figure 2-1 block diagram of a rectifier and a dc power...
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Circuit Analysis-II Spring-2015 EE -1112
Instructor: Hafiz Zaheer Hussain Email: [email protected]
www.hafizzaheer.pbworks.com
Department of Electrical Engineering The University of Lahore
Week 5
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Fundamentals of Electric Circuits
by Alexander-Sadiku
Chapter 10 Sinusoidal Steady-State
Analysis
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Chapter 10 Sinusoidal Steady-State Analysis
10.1 Introduction 10.2 Nodal Analysis 10.3 Mesh Analysis 10.4 Superposition Theorem 10.5 Source Transformation 10.6 Thevenin and Norton Equivalent Circuits 10.7 Op Amp AC Circuits 3/25/2015 4
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In Chapter 9, we learned that the forced or steady-state response of circuits to sinusoidal inputs can be obtained by using phasors. We also know that Ohm’s and Kirchhoff’s laws are applicable to ac circuits.
10.1 Introduction
In this chapter, we want to see how nodal analysis, mesh analysis, Thevenin’s theorem, Norton’s theorem, superposition, and source transformations are applied in analyzing ac circuits. Since these techniques were already introduced for dc circuits, our major effort here will be to illustrate with examples.
Analyzing ac circuits usually requires three steps.
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Steps to Analyze AC Circuits:
1. Transform the circuit to the phasor or frequency domain.
2. Solve the problem using circuit techniques (nodal analysis, mesh analysis, superposition, etc.).
3. Transform the resulting phasor to the time domain.
Time to Freq Solve variables in Freq
Freq to Time
10.1 Introduction
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Chapter 10 Sinusoidal Steady-State Analysis
10.1 Introduction 10.2 Nodal Analysis 10.3 Mesh Analysis 10.4 Superposition Theorem 10.5 Source Transformation 10.6 Thevenin and Norton Equivalent Circuits 10.7 Op Amp AC Circuits 3/25/2015 7
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Since you are already familiar with the Nodal method, we will not go into the explanation. We will only be solving few problems, to under the technique for AC steady state analysis.
10.2 Nodal Analysis
•Recap of Nodal Analysis
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Some Basic Concept
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Continue
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10.2 Nodal Analysis
Find ix in the circuit of Fig. 10.1 using nodal analysis. Example 10.1
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10.2 Nodal Analysis
We first convert the circuit to the frequency domain:
Thus, the frequency domain equivalent circuit is as shown in Fig.
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10.2 Nodal Analysis Applying KCL at node 1,
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10.2 Nodal Analysis
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PP 10. 1
Using nodal analysis, find v1 and v2 in the circuit of figure below.
v1(t) = 11.32 sin(2t + 60.01) V v2(t) = 33.02 sin(2t + 57.12) V
Answer:
10.2 Nodal Analysis
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10.2 Nodal Analysis (supernodes)
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10.2 Nodal Analysis ( supernodes)
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10.2 Nodal Analysis (supernodes)
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10.2 Nodal Analysis (supernodes) PP 10. 2
Chapter 10 Sinusoidal Steady-State Analysis
10.1 Introduction 10.2 Nodal Analysis 10.3 Mesh Analysis 10.4 Superposition Theorem 10.5 Source Transformation 10.6 Thevenin and Norton Equivalent Circuits 10.7 Op Amp AC Circuits 3/25/2015 24
Mesh Analysis
• Kirchoff’s voltage law (KVL) forms the basis of mesh analysis.
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Superposition Theorem
The superposition theorem is most useful when networks have sources of different frequencies.
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Superposition Theorem The superposition theorem is most useful when networks have
sources of different frequencies To consider the effects of each source we remove the remaining
sources; by setting every voltage sources to short-circuit, and every current sources by an open-circuit 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.
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Superposition Theorem
When a circuit has sources operating at different frequencies, The separate phasor circuit for each frequency must be
solved independently The total response is the sum of time-domain responses of
all the individual phasor circuits.
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Example 10.6
• Find vo of the circuit of Fig. 10.13 using the superposition theorem.
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To consider the effects of each source we remove the remaining sources; replace every voltage sources to short-circuit, every current sources by an open-circuit
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