Sinusoidal Steady State Analysis Chapter Objectives · Sinusoidal Steady State Analysis Chapter Objectives: Apply previously learn circuit techniques to sinusoidal steady-state analysis.

Sinusoidal Steady State Analysis

Chapter Objectives: Apply previously learn circuit techniques to sinusoidal steady-state

analysis.

Learn how to apply nodal and mesh analysis in the frequency domain.

Learn how to apply superposition, Thevenin’s and Norton’s theorems

in the frequency domain.

Steps to Analyze AC Circuits

Transform the circuit to the Phasor Domain.

Solve the problem using circuit techniques listed below

1) Nodal Analysis

2) Mesh Analysis

3) Superposition

4) Source transformation

5) Thevenin or Norton Equivalents

Transform the resulting circuit back to time domain.

Steps to Analyze AC Circuits

Transform the circuit to the phasor or frequency

domain.

Solve the problem using circuit techniques (nodal

analysis, mesh analysis, superposition, etc.).

Transform the resulting phasor to the time domain.

Time to Freq Solve

Variables in Freq Freq to Time

Nodal Analysis

Since KCL is valid for phasors, we can analyze AC circuits by

NODAL analysis.

Determine the number of nodes within the network.

Pick a reference node and label each remaining node with a

subscripted value of voltage: V1, V2 and so on.

Apply Kirchhoff’s current law at each node except the reference.

Assume that all unknown currents leave the node for each

application of Kirhhoff’s current law.

Solve the resulting equations for the nodal voltages.

For dependent current sources: Treat each dependent current

source like an independent source when Kirchhoff’s current law

is applied to each defined node. However, once the equations are

established, substitute the equation for the controlling quantity to

ensure that the unknowns are limited solely to the chosen nodal

voltages.

Nodal Analysis

Practice Problem 10.1: Find v1 and v2 using nodal analysis

Since KCL is valid for phasors, we can analyze AC circuits by

NODAL analysis.

Nodal Analysis Practice Problem 10.1

Nodal Analysis Practice Problem 10.1

Mesh Analysis

Practice Problem 10.4: Calculate the current Io

Meshes 2 and 3 form a

supermesh as shown in

the circuit below.

Since KVL is valid for phasors, we can analyze AC circuits by

MESH analysis.

Mesh Analysis Practice Problem 10.4: Calculate the current Io

Mesh Analysis Practice Problem 10.4: Calculate the current Io

Superposition Theorem The superposition theorem eliminates the need for solving simultaneous linear

equations by considering the effect on each source independently.

To consider the effects of each source we remove the remaining sources; by

setting the voltage sources to zero (short-circuit representation) and current sources

to zero (open-circuit representation).

The current through, or voltage across, a portion of the network produced by each

source is then added algebraically to find the total solution for current or voltage.

The only variation in applying the superposition theorem to AC networks with

independent sources is that we will be working with impedances and phasors

instead of just resistors and real numbers.

The superposition theorem is not applicable to power effects in AC networks

since we are still dealing with a nonlinear relationship.

It can be applied to networks with sources of different frequencies only if the

total response for each frequency is found independently and the results are

expanded in a nonsinusoidal expression .

One of the most frequent applications of the superposition theorem is to

electronic systems in which the DC and AC analyses are treated separately and the

total solution is the sum of the two.

Superposition Theorem

When a circuit has sources operating at different

frequencies,

• The separate phasor circuit for each frequency

must be solved independently, and

• The total response is the sum of time-domain

responses of all the individual phasor circuits.

Superposition Theorem

a) All sources except DC 5-V set to zero b) All sources except 10cos(10t) set to zero

Exp. 10.6 Superposition Technique for sources having different frequencies

Superposition Theorem applies to AC circuits as well.

For sources having different frequencies, the total response must be obtained by

adding individual responses in time domain.

c) All sources except 2 sin 5t set to zero

Superposition Theorem

Exp. 10.6 Superposition Technique for sources having different frequencies

vo= v1+ v2+ v3

Superposition Theorem

Superposition Theorem

Superposition Theorem

P.P.10.6 Superposition Technique for sources having different Frequencies

Superposition Theorem

Superposition Theorem