Physics 481 Experiment 1

Transcription

1 Physics 481 Experiment 1 LAST Name (print) FIRST Name (print) LINEAR CIRCUITS 1

2 Experiment 1 - Linear Circuits This experiment is designed for getting a hands-on experience with simple linear circuits. The project is intended to cover both building and analysis of such circuits, as well as usage of two measuring devices digital millimeters and oscilloscopes. The circuits covered in this project will utilize only passive electronic components: resistors, capacitors, and inductors, covering typical properties of RC, LC, and RLC circuits. The experiment will also address the effects of measuring devices on a circuit. Part 1. Effects of Measuring Instruments on Results Voltmeter and Voltage Divider One of the first things to be aware of in electronics is that the very instruments that are used can have an effect on the measurements that are being taken. Consider the input characteristics of the DMM. Set up a simple voltage divider consisting of two resistors of equal value on the breadboard as in Fig. 1. 5V R 2 Figure 1: Voltage Divider. Check the actual resistor values with the DMM to be sure. Make a note if the measured values are within the tolerance from the ones specified. Now use the 5 V power supply on the breadboard to apply a voltage to the divider. Use the DMM to measure the voltage across both resistors as well as each resistor separately. Start with 10kΩ resistors. Check if the voltage drops across each resistor sum to the drop across both resistors in series. Repeat the process with 100kΩ resistors and finally 1MΩ resistors, each time checking the sum of voltage drops with respect to the total potential difference for two resistors in series. Note at which conditions the internal resistance of the meter is most evident. With the data obtained on voltage divider with the 1MΩ resistors calculate the internal resistance of the DMM itself. Assume that this DMM resistance alters the effective resistance of the divider; thus causing the change in voltage from the expected results. Make a generalized conclusion about ideal characteristics for voltmeters and the effects of real voltmeters on circuits 2

3 Ammeter and Current Divider Construct a current divider on the breadboard. Use two equal resistors in parallel driven by the 5 volt supply as in Fig. 2. Use one DMM to measure the total current through both resistors and another DMM to measure the current through one resistor. 5V R 2 Figure 2: Current Divider. Start your setup with the 10kΩ resistors and measure the total and the branch currents (remember ammeters are to be connected in series). Check the junction rule. Repeat the measurements with the 1kΩ resistors (or 1.1kΩ as per availability), and then 51 Ω resistors. Explain for which setup the effects of ammeter on the circuit are most evident. Estimate the ammeter internal resistance. Finally, construct a simple series circuit with a 5 V power source, a 51 Ω resistor and one DMM in the 200 ma mode. Use the second DMM to measure the voltage across the first DMM. Calculate the resistance of the first DMM. Check if your result can explain the observations from the current divider? Make a generalized conclusion about ideal characteristics for ammeters and the effects of real ammeters on circuits 3

4 Part 2. RC-Circuits RC Integrator Construct the circuit shown in Fig. 3 and explore the properties of RC-Integrator circuit. Drive the circuit with a 500 Hz square wave and observe the output with oscilloscope. Explain if your result confirms the idea of this being an integrating circuit. Using the R and C specifications as in the figure, confirm that the circuit satisfies the necessary criteria of RC-integrator. 500 Hz Square Wave =1MΩ x Figure 3: RC-Integrator Circuit Oscillo scope Next drive the circuit with a triangle wave as an input. Sketch the output, and explain your results in context of integrator circuits. RC Differentiator By interchanging the resistor and capacitor and adjusting the values the RC integrator circuit can be transformed into an RC differentiator as shown in Fig. 4. Using the R and C specifications as in the figure, confirm that the circuit satisfies the necessary criteria for RCdifferentiator. 100 khz Saw Tooth Wave C=200pF =100Ω Oscillo scope Figure 4: RC-Differentiator Circuit x The operational (transfer) function of the circuit is now that of a differentiator. Drive the circuit with a 100 khz triangle wave. Sketch and explain the result. Repeat with a square wave. 4

5 Part 3. RLC-Circuit Ringing Construct the RLC circuit as shown in Fig. 5. Use the element specifications as in the Figure. The initial resistance value for to be 10 kω. Use a square wave with the frequency f=1 khz as the input for the circuit. Observe the output on your oscilloscope. You should see the classic "ringing" response - an example of an under-damped oscillation. Square Wave Figure 5: Ringing the RLC-circuit. G L=1000 uh The general solution for this circuit could be written as follows: V r (t) = V 0 e -αt 1 cos(ω t), where α =, ω = 2 ωr r α 2, ω r = 2RC 1 LC Measure the frequency of the ringing using the oscilloscope. Compare the result with the resonant frequency ω r Use the peaks of the ringing signal to plot out the e -αt form. Determine α graphically, by using semi-log axis in plotting. Compare this result with the calculated value. Resonant Circuit Construct a circuit as shown in Fig. 6. Show that the square of the resonant frequency is given by 1/LC. Run your generator through several ranges to find the peak output. Determine the resonant frequency ω r and compare this value with the expected resonant frequency. Next, find the frequencies ω 1 and ω 2 for which the output reaches the value of 0.707V r. Use the necessary information to calculate the selectivity ω r /BW, where BW stands for bandwidth, BW= ω 2 -ω 1 =100k L=10 mh V 0 cos(ωt) Figure 6: Resonant Circuit. V - 5