By Steven Karris

This article is written to be used in a moment path in circuit research. It includes a spectrum of topics starting from the main summary to the main sensible, and the fabric should be coated in a single semester or quarters.The reader of this ebook must have the conventional undergraduate wisdom of an introductory circuit research fabric corresponding to Circuit research I with MATLAB Computing and Simulink / SimPowerSystems Modeling, ISBN 978-1-934404-17-1. one other prerequisite will be a uncomplicated wisdom of differential equations, and mostly, engineering scholars at this point have taken all required arithmetic classes. Appendix H serves as a assessment of differential equations with emphasis on engineering comparable themes and it is suggested for readers who may have a overview of this topic. for more information. please stopover at the Orchard guides web site.

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**Example text**

A second order circuit contains two energy storing devices. Thus, an RLC circuit is a second order circuit. The total response is the summation of the natural and forced responses. If the differential equation describing a series RLC circuit that is excited by a constant (DC) voltage source is written in terms of the current, the forced response is zero and thus the total response is just the natural response. If the differential equation describing a parallel RLC circuit that is excited by a constant (DC) current source is written in terms of the voltage, the forced response is zero and thus the total response is just the natural response.

Circuit Analysis II with MATLAB Computing and Simulink / SimPowerSystems Modeling 149 Copyright © Orchard Publications Chapter 1 Second Order Circuits 2 2 The condition for critical damping is P – 0 = 0 where P = G 2C = 1 2R'C and 2 1 2 2 2 1 0 = 1 LC . Then, P = --------------------------- = 0 = ---------------------- where R' = R + 2 . Therefore, 2R' 1 12 3 1 12 12 2 -------------------= 4 , or 2R + 2 6 2 2 -----------= 4 , or R + 2 = 36 4 = 9 , or R + 2 = 3 and thus R = 1 .

96) is done with MATLAB. 008 . 97) We will use the initial conditions v C1 = v C2 = 0 to evaluate k 1 and k 2 . 98) To evaluate the constant k 2 , we make use of the initial condition v C1 0 = 0 . 100). 024*cos(1000*t)+k2*sin(1000*t))... 27. 27. 5 Summary Circuits that contain energy storing devices can be described by integrodifferential equations and upon differentiation can be simplified to differential equations with constant coefficients. A second order circuit contains two energy storing devices.