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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
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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