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 I o

4 Eeng224 Source Transformation  Practice Problem 10.4: Calculate the current I o

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.  V Th is the Open circuit voltage between the terminals a-b.  Z Th 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. I N is the Short circuit current flowing between the terminals a-b when the terminals are short circuited.  Thevenin and Norton equivalents are related by:

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 V th, 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 v o and current i o The frequency domain equivalent circuit.

13 Eeng224 OP Amp AC Circuits  Practice Problem 10.11: Calculate v o and current i o

14 Eeng224 OP Amp AC Circuits  Practice Problem 10.11: Calculate v o and current i o

15 Eeng224  Capacitance multiplier: The circuit acts as an equivalent capacitance C eq OP Amp Capacitance Multiplier Circuit

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 from the textbook which is also shown above.  Display the oscilloscope AC waveforms of V 2 and V o to show the phase relationship.  Submit the printout of your circuit schemmatic and the oscilloscope waveforms of V 2 and V o 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  The analytic solution is given in the next page to help your simulation. VoVo V2V2

19 Eeng224 Assignment (Analytic Solution) Chapter 10, Solution 91. voltage at the noninverting terminal of the op amp output voltage of the op amp For this to be purely real, At oscillation, This must be compensated for by

20 Eeng224 Similar Oscillator as the Assignment