This document contains chapter summaries and practice problems from a textbook on sinusoidal steady-state analysis of circuits. The chapter objectives are to apply circuit analysis techniques to AC circuits using nodal analysis, mesh analysis, superposition, Thevenin's and Norton's theorems. It also covers analyzing op-amp circuits, capacitance multipliers, and oscillators in the frequency domain. Sample problems are provided to calculate voltages, currents, and equivalents for various AC circuits including those with dependent sources. The assignment is to simulate an oscillator circuit in PSpice and verify the required phase shift and oscillation frequency.

1. ‹#›
Eeng224
Chapter 10
Sinusoidal Steady State Analysis
Huseyin Bilgekul
Eeng224 Circuit Theory II
Department of Electrical and Electronic Engineering
Eastern Mediterranean University
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.

2. ‹#›
Eeng224
 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

3. ‹#›
Eeng224
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

4. ‹#›
Eeng224
Source Transformation
 Practice Problem 10.4: Calculate the current Io

5. ‹#›
Eeng224
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.

6. ‹#›
Eeng224
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 N
V Z I Z Z
 

7. ‹#›
Eeng224
Thevenin Equivalent Circuit
P.P.10.8 Thevenin Equivalent At terminals a-b

8. ‹#›
Eeng224
Thevenin Equivalent Circuit
P.P.10.9 Thevenin and Norton Equivalent
for Circuits with Dependent Sources
To find Vth , consider the circuit in Fig. (a).

9. ‹#›
Eeng224
Thevenin Equivalent Circuit
P.P.10.9 Thevenin and Norton Equivalent for Circuits with Dependent Sources

10. ‹#›
Eeng224
Thevenin Equivalent Circuit
P.P.10.9 Thevenin and Norton Equivalent for Circuits with Dependent Sources

11. ‹#›
Eeng224
Thevenin Equivalent Circuit
P.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.

12. ‹#›
Eeng224
OP Amp AC Circuits
 Practice Problem 10.11: Calculate vo and current io
The frequency domain equivalent circuit.

13. ‹#›
Eeng224
OP Amp AC Circuits
 Practice Problem 10.11: Calculate vo and current io

14. ‹#›
Eeng224
OP Amp AC Circuits
 Practice Problem 10.11: Calculate vo and current io

15. ‹#›
Eeng224
 Capacitance multiplier: The circuit acts as an equivalent capacitance Ceq
2
1
1
1
i
i eq
i eq
V R
Z C C
I j C R

 
   
 
 
OP Amp Capacitance Multiplier Circuit
( )
1
i o
i i o
V V
I j C V V
j C



   0 2
0
1 2 1
0 0
i
i
V V R
V V
R R R
 
   
2 2
1 1
Substituting, (1 ) or (1 )
i
i i
i
I
R R
I j C V j C
R V R
 
   

16. ‹#›
Eeng224
Oscillators
 An oscillator is a circuit that produces an AC waveform as output when
powered by a DC input (The OP AMP circuit needs DC to operate).
 A circuit will oscillate if the following criteria (BARKHAUSEN) is satisfied.
 The overall gain of the oscillator must be unity or greater.
 The overall phase shift from the input to ouput and back to input must be
zero.

17. ‹#›
Eeng224
Oscillators
 An oscillator is a circuit that produces an AC waveform as output when powered by a
DC input (The OP AMP circuit needs DC to operate).
OUTPUT
+ INPUT
- INPUT
Phase shift circuit to
produce 180 degree
shift
Produce overall gain
greater than 1

18. ‹#›
Eeng224
Assignment to be Submitted
Construct the PSpice schemmatic of the oscillator shown Prob. 10.91 from the
textbook which is also shown above.
 Display the oscilloscope AC waveforms of V2 and Vo to show the phase
relationship.
 Submit the printout of your circuit schemmatic and the oscilloscope waveforms
of V2 and Vo as shown in the next page for a similar circuit.
 Do you obtain the required phase shift and the oscillation frequency? If not it will
not oscillate to produce a pure sine wave.
 Submission date 21 March 2007.
 The analytic solution is given in the next page to help your simulation.
Vo
V2

19. ‹#›
Eeng224
Assignment (Analytic Solution)
Chapter 10, Solution 91.
voltage at the noninverting terminal of the op amp

2
V

o
V output voltage of the op amp
1
10
p o s
k R R j L
j C


     
Z Z
2 2
2
) )
( ( 1
p o o
o s p o o
o
R CR
j C R R
R R j L
C
j LC





  
  
 
 
Z
V V
V Z Z V
For this to be purely real,
2
-3 -9
1 1 1
1 0
2 2 (0.4 10 )(2 10
180kHz Osc. Fr
)
eq.
o o o
LC f
LC LC
 
 
  
    
 
o
o
o
o
o
o
o
2
R
R
R
)
R
R
(
C
CR






V
V
At oscillation,
This must be compensated for by
2
80
40
1
1 5 4
20
k
5
o o
v o
o
R
R R
R R
     
   

V
A
V

20. ‹#›
Eeng224
Similar Oscillator as the Assignment