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Outline. Introduction - Behavior analysis- Audio amplifier exampleRLC circuit in time domain Frequency domainDefinition of transfer function- Impedance approachCircuit equivalenceDerivation of transfer function- Op amp circuitsConclusionReferences.. . . 2. RLC Circuit in Time Domain.
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1. Examples of Transfer Function
Professor Marian S. Stachowicz
Electrical and Computer Engineering Department,
University of Minnesota Duluth
January 26 - February 16, 2010
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2. Outline Introduction
- Behavior analysis
- Audio amplifier example
RLC circuit in time domain
Frequency domain
Definition of transfer function
- Impedance approach
Circuit equivalence
Derivation of transfer function
- Op amp circuits
Conclusion
References. 2
3. RLC Circuit in Time Domain 3 KCL and KVLKCL and KVL
4. RLC Circuits in Time Domain 4 By solving the RLC circuit we end with differential equations.
We need another approach that is easier to analyze the circuit. By solving the RLC circuit we end with differential equations.
We need another approach that is easier to analyze the circuit.
5. Frequency Domain 5
7. Frequency Domain
8. Definition of Transfer Function 8
9. Definition of Transfer Function Transfer Function reveals how the circuit modifies the input amplitude in creating output amplitude.
Therefore, transfer function describes how the circuit processes the input to produce output. 9
10. Impedance approach
Impedance Z(s) of a passive circuit is the ratio of the Laplace Transform of voltage across the circuit to the Laplace transform of the current through the circuit under the assumption of zero initial conditions.
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11. Frequency Domain
12. Impedances in series 12 Impedance Z(s) of a passive circuit is the ratio of the Laplace transform of voltage across the circuit to the Laplace transform of the current through the circuit under the assumption of zero initial conditions.
For impedance in series, the equivalent impedance is equal to the sum of the individual impedances.Impedance Z(s) of a passive circuit is the ratio of the Laplace transform of voltage across the circuit to the Laplace transform of the current through the circuit under the assumption of zero initial conditions.
For impedance in series, the equivalent impedance is equal to the sum of the individual impedances.
13. Impedances in parallel 13 For impedances in parallel, the reciprocal of the equivalent impedance is equal to the sum of the reciprocals of the individual impedances.For impedances in parallel, the reciprocal of the equivalent impedance is equal to the sum of the reciprocals of the individual impedances.
14. Impedance Approach 14
15. Circuit Equivalence 15
16. Derivation of Transfer Function 16
17. Derivation of Transfer Function 17
18. Derivation of Transfer Function 18
19. Derivation of Transfer Function 19
20. 20 Derivation of Transfer Function
21. Derivation of Transfer Function 21
22. Op Amp Circuits 22
23. Op Amp Circuits 23
24. 24 Op Amp Circuits Next slides assume that initial voltage of capacitor is zero.Next slides assume that initial voltage of capacitor is zero.
25. Op Amp Circuits 25
26. Op Amp Circuits 26
27. Op Amp Circuits 27
28. Op Amp Circuits 28
29. Conclusion 29
30. References http://www.jsu.edu/depart/psychology/sebac/fac-sch/k-sqab/Kessel_Poster.htm
Gopal M, R. Control Systems Principles and Design. McGraw Hill.
http://web.cecs.pdx.edu/~ece2xx/ECE222/Slides/LaplaceCircuits.pdf
http://cnx.org/content/m0028/latest/
http://en.wikibooks.org/wiki/Control_Systems/Transfer_Functions
http://en.wikipedia.org/wiki/Voltage_divider
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31. Questions 31
