1 / 22

Lecture 26

Lecture 26. Review Steady state sinusoidal response Phasor representation of sinusoids Phasor diagrams Phasor representation of circuit elements Related educational materials: Chapter 10.3, 10.4. Steady state sinusoidal response – overview.

evansgeorge
Download Presentation

Lecture 26

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lecture 26 Review Steady state sinusoidal response Phasor representation of sinusoids Phasor diagrams Phasor representation of circuit elements Related educational materials: Chapter 10.3, 10.4

  2. Steady state sinusoidal response – overview • Sinusoidal input; we want the steady state response • Apply a conceptual input consisting of a complex exponential input with the same frequency, amplitude and phase • The actual input is the real part of the conceptual input • Determine the response to the conceptual input • The governing equations will become algebraic • The actual response is the real part of this response

  3. Review lecture 25 example • Determine i(t), t, if Vs(t) = Vmcos(100t). • Let Vs(t) be: • Phasor: • The phasor current is: • So that

  4. Phasor Diagrams • Relationships between phasors are sometimes presented graphically • Called phasor diagrams • The phasors are represented by vectors in the complex plane • A “snapshot” of the relative phasor positions • For our example: • ,

  5. Phasor Diagrams – notes • Phasor lengths on diagram generally not to scale • They may not even share the same units • Phasor lengths are generally labeled on the diagram • The phase difference between the phasors is labeled on the diagram

  6. Phasors and time domain signals • The time-domain (sinusoidal) signals are completely described by the phasors • Our example from Lecture 25:

  7. Example 1 – Circuit analysis using phasors • Use phasors to determine the steady state current i(t) in the circuit below if Vs(t) = 12cos(120t). Sketch a phasor diagram showing the source voltage and resulting current.

  8. Example 1: governing equation

  9. Example 1: Apply phasor signals to equation • Governing equation: • Input: • Output:

  10. Example 1: Phasor diagram • Input voltage phasor: • Output current phasor:

  11. Circuit element voltage-current relations • We have used phasor representations of signals in the circuit’s governing differential equation to obtain algebraic equations in the frequency domain • This process can be simplified: • Write phasor-domain voltage-current relations for circuit elements • Convert the overall circuit to the frequency domain • Write the governing algebraic equations directly in the frequency domain

  12. Resistor i-v relations • Time domain: • Voltage-current relation: • Conversion to phasor: • Voltage-current relation:

  13. Resistor phasor voltage-current relations • Phasor voltage-current relation for resistors: • Phasor diagram: • Note: voltage and current have same phase for resistor

  14. Resistor voltage-current waveforms • Notes: Resistor current and voltage are in phase; lack of energy storage implies no phase shift

  15. Inductor i-v relations • Time domain: • Voltage-current relation: • Conversion to phasor: • Voltage-current relation:

  16. Inductor phasor voltage-current relations • Phasor voltage-current relation for inductors: • Phasor diagram: • Note: current lags voltage by 90 for inductors

  17. Inductor voltage-current waveforms • Notes: Current and voltage are 90 out of phase; derivative associated with energy storage causes current to lag voltage

  18. Capacitor i-v relations • Time domain: • Voltage-current relation: • Conversion to phasor: • Voltage-current relation:

  19. Capacitor phasor voltage-current relations • Phasor voltage-current relation for capacitors: • Phasor diagram: • Note: voltage lags current by 90 for capacitors

  20. Capacitor voltage-current waveforms • Notes: Current and voltage are 90 out of phase; derivative associated with energy storage causes voltage to lag current

More Related