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Unformatted text preview: Complex Frequency Complex Representation of TimeDomain Signals Example The splane Unit 2: Modeling in the Frequency Domain Part 1: Complex Frequency Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland January 16, 2009 ENGI 5821 Unit 2, Part 1: Complex Frequency Complex Frequency Complex Representation of TimeDomain Signals Example The splane 1 Complex Frequency 1 Complex Representation of TimeDomain Signals 1 Example 1 The splane ENGI 5821 Unit 2, Part 1: Complex Frequency Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: COVERED ON BOARD Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: COVERED ON BOARD L di ( t ) dt + Ri ( t ) = V s Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: COVERED ON BOARD L di ( t ) dt + Ri ( t ) = V s The solution for this equation is of the following form: Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: COVERED ON BOARD L di ( t ) dt + Ri ( t ) = V s The solution for this equation is of the following form: i ( t ) = A + Be t Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: COVERED ON BOARD L di ( t ) dt + Ri ( t ) = V s The solution for this equation is of the following form: i ( t ) = A + Be t Where A , B , and are constants determined from the circuits initial conditions and the DE itself. Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: COVERED ON BOARD L di ( t ) dt + Ri ( t ) = V s The solution for this equation is of the following form: i ( t ) = A + Be t Where A , B , and are constants determined from the circuits initial conditions and the DE itself. Note that the response has two components: Complex Frequency Consider a typical electrical system: the series RL circuit excited by a DC source. We can develop a DE for this system: COVERED ON BOARD L di ( t ) dt + Ri ( t ) = V s The solution for this equation is of the following form: i ( t ) = A + Be t Where A , B , and are constants determined from the circuits initial conditions and the DE itself....
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This note was uploaded on 09/07/2009 for the course ENGINEERIN 5821 taught by Professor Andrewvardy, during the Spring '09 term at Memorial University.
 Spring '09
 AndrewVardy,
 Frequency

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