The following represents the steps necessary for obtaining a set of simultaneous equations (nodal analysis) to be used to solve for node voltages.

1. Make a neat and simple circuit diagram. Indicate all element and source values. Conductance values are preferable to resistance values. Each source should have its reference symbol.

 

2. Assuming that circuit has "N" independent nodes, choose one of these nodes as a reference node. Then write the node voltages V₁, V₂,...,V_N-1 at their respective nodes, remembering that each node voltage is understood to be measured with respect to the chosen reference.

 

3. If the circuit contains only current sources, apply Kirchoff's current law at each non-reference node. To obtain the conductance matrix if a circuit has only independent current sources, equate the total current leaving each node through all conductances to the total source current entering that node. Order the terms from V₁ to V_N-1. For each dependent current source present, relate the source current and the controlling quantity to the variables V₁, V₂,...,V_N-1, if they are not already in that form.

 

4. If the circuit contains voltage sources, temporarily modify the given circuit by replacing each such source by a short circuit (creating a supernode) thus reducing the number of nodes by one for each voltage source that is present. The assigned node voltages should not be changed. Using these assigned node-to-reference voltages, apply Kirchoff's current law at each of the nodes or supernode in this modified circuit. Relate each source voltage to the variables V₁, V₂,...,V_N-1, if it is not already in that form.

The following represents the steps necessary for obtaining a set of simultaneous equations (mesh analysis) to be used to solve for mesh currents.

1. Make certain that the network is a "planar" network. If it is non-planar, mesh analysis is not applicable.

 

2. Make a neat and simple circuit diagram. Indicate all element and source values. Resistance values are preferable to conductance values. Each source should have its reference symbol.

 

3. Assuming that circuit has "M" independent meshes, assign a clockwise mesh current in each mesh, i₁, i₂, ..., i_M.

 

4. If the circuit contains only voltage sources, apply Kirchoff's voltage law around each mesh. To obtain the resistance matrix if a circuit has only independent voltage sources, equate the clockwise sum of all the resistor voltages to the counter-clockwise sum of all the source voltages, and order the terms i₁ to i_M. For each dependent voltage source present, relate the source voltage and the controlling quantity to the variables i₁, i₂, ..., i_M, if they are not already in that form.

 

5. If the circuit contains current sources, temporarily modify the given circuit by replacing each such source by an open circuit (creating a supermesh) thus reducing the number of meshes by one for each current source that is present. The assigned mesh currents should not be changed. Using these assigned mesh currents, apply Kirchoff's voltage law around each of the meshes or supermeshes in this modified circuit. Relate each source current to the variables i₁, i₂, ..., i_M, if it is not already in that form.