second order circuits - Second Order Circuits EENG 223...

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Second Order Circuits EENG 223 ircuit Circuit Theory I
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Second Order Circuits Order of circuit Order of the differential quation (DE) required to The number of independent* nergy storage elements == a circuit equation (DE) required to describe the circuit energy storage elements (C’s and L’s) * C’s and L’s are independent if they cannot be combined with other C’s and py L’s (in series or parallel, for example)
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econd Order Circuits Second Order Circuits •2 nd -order circuits have 2 independent energy storage elements (inductors and/or capacitors) • Analysis of a 2 nd -order circuit yields a 2 nd -order differential equation (DE) • A 2nd-order differential equation has the form: 2 x dx • Solution of a 2 nd -order differential equation requires two initial conditions: x(0) and x’(0) All higher order circuits (3 rd , 4 th , etc) have the same types of responses as seen in 1 st - 1o 2 a a x(t) f(t) dt dt ++ = order and 2 nd -order circuits • Since 2nd-order circuits have two energy-storage types, the circuits can have the following forms: ) Two capacitors 1) Two capacitors 2) Two inductors 3) One capacitor and one inductor A) Series RLC circuit B) Parallel RLC circuit C) Others
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Form of the solution to differential equations As seen with 1 st -order circuits in Chapter 7, the general solution to a differential equation has two parts: x(t) = x h + x p = homogeneous solution + particular solution or x(t) = x n + x f
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second order circuits - Second Order Circuits EENG 223...

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