

Circuits with resistors and independent and dependent voltage and current sources.

Node voltage method:

The mesh current method uses a new type of variable called the node voltage. The "node voltage" equations are a

set of simultaneous equations that represent a given electric circuit.

The unknown variables are the node voltages .

When to use?

Circuits with resistors and independent current sources.

Circuits with resistors and independent current and voltage sources.

Circuits with resistors and independent and dependent voltage and current sources.

A mesh is a loop that does not contain any other loops with in it.

We use the convention of a mesh current in the clockwise direction.

To write a set of mesg equations:

Express element voltages as functions of the mesh currents.

Apply Kirchhoff's voltage law (KVL) at each of the meshes.

Mesh current analysis with current and voltage sources

If the circuit has an independent current source, we recognize that the second mesh current is equal to the negative of the current source current.

Supermesh: one larger mesh created from two meshes that have an independent current source in common.

Mesh current analysis with dependent sources

When a circuit contains a dependent source, the controlling current or voltage of that source must be expressed as a functions of the mesh currents.

Node Voltage

Mesh Current