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Examples of Transfer Function

Examples of Transfer Function

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Examples of Transfer Function

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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 1

    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. 10

    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 30

    31. Questions 31