By Steven T. Karris
Designed to be used in a moment path in circuit research, this article engages an entire spectrum of circuit research comparable topics starting from the main summary to the main functional. this isn't a math textual content. even though, the differential equations and Laplace transformation fabric provided during this textual content is enough for the derivation of pertinent relatives and there's no have to discuss with complicated math texts. Featured are equipment of expressing signs by way of the simple services, an creation to moment order circuits, and a number of other examples of examining electrical circuits utilizing Laplace transformation equipment. although now not written explicitly for use with MATLAB, this article presents many beneficial suggestions and methods for MATLAB, permitting scholars to get the main out of the preferred software. the entire info supplied is designed to be lined in a single semester or quarters. for additional info. please stopover at the Orchard courses web site.
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Extra info for Circuit Analysis II with MATLAB Applications
20. 9 Summary x Circuits that contain energy storing devices can be described by integrodifferential equations and upon differentiation can be simplified to differential equations with constant coefficients. x A second order circuit contains two energy storing devices. Thus, an RLC circuit is a second order circuit. x The total response is the summation of the natural and forced responses. x 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.
75). From the columns of that spreadsheet we can read the following maximum and minimum values and the times these occur. 75) and setting it equal to zero. 7 Response of Parallel GLC Circuits with AC Excitation The total response of a parallel GLC (or RLC) circuit that is excited by a sinusoidal source also consists of the natural and forced response components. The natural response will be overdamped, critically damped, or underdamped. The forced component will be a sinusoid of the same frequency as that of the excitation, and since it represents the AC steady-state condition, we can use phasor analysis to find the forced response.
We will find the forced (steady-state) response using phasor circuit analysis where Z = 1 , jZL = j20 , – j e ZC = – j120 , and 100 cos t 100 0q . The phasor circuit is shown below. 100 : j20 : VS + – j 120 : V S = 100 0q V + V C Using the voltage division expression we get – j120 – j120 120 – 90q u 100 0q V C = ---------------------------------------- 100 0q = -------------------------- 100 0q = ---------------------------------------------------- = 60 2 – 135q 100 + j100 100 + j20 – j120 100 2 45q and in the t -domain v C f = 60 2 cos t – 135q .