# Circuit Analysis I with MATLAB Computing and by Steven Karris

By Steven Karris

This article is an creation to the elemental rules of electric engineering and covers DC and AC circuit research and Transients. it really is meant for all engineering majors and presumes wisdom of first yr differential and critical calculus and physics. The final chapters contain step by step methods for the options of easy differential equations utilized in the derivation of the average and forces responses. Appendices A, B, and C are introductions to MATLAB, Simulink, and SimPowerSystems respectively. Appendix D is a assessment of complicated Numbers, and Appendix E is an advent to matrices and determinants. for additional info. please stopover at the Orchard courses website

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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.

This results in the overdamped natural response and has the form vn t = k1 e s1 t + k2 e s2 t If 2P = 20 , the roots s 1 and s 2 are real, negative, and equal. This results in the critically damped natural response and has the form vn t = e –P t k1 + k2 t If 20 2P , the roots s 1 and s 2 are complex conjugates. This results in the underdamped or oscillatory natural response and has the form vn t = e –P t k 1 cos nP t + k 2 sin nP t = k 3 e –P t cos nP t + If a second order circuit is neither series nor parallel, the natural response if found from yn = k1 e or or s1 t + k2 e s2 t yN = k1 + k2 t e yn = e – t s1 t k 3 cos t + k 4 sin t = e – t k 5 cos t + depending on the roots of the characteristic equation being real and unequal, real and equal, or complex conjugates respectively.

24. 24. 23. 25. 4 Other Second Order Circuits Second order circuits are not restricted to RLC circuits. They include amplifiers and filter among others, and since it is beyond the scope of this text to analyze such circuits in detail, we will illustrate the transient analysis of a second order active lowpass filter. 26 a known as a Multiple Feed Back (MFB) active lowpass filter. For this circuit, the initial conditions are v C1 = v C2 = 0 . Compute and sketch v out t for t 0 . 26. 83) 130 Circuit Analysis II with MATLAB Computing and Simulink / SimPowerSystems Modeling Copyright © Orchard Publications Other Second Order Circuits We observe that v 2 = 0 (virtual ground).