1. 1 Second Order Circuits SEE 1023 Circuit Theory Introduction to Transient Response

2. 2 Second Order Circuit The differential equation is second order when the highest derivative in the equation is second derivative. Second order circuits contain two energy storage elements that can not be replaced by a single equivalent element. The circuits can be described by second order differential equation.

3. 3 Transient Response The behavior of a system following a sudden change in its input The behavior of a system following a sudden change in its input. We want to see how the quantities change with time from its equilibrium state.

4. 4 State variables The variables in differential equations. The variables in differential equations. Determine the amount of energy in the circuit. Determine the amount of energy in the circuit. Contains sufficient information about the past to determine the future circuit response. Contains sufficient information about the past to determine the future circuit response. Must be continuous function of time Must be continuous function of time

5. 5 Series RLC Circuit: Step response If we apply a sudden DC source to the circuit, we obtain the step response. We want to study the step responses of v c (t), i L (t), v L (t), V R (t) and etc. VsVs R L C I + V R - + V L - +VC-+VC- t = 0 1V The response for this circuit with source is also referred to as forced response.

6. 6 Step responses t i L, V c Key responses: i L, V c The responses depend on circuit parameters i.e. R, L, C, and source, Vs

7. 7 Source Free Circuit: Natural response The circuit has no independent source. It is being excited by the energy initially stored in the C and/or L. Energy in L is represented by its current and in C by its voltage. R L C I + V R - + V L - +VC-+VC- The response for this source free circuit is referred to as natural response.

8. 8 Natural responses t i L, V c The responses depend on circuit parameters only i.e. R, L, C

9. 9 Series RLC Circuit in PSpice It is too hard to study the transient response manually. V DC R L C I + V R - + V L - +VC-+VC- It is too easy to study the transient response PSpicely. 0 1 2 3

10. 10 PSPICE NETLIST Series second order circuit.Param R=1.Param L=0.5.Param C=0.02 VDC 1 0 DC 10V R1 1 2 {R} L1 2 3 {L} IC=0A C1 3 0 {C} IC=10V.Tran 1m 2s 0 1m UIC ****.STEP PARAM R LIST 1 10 20.Probe.End

11. 11 Run Pspice File Transient Response of The Current