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ENGR 43 Lab Activity Student Guide LAB 7 – Skin Effect and Transmission Lines Student Name: ___________________________________________________ summary of the effects of frequency and termination impedance on signals transmitted through cables. Overview In this lab, you will collect data on measurements, observe skin effect in wires and propagation delay in a cable, and summarize your findings. Before Starting This Activity You should be able to perform the following tasks before starting this activity: Basic operation of the function generator: setting frequency, waveform, and amplitude. Operate a digital oscilloscope to trigger and measure voltage and time of waveforms. Calculate series voltage drops using the voltage divider formula. Calculate attenuation (logarithms). Enter data and create charts using Microsoft Excel spreadsheets. Learning Outcomes For Activity Relevant knowledge (K), skill (S), or attitude (A) student learning outcomes K1. Identify situations where wire and cable can have a significant effect on the operation of an electronic system. S1. Measure voltage and phase of lowamplitude signals with an oscilloscope. S2. Compare measured data with the preparatory calculations, and describe how the data show the effects of resistance and inductance in wires, and propagation time and impedance in cables. A1. Appreciate that secondary effects, such as skin effect and cable impedance, can have significant effects of circuits. Getting Started Lab Activity and Deliverables: It should take students approximately 3 hours to complete the lab activity, and 1 hour of homework time to complete the lab report. Equipment & Supplies Item Tek MSO2014 scope Fluke 271 function generator BNC-clip cable 1x/10x scope probes 100-foot roll of CAT 5e cable 2-foot wire sample bundle 51 Ω, ¼ W resistor (green, brown, black, gold) 100 Ω, ¼ W W resistor (brown, black, brown, gold) Quantity 1 1 1 3 1 1 1 1 Special Safety Requirements None Lab Preparation You may start with Task #1 or Task #2, depending on the availability of the wire bundles or CAT 5e cable rolls. S3. Prepare a presentation that includes a table and chart to show resistive and skin effects in multiple wires and a Lab 7 – Skin Effect and Transmission Lines ENGR 43 Page 1 © 2012 ENGR 43 Lab Activity Student Guide Task #1 – Skin Effect When we first learned about electric circuits, we learned that the solid lines on the schematic diagram represented wires, all points connected by a wire were always at the same voltage potential, and current flowing through a wire did not produce a voltage drop because wires had zero resistance. While this may be close enough to the truth for short wires and low frequency AC and DC circuits, the highspeed circuitry in today’s electronics requires greater recognition of the effects wire and cable can have in a circuit. 1. Locate an American wire gauge table that lists the milohms per foot resistance and diameter (in millimeters) for solid conductors. An easy place to find such a table is at Wikipedia (http://en.wikipedia.org/wiki/American_ wire_gage). Although we are using stranded wire for the larger gauges, the performance is similar to solid wire. Enter the diameter and resistance for each gauge wire in Table 1 of the Excel worksheet. 2. For each of the 2-foot lengths of wire, use the wire gauge table from step 1 to calculate the resistance in milohms (thousandths of an ohm). Enter these values in Table 1. 3. Calculate the frequency where skin effect will add approximately 10% to the total impedance using the following formula (derived from Terman, F. E. Radio Engineers' Handbook. New York: McGraw-Hill, 1943) æ 200mm ö2 freq = ç ÷ è Dw ø , where Dw is the wire diameter, in millimeters. Enter your values in Table 1. Lab 7 – Skin Effect and Transmission Lines ENGR 43 4. Refer to the test circuit schematic in figure 1, shown below. 5. Using the voltage divider formula, calculate the expected voltage drop across the wire under test (TP2 to ground) when a low-frequency 5 VPP sine wave is applied, as measured at TP1. Enter these values in Table 1. 6. Connect the skin effect test circuit shown in figure 1, above. Start with the 28 AWG 2-foot wire. Ensure that the ground connections for the function generator and scope probes are as close as practical. 7. Set the function generator to apply a 1 kHz, 5 VPP sine wave as measured at TP1. Measure the voltage at TP2. Enter this value in Table 2 of the Excel worksheet. Compare with your calculated value in Table 1. Are you able to measure a stable voltage at TP2? What is degrading your measurement? _______________________________ _______________________________ _______________________________ _______________________________ 8. In order to measure small voltages and minimize the background noise, change the acquisition mode of the digital oscope to sample mode, and increase the number of samples until the noise is reduced on the TP2 waveform and the Page 2 © 2012 ENGR 43 Lab Activity Student Guide measurement is stable within 1 mV. Set the trigger mode to trigger on the input voltage at TP1. You should be able to see voltages down to a few millivolts. Why is it necessary to trigger the scope on TP1? 12. After you have entered all of your measurement data, click on the Linear Chart tab to see the data plotted on linear scale X/Y axes. Can you easily determine where the skin effect begins for each wire? Why not? _______________________________ _______________________________ _______________________________ _______________________________ _______________________________ _______________________________ 9. Measure the p-p voltage at TP2. Compare the phase of the waveforms at TP1 and TP2 by measuring time delta, ∆, (difference) between the rising zerocrossing points on each waveform (or by selecting “phase” from the measure menu). For the low-amplitude voltages at TP2 you may note “in phase,” “leading,” or “lagging” instead of a specific number of degrees of phase shift. When voltages at TP2 are at least 4 divisions vertically, measure the time delta between waveforms and calculate phase with the following formula: phase=0.360• ∆(µs)•freq(kHz) Enter your measurements in Table 2. 10. Repeat the voltage and phase measuerments at frequencies of 2kHz, 5 kHz, 10 kHz, 20 kHz, 50 kHz, 100 kHz, 200 kHz, 500 kHz, and 1 MHz. At each frequency, adjust the output level of the function generator as needed to maintain the 5 VPP at TP1. 11. Repeat the voltage and phase measurements at the same frequencies for each of the other 2-foot test wires. Remember to check and adjust the voltage at TP1 for each frequency. 13. Click on the Log-Log tab to see the same data plotted on logarithmic X/Y axes. What can you determine about skin effect frequency and wire gauge? _______________________________ _______________________________ _______________________________ 14. Compare the 28 gauge wire-wrap wire plotted data with all the other wires. What was different about this wire, and why? (hint: wire-wrap wire is silverplated copper.) _______________________________ _______________________________ _______________________________ 15. What does the phase data tell you about skin effect? _______________________________ _______________________________ _______________________________ Lab 7 – Skin Effect and Transmission Lines ENGR 43 Page 3 © 2012 ENGR 43 Lab Activity Student Guide Task #2 – Transmission Line Pulse Reflection For most circuits we assume that electrons flow through a wire at the speed of light. When the combination of wire length and signal frequency result in the distance through the wire being ¼ of the wavelength of that frequency, we must account for the time that it takes for a signal to travel through the wire. When we reach the ¼ wavelength threshold, we refer to the wire or cable (two or more wires) as being a transmission line. TP1 = ______________ TP2 = ______________ TP3 = ______________ What is the shape of the waveform at each test point? Is there any severe distortion at the rising and falling edges? Save the screen image to your flash drive, showing the three test point waveforms. This it the “100Ω termination” data. _________________________________ _________________________________ _________________________________ 2. Remove the 100Ω termination load, leaving the scope probe and ground connected. What are the p-p voltages at TP1, TP2, and TP3? TP1 = ______________ TP2 = ______________ TP3 = ______________ What is the shape of the waveform at each test point? Is there any severe distortion at the rising and falling edges? Part 1: Square Wave Transmission With the 100Ω termination removed, the 1. Connect the circuit shown in Figure 2. signal travels down the wire, has no load Use any one of the four twisted pairs, to deliver its energy, so it travels back up such as the blue and blue/white wires. the wire where it is dissipated in the Set the function generator for a 5 Vp-p, source resistance. Save the screen image 250 kHz squarewave output. Verify the to your flash drive, showing the three generator output impedance is set to test point waveforms. This is your 50Ω. With the 100 Ω termination load “open termination” data. RL and the 51Ω series source resistor RS, 3. Looking at TP2, can you determine the what are the p-p voltages at TP1, TP2, time needed to “charge the line” (the and TP3? delay between the transmitted signal and the reflected signal)? Taking in to Lab 7 – Skin Effect and Transmission Lines Page 4 © 2012 ENGR 43 ENGR 43 Lab Activity Student Guide account that the signal has traveled double the distance of the cable (down and back), divide the “line charging” time by 2 to determine the propagation delay (the time to travel through the transmission line). You will need the propagation time value for step 5. Charge time ÷ 2 = propagation delay __________÷2 = _______________ 4. Short the end of the transmission line. Save the screen image of TP1 and TP2 (TP 3 is shorted to ground). This is your “shorted termination” data. Compare this with your open termination waveforms. Can you describe what is happening at TP2? _______________________________ _______________________________ _______________________________ Did this effect the propagation time? _______________________________ 5. Calculate the time needed for a pulse to travel 100 feet (30.5 m) at the speed of light (c = 3x108 m/s). 30.5 m ÷ 3x108 m/s = ___________ Calculate the propagation velocity vp by dividing the length of the transmission line by the propagation delay line, then use the formula vp=(LC)-1/2 to find the inductance. L = ______________ Part 2: Sine Wave Transmission 7. Connect the 100Ω termination load. Set the function generator for a 5 Vp-p, 250 kHz sinewave. Measure the voltages at TP2 and TP3 and calculate the attenuation for the 100 ft line. Att(dB) = 20 log (VTP3/VTP2). Also measure the attenuation at 1 MHz and 10 MHz. Att (250 kHz)__________________ Att (1 MHz)____________________ Att (10 MHz)___________________ 8. Set the function generator to 500 kHz. Remove the termination resistor, but leave the probe connected to TP3. Slowly increase the frequency and observe the peaks and dips in amplitude at TP2 until you reach 10 MHz. At each peak and dip, record the voltage at TP2, TP3, and the phase angle between TP2 and TP3. frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ 30.5 m ÷ ___________=_____________ Calculate the velocity factor VF for the CAT5e cable by dividing the propagation velocity vp by the speed of light (VF should be around 0.75). VF = ___________÷3x108 m/s=_______ 6. Bonus question: Measure the capacitance of the 100 ft transmission Lab 7 – Skin Effect and Transmission Lines ENGR 43 frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ Page 5 © 2012 ENGR 43 Lab Activity Student Guide frequency=________ peak or dip=____ frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ VTP2=______VTP3______phase = ____ frequency=________ peak or dip=____ 10. How do the peaks and dips compare with step 2? VTP2=______VTP3______phase = ____ _______________________________ frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ 9. Now short the end of the transmission line. Repeat the sweep of frequency from 500 kHz to 10 MHz and note the peaks and dips at TP2. frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ _______________________________ 11. How do the peaks and dips relate to the frequency (or quarter wavelength)? _______________________________ _______________________________ 12. What guidelines can you give for recognizing the effects that wire may have in a circuit? (When does gauge, frequency, cable length become significant?) 13. _______________________________ frequency=________ peak or dip=____ _________________________________ VTP2=______VTP3______phase = ____ _________________________________ frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ frequency=________ peak or dip=____ Deliverable(s) Print and label the saved screen images for 100Ω, open, and shorted terminations from Task #2, Part 1. Print the Excel worksheet and the log-log chart. Save these documents along with this activity sheet in your lab activity binder. VTP2=______VTP3______phase = ____ frequency=________ peak or dip=____ VTP2=______VTP3______phase = ____ Lab 7 – Skin Effect and Transmission Lines ENGR 43 Page 6 © 2012