INTRODUCTION

Electrical components and simple dynamic electrical systems are the subject of this experiment. Three separate electrical circuits are considered. The first is driven directly by a function generator and includes a nonlinear electrical component. The two dynamic systems (which can be described by differential equations) are driven by a power supply and activated by a simple switch. A Matlab simulation is required in Question #4 to give you experience in simulating a dynamic system. Notice that since you are working in a strictly electrical world here, no calibrations are necessary.

EQUIPMENT SET-UP AND DATA COLLECTION

Part A of this experiment uses the circuit shown in Figure 1 below to study the behavior of a diode. The resistor R is nominally 6800 Ohms. The diode has the property of having very low resistance when current is flowing forward through the diode and very high resistance as current flows in the other direction. Connect the circuit as shown with the function generator operating in sine wave mode at a magnitude of about +/- 2 volts and a frequency of about one Hz. Use the VirtualBench-Scope to obtain a suitable time plot showing the voltages on channels one and two (this is required plot #1). This plot should be reasonably time scaled and have a vertical axis scale that allows the signal shapes to be clearly seen. Plotting with Excel is the preferred approach.

Part B of the experiment is to study the transient response of a first order system with a step input. Arrange the circuit below with the power supply set to about three volts.

The capacitor C = 4 microFarads. The resistor R is nominally 6800 Ohms and the resistor R10 is ten Ohms. The purpose of R10 is to allow the capacitor to discharge when the switch is open. With channels one and two connected as shown above and your VirtualBench-Scope in free run, close and open the switch a few times and observe the resulting transients. When a full up and down cycle of the capacitor voltage is displayed on the screen, store it by clicking on "Single" to hold it. Excel can be used to spread out the transient and display the first order response (this is required plot #2). Use the digital multimeter on your bench to measure the actual resistance of "your R".

Part C is a second order RLC system which should be arranged as below:

In this circuit, the ten Ohm R10 resistor is again used as a discharge resistor. Additional resistance inherent in the LC components provides the bulk of the energy loss. The power supply is turned down to approximately two volts so that the capacitor voltage measured on channel two fits comfortably in the range of the A/D converter. Using the same technique as in Part B, open and close the switch a few times to see the system transients displayed on the VirtualBench-Scope. Click on "Single" when you have captured an up and down voltage change on the display. Use Excel to scale your results

so that the details of the capacitor voltage oscillations can be seen clearly (this is required plot #3).

QUESTIONS AND THINGS TO DO

1. Discuss the results to Part A shown in required plot #1. Explain the differences in the signals on channels one and two. From the curves that you see, is your diode behaving ideally? Explain.

2. For Part B, use Excel to focus on the capacitor voltage rise which occurs as the switch is closed. Delete data and shift the time scale to be zero as the rise begins and delete the data after the transient has settled (perhaps about four time constants). Derive and solve the first order differential equation for the capacitor voltage response in terms of the values of R and C. On a well labeled Excel plot, compare the experimental response and the differential equation solution for the nominal values of R and C. Also show a solution curve using your measured resistance value (this is required plot #4).

3. For Part B, what do you think would happen if the R10 resistor were not in place? You can try removing it in the lab, closing and opening the switch a few times to confirm your opinion.

4. For Part C, again use Excel to focus on the rising capacitor voltage as the switch is closed, deleting data before, adjusting the zero, removing data after the transient, etc. Also divide all the transient data by the final voltage value so that your response is in unit step response form. Write a set of state equations that describe the behavior of a series RLC circuit. Create a Matlab ".m" program to solve the set of state equations for a unit step. Also use Matlab to read in your unit step response Excel data for time and the capacitor voltage rise. Assume that C = 4microFarads is correct and adjust L and the effective R in your Matlab program until you have your best agreement between the Matlab solution and the laboratory data. Turn in your final Matlab plot of the unit step comparison (this is required plot #5 - it should look something like the one below). What values of R and L did you find?