Datasheet for Lab 10: First-Order Time-Domain Simulation Name(s): _______________________ Date: ________________________ Approximate Time To Complete (to 0.1 hours)______________________ Prelab the videos: –Watch and Exercises Your datasheet should include ALL circuit diagrams from your circuit simulator, and ALL calculations clearly shown. In addition, you will need to capture plots of the transient curves from your circuit simulator and for the various exercises and include them in your datasheet. The switch in the circuit below has been opened for a long time and is closed at t = 0. Calculate and i0(t) for t > 0 and confirm your results with a circuit simulator following the steps below. Procedure: Although the problem requests io(t), we initially need to focus on Vc(t), the voltage of the capacitor, since that is the controlling variable for the transient response of an RC circuit. The following steps will help you arrive at a solution for Vc(t), which, you may recall, for a step response, will be of the form Vc(t) = - V∞ + (Vo V∞)e-t/τ First, using your knowledge of circuit theory, find the Initial Voltage (Vo) across the capacitor: Final Voltage across the capacitor: (V∞) Equivalent resistance seen by capacitor when the switch is closed Time constant (τ) for the response: Use the above to construct your analytical solution for the equation for Vc(t) Develop an expression to calculate io(t) from Vc(t) Now, verify your solution by comparing a plot of your solution for io(t) with a circuit simulatin result.
Datasheet for Lab 10: First-Order Time-Domain Simulation Name(s): _______________________ Date: ________________________ Approximate Time To Complete (to 0.1 hours)______________________ Prelab –Watch the videos: and Exercises Your datasheet should include ALL circuit diagrams from your circuit simulator, and ALL calculations clearly shown. In addition, you will need to capture plots of the transient curves from your circuit simulator and for the various exercises and include them in your datasheet. The switch in the circuit below has been opened for a long time and is closed at t = 0. Calculate and i0(t) for t > 0 and confirm your results with a circuit simulator following the steps below. Procedure: Although the problem requests io(t), we initially need to focus on Vc(t), the voltage of the capacitor, since that is the controlling variable for the transient response of an RC circuit. The following steps will help you arrive at a solution for Vc(t), which, you may recall, for a step response, will be of the form Vc(t) = V∞ + (Vo - V∞)e-t/τ First, using your knowledge of circuit theory, find the Initial Voltage (Vo) across the capacitor: Final Voltage (V∞) across the capacitor: Equivalent resistance seen by capacitor when the switch is closed Time constant (τ) for the response: Use the above to construct your analytical solution for the equation for Vc(t) Develop an expression to calculate io(t) from Vc(t) Now, verify your solution by comparing a plot of your solution for io(t) with a circuit simulatin result.