Examples of Transfer Function

# Examples of Transfer Function

## Examples of Transfer Function

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##### Presentation Transcript

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