## Mesh Current Equations and Node Voltage Equations

Objectives: We want to be able to
• identify the node voltages and mesh currents in a circuit diagram.
• analyze a dc circuit by writing and solving node voltage equations.
• analyze a dc circuit by writing and solving mesh current equations.
• identify the supernodes and supermeshes in a circuit diagram.
• determine the element voltages and current from the node voltages or mesh currents.

Reading: Chapter 4.

1. Node voltages are described in Section 4.2. In particular, Figure 4.2-1 and asscociated text illustrates the meaning of the term "a node voltage".
2. Figure 4.2-2 shows how to express element currents and voltages as functions of the node voltages.
3. There isn't any easy way to express voltage source currents as functions of the node voltages, so in Section 4.2 we first consider circuits consisting only of resistors and current sources.
4. Section 4.3 shows how to write node equations for circuits that contain voltage sources. Supernodes are introduced as a shortcut for writing node equations for circuits with certain voltage sources. A supernode is illustrated in Figure 4.3-2.
5. Section 4.4 shows how to write node equations for circuits that contain dependent sources.
6. Mesh currents are described in Section 4.5. In particular, Figure 4.5-3 shows how to measure the mesh currents.
7. Figure 4.5-4 shows how to express element currents and voltages as functions of the mesh currents.
8. There isn't any easy way to express current source voltages as functions of the mesh currents, so in Section 4.5 we first consider circuits consisting only of resistors and voltage sources.
9. Section 4.6 shows how to write mesh equations for circuits that contain current sources. Supermeshes are introduced as a shortcut for writing mesh equations for circuits with certain current sources. A supermesh is illustrated in Figure 4.6-7.
10. Section 4.7 shows how to write mesh equations for circuits that contain dependent sources.
11. Should we use node equations or mesh equations? Section 4.8 compares these methods..
12. Section 4.9 illustrates the use MATLAB to solve node or mesh equations.
13. Section 4.10 shows how to use Ohm's and Kirchhoff's laws to check the results of circuit analysis using mesh or node equations.

Lecture Notes: Small circuits can be analyzed by writing and solving Ohm's and Kirchhoff's law equations. As the circuit size increases, so does the number of equations. Formal methods - Node Voltage Analysis and Mesh Current Analysis - use fewer equations.

• Node Voltage Analysis involves writing and solving the node equations, a set of simultaneous equations whose unknowns are the node voltages. To write the node equations, we

1. Identify the node voltages.
2. Express the element currents and voltages as functions of the node voltages.
3. Apply KCL at the nodes of the circuit.

• Mesh Current Analysis involves writing and solving the Mesh Equations, a set of simultaneous equations whose unknowns are the mesh currents. To write the mesh equations, we

1. Identify the mesh currents.
2. Express the element currents and voltages as functions of the mesh currents.
3. Apply KVL to the meshes of the circuit.

• Detemining element voltages and currents from node voltages or mesh currents.

• Supernodes and supermeshes.

Handouts:

Return to
ES250 Home Page.