Physics 5620 Laboratory 2 DC, RC and Passive Low Pass and High Pass Circuits

Transcription

1 Physics 5620 Laboratory 2 D, and Passie Low Pass and High Pass ircuits Objectie: In this lab you will study D circuits using Kirchoff s laws and Theenin s theorem. You will also study the behaior of circuits and way the output oltages change in these circuits when input oltages are suddenly applied and remoed (i.e. a square wae input from a function generator). You will also examine the behaior of circuits as a function of the frequency of a sinusoidal input signal from a function generator. Introduction: The two quantities we strie to know about a collection of circuit elements is the oltage across each element and the other is the current through them. In doing so we may make use of two ery useful rules concerning currents and oltages: Kirchoff s oltage rule and his current rule. These along with the definition of power as P=VI and the use of Ohm s law for resistors and other Ohmic elements will allow us to fully characterize many simple circuits. In particular we may simplify a collection of circuit elements using Theenin's theorem which allows us to replace a complicated collection of power supplies and resistors with a single equialent oltage source and a series resistance. We also must consider elements which store energy; capacitors and inductors. We hae learned that by considering oltages and currents to be quantities in the complex plane, we can use a generalization of Ohm s Law along with the definition of a complex impedance, Z, to analyze circuits containing these reactie elements. See Diefenderfer and Holton, chapters 2 and 3. Specifically, refer to sections.,.2, 2.6 and 3.4. Experiments: 2. D ircuits and Demonstration of Theenin's Theorem Using the same resistor alues, construct the circuit in Figure Question : alculate the Theinin equialent oltage and resistance for the circuit shown in Figure, using the alues, = 3.9 kω, 2 = 0 kω. Draw the Theenin equialent circuit, indicating the alues of the components. Measurement : Determine V Th and Th by making measurements directly on the circuit. ompare with your calculated alues. A 5V 2 B Figure : ircuit for demonstrating Theenin's theorem.

2 2 Question 2: Use your Theenin equialent circuit to calculate V AB for a load resistor, L = 4.7 kω, connected between points A and B. Measurement 2: Now, connect a load resistor L = 4.7 kω between points A and B, and measure V AB. ompare the measured and calculated alues. Do they agree within the error expected from the resistor tolerance? 2.2 ircuit I On the breadboard, wire the circuit shown in Figure 2. You should choose a resistor and capacitor such that the time constant of the circuit, τ = 300 μs. ecord the alues of the capacitor and resistor that you use, and be careful to use nonpolarized capacitors -- ask the instructor if you need help. We will use this circuit to inestigate charging and discharging of circuits. By using a square wae oltage source, you are effectiely charging and discharging the circuit on eery cycle. Figure 2: ircuit I. Question 3: What is the time constant, τ =, of your circuit? Measurement 3: Using a square wae input (5 V pp ) signal, sketch the input and output signals as seen on the oscilloscope for the following frequencies:. f = 0τ 0 2. f = τ onnect the input signal to H and the output signal to H 2 of the oscilloscope. ecord the time base and oltage scale settings of the oscilloscope. Question 4: Explain your obserations in terms of charging and discharging of the circuit. 2.3 ircuit II

3 3 On the breadboard, wire the circuit shown in Figure 3. Use the same components as for the preious circuit. Measurement 4: Using a square wae input (5 V pp ) signal, sketch the input and output signals as seen on the oscilloscope for the following frequencies:. 2. f f = 0τ 0 = τ Figure 3: ircuit II. Question 5: Explain your obserations in terms of charging and discharging of the circuit. 2.4 Low-Pass Filter ircuit For a low-pass filter, the oltage gain ( A ) and phase shift (θ) as functions of frequency are: o A = = () 2 i + ( ω) θ = arctan( ω) (2) On the breadboard wire the low-pass filter circuit shown in Figure 4 with = μf and =0 kω. Use the function generator as the oltage source. Set it to generate sine waes and zero the D offset. Figure 4: Low-Pass Filter ircuit.

4 4 Measurement 5: Measure the input and output oltages as functions of the sine wae frequency as well as the phase shift of the output sine wae as compared to the input sine wae on the oscilloscope. Use an input amplitude of 5 V pp. If necessary, adjust the amplitude of the function generator to maintain a constant V i. The frequencies in Table are suggested; feel free to make measurements at additional frequencies. Question 6: With your data, perform the following analysis. a. alculate the expected gain and phase shift for the same frequencies as your measurements. Add these to your table of measurements. b. Make a semi-log plot of the gain s. frequency (either use semi-log graph paper, or make the frequency axis logarithmic). ompare with calculations ( i.e. draw the cure for A). c. From your graph, determine the cut-off frequency f 0 (also called the -3dB frequency or break point frequency). ompare with calculations. d. Plot the phase angle difference θ between V o and V i s. frequency. Again, make the plot semi-log, and compare with calculations. e. Show that the output attenuates at 6 db/octae = 20 db/decade at frequencies à f 0. Include uncertainties in data and calculations as appropriate. Frequency i (pp) (Volts) o (pp) (Volts) A 0 Hz 30 Hz 00 Hz 300 Hz khz 3 khz 0 khz 30 khz Table : Suggested frequencies for testing the low-pass filter circuit. θ 2.5 High-Pass Filter ircuit For a high-pass filter, the oltage gain and phase shift as functions of frequency are: A o = = i ω + ( ω) 2 (3)

5 5 θ = arctan (4) ω On the breadboard, wire the high-pass filter circuit in Figure 5 with = μf and = 22 kω. epeat the measurements you did aboe for the low-pass filter. Question 7: Analyze your data as you did with the low pass filter: a. alculate the expected gain and phase shift for the same frequencies as your measurements. Add these to your table of measurements. b. Make a semi-log plot of the gain s. frequency (use a semi-log graph). ompare with calculations ( i.e. draw the cure for A). c. From your graph, determine the cut-off frequency f 0 (also called the -3dB frequency or break point frequency). ompare with calculations. d. Plot the phase angle difference θ between V o and V i s. frequency. Again, make the plot semi-log, and compare with calculations. e. Show that the output attenuates at 6 db/octae = 20 db/decade at frequencies á f 0. Include uncertainties in data and calculations as appropriate. Figure 5: High-Pass Filter ircuit. Frequency i (pp) (Volts) o (pp) (Volts) A 0 Hz 30 Hz 00 Hz 300 Hz khz 3 khz 0 khz 30 khz Table 2: Suggested frequencies for testing the high-pass filter circuit. θ