# UK EE 221 - Time Domain Response of First-Order Circuit (9 pages)

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## Time Domain Response of First-Order Circuit

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- Pages:
- 9
- School:
- University of Kentucky
- Course:
- Ee 221 - Circuits Ii

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9 1 Time Domain Response of First Order Circuit A phasor analysis of a circuit only provides a description of voltage and current steady state behavior When the source waveform changes at some time t0 a transient response is produced which dies out over a period of time leaving the new steady state behavior The circuit s differential equation must be used to determine complete voltage and current responses Example Describe v0 for all t Identify transient and steady state responses t 0 VDC R C t 0 v0 Show t VDC 1 exp volts v0 t RC 0 volts for t 0 for t 0 For steady state response let t for transient response subtract complete response steady state response in each t interval Instantaneous Voltage and Current Change in Capacitors and Inductors 9 2 What would be the required current ic in this circuit for the voltage on the capacitor to change instantaneously ic VDC t 0 C vC What would be the required voltage vL in this circuit for the current in the inductor to change instantaneously iL IDC t 0 L vL Conclusion If the source cannot produce infinite instantaneous power then neither the capacitor voltage nor the inductor current can change instantaneously Switch Notation and Initial Conditions 9 3 In order to denote the time right before t 0 limit from the left as t 0 and the time right after t 0 limit from the right as t 0 the following notation will be used t 0 where t 0 is the moment after the switch is thrown and t 0 is the moment before the switch is thrown In order to determine initial conditions for solving the differential equations the following statement can be used For circuits with practical sources The voltage across a capacitor cannot change instantaneously vc 0 vc 0 The current in an inductor cannot change instantaneously iL 0 iL 0 Finding the Complete Solution There are 5 major steps in finding the complete solution 9 4 1 2 3 4 5 Find the differential equation for either capacitor voltage or inductor current Determine the natural solution homogenous

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