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Nodal Analysis

- Find all essential nodes.
- Choose one essential node as the reference node, then label
the remaining essential nodes with node voltage variables (V
_{A}, V_{B}, etc.) - If the circuit contains dependent sources, express all parameters upon which these sources depend in terms of the node voltages.
- If the circuit contains any voltage sources directly connecting two essential nodes, equate the value of each such voltage to the difference in the node voltages to which the source is connected.
- For each voltage source in step 4, form a supernode (this can be done by replacing the voltage source with a wire, or follow the method for marking supernodes given here.)
- For each remaining essential node (except the reference node) and supernode which does not contain the reference node , write a KCL equation, using Ohm's Law as necessary to express the current through resistors in terms of the node voltages.
- For any equations from Steps 4 and 6 containing dependent sources, substitute the expressions from Step 3 into these so that all equations contain only the node voltage variables.
- Solve the set of equations for the node voltages, then any other parameter in the circuit can be obtained by Kirchoff's Laws and Ohm's Law.

Mesh Analysis

- If the circuit has crossing wires, redraw it with no wires crossing. If it cannot be redrawn in this manner, then it is not a planar circuit and mesh analysis cannot be used.
- For each mesh in the circuit, define a mesh current (I
_{A}, I_{B}, etc.) - If the circuit contains dependent sources, express all parameters upon which these sources depend in terms of the mesh currents.
- If any current sources are present, express the value of each in terms of the mesh currents through the branch containing the source.
- Delete (erase) each current source thus forming supermeshes (or if the current source is in a branch which is part of only one mesh, eliminating a mesh).
- For each supermesh and each remaining mesh, write a KVL equation, using Ohm's law as necessary to express the voltage across resistors in terms of the mesh currents.
- For any equations from Steps 4 and 6 containing dependent sources, substitute the expressions from Step 3 into these so that all equations contain only the mesh current variables.
- Solve the set of equations for the mesh currents, then any other parameter in the circuit can be obtained by Kirchoff's Laws and Ohm's Law.

Thevenin and Norton Equivalent Circuits

There are several methods for finding the Thevinin and Norton equivalent circuits, and only experience will allow you to easily identify which technique is the easiest in any given situation. If unsure, pick Method 2 since it will work in all cases.

The Thevenin Equivalent looking into any two terminals of any circuit containing only linear components comprises a voltage source and a resistor (In Chapter 9 this will be generalized to an impedance) in series.

The Norton equivalent comprises a current source in parallel with a resistor (impedance).

The Thevenin and Norton equivalents are interchangeable through source transformation, thus the resistance (impedance) is the same for both.

METHOD 0 (Used only if the circuit contains NO dependent sources.)

Use combinations of source transforms and resistor combinations (possibly including delta-Y and Y-delta transforms) until the circuit tis reduced to the Thevenin or Norton equivalent. If the circuit contains only resistors (no sources) then the Thevenin and Norton equivalents will simply be a single resistor.

METHOD 1 (Used only if the circuit contains at least one independent source.)

If a load is connected to the two terminals in question, remove
it, leaving only the circuit for which you wish the equivalent.
Denote the voltage between the terminals as V_{OC}
(open-circuit voltage). Determine V_{OC}
by any means you wish (nodal analysis, mesh analysis, circuit
reduction, etc.). V_{OC} is the
value of the Thevinin equivalent voltage source (V_{Th}=V_{OC}), and the positive terminal of
the source is oriented toward the terminal which was labelled
as the positive reference of V_{OC}.

Next, connect a wire between the two terminals, and define
a current I_{SC} (short-circuit
current) with the arrow going from the terminal that was previously
the positive reference for V_{OC}
and toward the terminal that was the negative reference for V_{OC}. (Note that V_{OC}
no longer exists since we shorted out the terminals!) Determine
this current by any method you wish (mesh, node, reduction, etc.).
I_{SC} is the value of the Norton
equivalent source. Note that the arrow of this source must point
toward the terminal from which I_{SC}
was leaving (i.e., the one that was originally marked with the
positive reference of V_{OC}).

The Thevinin equivalent resistance may now be determined using
Ohm's Law from V_{OC} and I_{SC}. R_{Th}
= V_{OC}/I_{SC}.
Remember that the Norton resistance is the same as the Thevenin
resistance.

METHOD 2

Determine either V_{OC} (V_{Th}) or I_{SC}
(I_{N}) as in Method 1 above. If
there are no independent sources, both of these values will be
zero, and the Thevenin and Norton equivalent circuits consist
of a single resistor (impedance).

Determine R_{Th}. There are
two cases.

Case 1 - No dependent sources present.

- Kill all independent sources (remove current sources, replace voltage sources with a wire).
- Find R
_{Th}using circuit reduction techniques.Note that case 1 may also be solved using the technique explained for Case 2 below.

Case 2 - Dependent sources may be present.

- Kill any independent sources as mentioned in case 1.
- Connect a one volt source between the terminals on the circuit in question. *
- Determine by any means (mesh, node, reduction, etc.) the current I leaving the positive terminal of the one-volt source.
- Calculate the Thevenin equivalent resistance by dividing one volt by the current it generated into the circuit. (Note that if dependent sources are present you might get a negative resistance!) R
_{Th}= 1 / I*Alternately, you could connect a one ampere source and determine the voltage V created across the terminals, then the numerical value of the resistance equals that of the generated voltage (R

_{Th}= V / 1 ).

RL and RC Circuits with DC sources

This material still in preparation.

RLC Circuits with DC sources

This material still in preparation.