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Chapter 10 Sinusoidal Steady State Analysis

Chapter 10 Sinusoidal 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.

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Chapter 10 Sinusoidal Steady State Analysis

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  1. Chapter 10Sinusoidal 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. • 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. Huseyin Bilgekul Eeng224 Circuit Theory II Department of Electrical and Electronic Engineering Eastern Mediterranean University

  2. Source Transformation Transform a voltage source in series with an impedance to a current source in parallel with an impedance for simplification or vice versa.

  3. Source Transformation • Practice Problem 10.4: Calculate the current Io If we transform the current source to a voltage source, we obtain the circuit shown in Fig. (a).

  4. Source Transformation • Practice Problem 10.4: Calculate the current Io

  5. 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 areset to zero.

  6. 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:

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

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

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

  11. 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. OP Amp AC Circuits • Practice Problem 10.11: Calculate voand current io The frequency domain equivalent circuit.

  13. OP Amp AC Circuits • Practice Problem 10.11: Calculate voand current io

  14. OP Amp AC Circuits • Practice Problem 10.11: Calculate voand current io

  15. OP Amp Capacitance Multiplier Circuit Capacitance multiplier: The circuit acts as an equivalent capacitance Ceq

  16. 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. 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). Produce overall gain greater than 1 - INPUT OUTPUT + INPUT Phase shift circuit to produce 180 degree shift

  18. Assignment to be Submitted Vo V2 • 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.

  19. 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. Similar Oscillator as the Assignment

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