Week 14 Sinusoidal Steady State Analysis Chapter Objectivesncbs.knu.ac.kr/Teaching/CT1_Files/CT1_Weeks_14.pdf · 2017-03-06 · KNU/EECS/CT1 Dr. Kalyana Veluvolu 1 Week 14 Sinusoidal

1KNU/EECS/CT1 Dr. Kalyana Veluvolu

Week 14Sinusoidal 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.


20cos(5 30 ) At − °1

5Ω 2 F

1H

10


Z1

Find V0 in the circuit shown below


Problem


Chapter 9, Problem 51.


Problem 9.46 If is

= 5 cos (10t + 40°) A in the circuit in the Figure, find io.


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.


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


Mesh Analysis


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.



Exp. 10.6 Superposition Technique for sources having different frequencies

Superposition Theorem applies to AC circuits as well.

For sources having different frequencies, separate phasor circuit for each frequency

must be solved independently, and the total response must be obtained by adding

individual responses in time domain.


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


vo= v1+ v2+ v3

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



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






Transform a voltage source in series with an impedance to a current source in

parallel with an impedance for simplification or vice versa.

Source Transformation


Source Transformation

If we transform the current source to a voltage source, we obtain the circuit shown in Fig. (a).

Practice Problem 10.4: Calculate the current Io


Source Transformation Practice Problem 10.4: Calculate the current Io


Thevenin Equivalent Circuit Thévenin’s theorem, as stated for sinusoidal AC circuits, is changed only to

include the term impedance instead of resistance.

Any two-terminal linear ac network can be replaced with an equivalent

circuit consisting of a voltage source and an impedance in series. VTh is the Open circuit voltage between the terminals a-b.

ZTh is the impedance seen from the terminals when the independent sources are

set to zero.


Norton Equivalent Circuit The linear circuit is replaced by a current source in parallel with an impedance.

IN is the Short circuit current flowing between the terminals a-b when the

terminals are short circuited.

Thevenin and Norton equivalents are related by:

Th N N Th NV Z I Z Z= =


Thevenin Equivalent CircuitP.P.10.8 Thevenin Equivalent At terminals a-b


Thevenin Equivalent CircuitP.P.10.9 Thevenin and Norton Equivalent

for Circuits with Dependent Sources

To find Vth , consider the circuit in Fig. (a).


Thevenin Equivalent CircuitP.P.10.9 Thevenin and Norton Equivalent for Circuits with Dependent Sources





Since there is a dependent source, we can find the impedance by inserting a voltage source

and calculating the current supplied by the source from the terminals a-b.


Grades will be posted on my Website, Check after 24-June.

Best of Luck for you Final Exam

Thanks for attending my Lectures

End of Circuit Theory class………

Documents

Week 14 Sinusoidal Steady State Analysis Chapter Objectivesncbs.knu.ac.kr/Teaching/CT1_Files/CT1_Weeks_14.pdf · 2017-03-06 · KNU/EECS/CT1 Dr. Kalyana Veluvolu 1 Week 14 Sinusoidal