ECET_345_W3_Lab_LaplaceAnalysis_AJK - ECET345 Signals and...

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ECET345 Signals and Systems—Lab #3 Page 1 DeVry University ECET345 Signals and Systems Name of Student ___________________________________________________________ Transfer Function Analysis of Continuous Systems in s Domain Using MATLAB Objective of the lab experiment: The objective of this experiment is to create continuous ( s domain) transfer functions in MATLAB and explore how they can be manipulated to extract relevant data. We shall first present an example of how MATLAB is used for s (Laplace) domain analysis, and then the student shall be required to perform specified analysis on a given circuit. Equipment list: MATLAB version 7.0 or higher Software needed: Sdomainanalysis.m . This file is available in Doc Sharing. If not, it can be obtained from Professor Ajeet Singh of Devry University, Fremont, CA ([email protected]). Theory Brief Explanation of Creating Transfer Functions of Circuits in Laplace Domain We shall illustrate such analysis by calculating the TF of a filter. Aside from resistors, there are two other common analog components that are found in circuits: capacitors and inductors. These are reactive components; that is, they are capable of storing (and giving back) energy, in contrast to resistors, which can only convert electrical energy into heat but cannot store it. The volt ampere relationship of the two reactive components are given by v ( t ) = L ( di ( t ) dt ) i ( t ) = C ( dv ( t ) dt ) where L is the inductance and C is the capacitance. This is in contrast with the resistive case, where v(t) = i(t) R, (Ohm’s law), a linear and simple algebraic relationship without any derivative terms. If one of these reactive components is located in a circuit, then a differential equation would need to be solved in order to see their output over time. The presence of two reactive components would mean a second-order differential equation; three would mean a third order, and so on. As the number of reactive components increases, generating a solution by hand is very tedious, if not impossible. In this case, computer software such as MATLAB is utilized to generate Professor Ajeet Singh, Ph.D Richard Butler, EET
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ECET345 Signals and Systems—Lab #3 Page 2 the desired answer. This lab will explore how to convert differential equations into a MATLAB-compatible form, using Laplace transforms and what MATLAB commands can do to find information of interest about circuits and systems. In order to model the previous derivative relationships in MATLAB, Laplace transform operations will have to be performed on the volt ampere relationship of capacitor and inductor. V ( s ) = L I ( s ) s I ( s ) = C V ( s ) s This is true where V(s) and I(S) are the voltages across and the current through the reactive components respectively and s is the Laplace operator , a complex number that we write as σ + j ω. The impedance of the reactive components can now be defined in Laplace domain as algebraic ratios (rather than as derivative relations).

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