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Chapter 10 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. Learn how to analyze AC Op Amp circuits.

Be able to use PSpice to analyze AC circuits.

Apply what is learnt to capacitance multiplier and oscillators.

•

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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.

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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.

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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.

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

Nodal Analysis Practice Problem 10.1

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

Nodal Analysis Practice Problem 10.1

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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.

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Mesh Analysis Practice Problem 10.4: Calculate the current Io

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

Mesh Analysis Practice Problem 10.4: Calculate the current Io

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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.

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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.

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

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.

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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

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

Superposition Theorem

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university

‹#› Eeng 224

Superposition Theorem

‹#› Eeng 224

Superposition Theorem

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

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Superposition Theorem

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Superposition Theorem

Payam zarbakhsh

EElE301 Circuit Theory II

Department of Electrical and Electronic Engineering

Cyprus International university