sinusoidal steady state analysis chapter objectives · sinusoidal steady state analysis huseyin...

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.

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

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).

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

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

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.

OP Amp AC Circuits Practice Problem 10.11: Calculate vo and current io

OP Amp AC Circuits Practice Problem 10.11: Calculate vo and current io

Capacitance multiplier: The circuit acts as an equivalent capacitance Ceq

2

1

11i

i eq

i eq

V RZ C C

I j C R

OP Amp Capacitance Multiplier Circuit

( )1i o

i i o

V VI j C V V

j C

0 2

0

1 2 1

0 0ii

V V RV V

R R R

2 2

1 1

Substituting, (1 ) or (1 )ii i

i

IR RI j C V j C

R V R

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.

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

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

Assignment (Analytic Solution)

Chapter 10, Solution 91.

voltage at the noninverting terminal of the op amp 2V

oV output voltage of the op amp

110 p o sk R R j L

j C

Z Z

2 2

2

) )( ( 1

p o o

o s p o oo

R CR

j C R RR R j L

C

j LC

ZV V

V Z Z V

For this to be purely real,

2

-3 -9

1 1 11 0

2 2 (0.4 10 )(2 10180kHz Osc. Fr

)eq.o o oLC f

LC LC

o

o

oo

oo

o

2

RR

R

)RR(C

CR

V

VAt oscillation,

This must be compensated for by

2

8040

11 5 4

20k

5

o ov o

o

RR R

R R

VA

V

Similar Oscillator as the Assignment

OP Amp AC Circuits Practice Problem 10.11: Calculate vo and current io

The frequency domain equivalent circuit.