1. SE207 Modeling and Simulation Lab # 3: Analog Simulation of a First Order System (RC circuit)

2. Objectives The objective of this experiment is to simulate a first order system (an RC circuit) and study its behavior.

3. Equipment GP-6 Analog Computer X-Y plotter

4. First Order Systems First order systems are modeled by first order Differential equations. Any circuit containing a resistor and a capacitor can be modeled by a first order model.

5. RC Circuit The RC circuit is modeled by the equation. +_+_ Vc (t) R C

6. Time constant of a First Order System The final value of Vc(t) =E The time at which Vc(t)=0.63 * final value is called the time constant of the system. Final value of Vc(t) 63% of Final value of Vc(t) Time constant t Vc(t)

7. Time constant Time constant depends on C and R Larger time constant means the capacitor needs longer time to charge.

8. Drawing Simulation Diagrams

11. Drawing Simulation Diagrams First order Example 0.5x(t) -0.25 x(t)

12. Drawing Simulation Diagrams First order Example (cont.) 1111 0.5x(t) -0.25 x(t) 0.5 0.25

13. Procedure 1. Write the system of equation in a form suitable for drawing analog simulation diagram 2. Draw the analog simulation diagram corresponding to the value given in the table. Assume E(t) = 1.0 Volt and Vc(0)=0 CRTime 10110 Sec 5120 Sec

15. Procedure (cont.) 3. For the first set of values, connect the analog computer circuit on the GP-6 using one integrator. 4. Set the Y/Pot-address to GND/X and mode selector to OPR. 5. Select the output amplifier from the X-address, press OP button and monitor the output of the system Vc(t) 6. Repeat step (4) and plot the output on the X-Y plotter 7. Repeat steps (1- to 5) for the second set of values of R and C.

16. Report Your report should include the following A plot of the output voltage for the two cases Estimates of the system’s time constants in both cases Comparison of the theoretical and experimental values of the time constants in both cases Comments and conclusions on your observations