Methods of Analysis

EE 2010: Fundamentals of Electric CircuitsMujahed AlDhaifallah

Nodal Analysis

Identify the nodes in the circuit. Pick a reference node (usually the ground) Define node voltages with respect to the

reference for all nodes. Apply KCL at all nodes. Solve the resulting linear equations.

Example

Nodal Analysis with DependentSources Dependent sources are handled the same way

we handled independent sources The node voltage equations must be

supplemented with an additional equation resulting from the dependent source

Observations from visual inspection don’t apply for circuits containing dependent sources

Examples

Nodal Analysiswith Voltage Sources 3 cases: The voltage source connects one of the

nodes and the ground The voltage source lies between two

nonreference nodes The voltage source has a series resistor

Nodal Analysis with Voltage Sources (I) The voltage source connects one of the

nodes and the ground: Solution: node voltage = voltage of the

voltage source

Nodal Analysis with Voltage Sources (II) The voltage source is connected between two

nonreference nodes: Problem: the current through the voltage source is

unknown Solution: form a “supernode” and apply KCL+KVL to

the supernode

Nodal Analysis with Voltage Sources (III)

Bridge Circuits

R2

R4

R1

R5

R3

Bridge Circuit

Planar / Non–planar circuits?

Planar vs. Non-planar

Bridge Circuits

Symmetrical Lattice Network if R1 = R4 and R2 = R3

R2

R4

R1

R5

R3

Y - Δ Conversions

R2R1

R3

RC

RBRA

Y-∆ (T- π) and ∆ -Y (π -T) Conversions Circuit configurations are encountered in which

the resistors do not appear to be in series or parallel; it may be necessary to convert the circuit from one form to another to solve for the unknown quantities if mesh and nodal analysis are not applied. Two circuit configurations that often account for

these difficulties are the wye (Y) and delta (∆) configurations.

They are also referred to as tee (T) and the pi (π) configurations.

Y-∆ (T- π) and ∆ -Y (π -T) Conversions

1) ∆ -Y (π -T) Conversion

Note that each resistor of the Y is equal to the product of the resistors in the two closest branches of the ∆ divided by the sum of the resistors in the ∆.

EXAMPLE Find the total resistance of the network shown in

the Fig., where RA = 3 , RB = 3 , and RC = 6.

Another Example