Transcription of Review of Circuits as LTI Systems - Ted Pavlic
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Review of Circuits as LTI Systems - Ted Pavlic
ECE 209: Circuits and Electronics LaboratoryReview of Circuits as LTI Systems Math Background: ODE s, LTI Systems , and Laplace TransformsEngineers must have analytical machinery to understand how Systems change over time. For example,springs and dampers in car suspension Systems absorb kinetic energy after road disturbances and dissipatethe energygentlyover time. Electronic filters protect Circuits from large input transients in a similar , engineers need to know how to choose components Systems and ODEs:The motion of many physical Systems can be modeled knowing only a fewof its derivatives. For example, a car s position over time can be described well knowing its velocity oracceleration. So we focus on thelinear time-invariant(LTI) systemx(t)LTI Systemy(t)which has inputx(t) ( , height of terrain under the car) and outputy(t) ( , height of passenger s seat).By our assumption that all we need are a few derivatives of the inputand the output, then a typicalordinarydifferential equation(ODE) that might model such a system isy + 3y + 2y=x x(1)wherey andy are the first and second derivatives of signaly(t).
ECE 209 Review of Circuits as LTI Systems both solve Equation (3). Hence, the zero-input transient response of Equation (1) is y 0(t) = Ae−1t +Be−2t where A and B are complex numbers that correspond to different initial conditions.
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