Experiment No. 6 Pre-Lab Transmission Lines and Time Domain Reflectometry

Transcription

1 Experiment No. 6 Pre-Lab Transmission Lines and Time Domain Reflectometry The Pre-Labs are informational and although they follow the procedures in the experiment, they are to be completed outside of the laboratory. There are questions given in the pre-lab. Your answers are to be submitted to your lab instructor before the experimental procedure is performed. Introduction When voltages and currents are applied to a transmission line they do not reach the end of the line instantaneously. The energy is transferred at the speed of light in a line with an air dielectric line and at about 2/3 of that speed in flexible coaxial cables. When a line is properly terminated in its characteristic impedance all of the energy propagating will be absorbed by the load. Otherwise there will be reflections of voltage and current on the line. A time domain reflectometer, or TDR, is an instrument designed to determine properties of the load or abnormalities at any location along the line using reflections that are observed at the source end of the line. Standing waves on a transmission line occur when a periodic signal is applied at one end of the line and there is reflected energy somewhere along the line. The electrical length of a line is the length measured in units of wavelengths of the signal propagating in it. It depends on the physical length of the line and the signal frequency. If the line is electrically short the reflections will have little effect. However, when the line is electrically long the voltage and current in the line will vary along the line. The experiment will investigate the properties of a pulse propagating down a transmission line and determine the effects of the reflected energy when the energy is not fully absorbed by the load. It will be shown that these reflections can be used to determine properties of the load as well as abnormalities at any location along the line A sinusoidal signal will be used to investigate how the load impedance and the electrical length of the line affect standing waves. Part A: Reflections on a Transmission Line 1

2 Objective: To observe the effect of reflections on a transmission line For this lab, you will use an RG-58 coaxial cable at least 40 ft long with bare wires or clip leads at the one end and a BNC connector at the other end. Be sure to check the printing on the outside of the cable to confirm this. The distributed values of inductance and capacitance in an RG-58 cable are specified to be 80 nh/ft and 29 pf/ft respectively. With the function generator set it to produce a 0 to 5V square wave at 1 MHz, a long coaxial cable will be connected to both the function generator and oscilloscope using a BNC T-connector. The voltage at both ends of the long cable will be monitored using the oscilloscope. Q1. Using the specifications for capacitance and inductance given above, calculate the characteristic impedance of the cable using the formula (L/C) 1/2. Note that the length dimension (ft) cancels in the formula. Answer: Z0 = L/C = 80nH/ft/29pF/ft = 52.5 A resistor as close in value to the characteristic impedance as possible will be connected to the far end of the long cable. You will observe the waveform at the source end and also the load end of the cable using both oscilloscope channels. Q2. What voltage would you expect to see at the source end of the cable? Answer: 0 to 2.5V square wave Q3. What voltage would you expect to see at the load end of the cable? Answer: 0 to 2.5V square wave Q4. Will there be a time difference between the waveforms at the source and load? Answer: Yes, the load voltage will lag the source voltage. Q5. Assuming a time difference between the leading edges of 80 ns and a propagation velocity determined by the distributed values of capacitance and inductance, calculate the length of the cable (See Footnote #1). Answer: Vp = velocity of propagation is 1/LC = 6.6 x 10 8 ft/s, d = Vp x t = 6.6 x 10 8 ft/s x 80 ns = 52.8 ft The resistor from the end of the cable will be removed and you will observe the waveforms at each end of the cable. You should see that both signals have doubled in size. However, it takes twice the travel time at the source end for this to happen because 2

3 now there is a reflected wave that has to travel back to the source end. You will see the same time difference between leading edges of the two waveforms, but the source end will double in size when the reflection reaches the source. Q6. What time difference would you expect between the leading edge of the signal at the source end and when the signal doubles in size (See Footnote #2)? Answer: 2 x 80 ns = 160 ns, the two way travel time You will repeat the measurement with the load end shorted instead of open. Both waveforms should be at zero volts except that a short pulse appears on the source end of the cable. Q7. What time difference would you expect between the leading edge of the signal at the source end and when the signal goes to zero? Answer: 160 ns, the two way travel time Q8. Why doesn't the source end start at zero? Explain why the voltage goes back to zero at the source end. Answer: The source sees Z0 (surge impedance) until the reflected wave returns to subtract from the source voltage. Q9. From observing Ch1 alone, how could you determine the length of the cable? Answer: The cable length will be 80ns (one way travel time) multiplied by the velocity of propagation in the line. Q10. Is there a load condition that would prevent this? Answer: Yes, if the cable is terminated in Z0, there will be no reflected wave and there will be no voltage change at the source end. Part B: Simulating a TDR Objective: To use an oscilloscope to verify the operation of a TDR A TDR is a device that sends a square wave pulse down the transmission line and reflections from positions along the line are observed on the instrument s oscilloscope screen. The device is able to locate faults along the line and determine when the line is properly terminated in the characteristic impedance of the line. 3

4 You will disconnect the oscilloscope from Ch2 and connect a 100 resistor to the load end of the cable. The source end of the cable will be observed and you will measure the two way travel time in the cable. Q11. Suppose the two way travel time is 160 ns. Determine the length of the cable. (See Footnote #3). Answer: Length = (160 ns/2) x 6.6 x 10 8 ft/s = 52.8 ft (same as in Q 5) The 100 resistor will be changed to 25. Q12. Describe how the signal at the source end will change. Answer: The voltage will go from 2.5V to 1.67V when the reflection returns. This value was determined using the voltage divider formula and the 50 source (function generator) resistance. Q13. By observing the waveforms at the source end with the two different resistor values how would you know which resistor is at the other end? Answer: If the voltage goes from 2.5V to 3.33V the resistor is 100. If the voltage goes from 2.5V to 1.67V the resistor is 25. Next you will measure the length of the cable by using a tape measure with the cable lying on the floor. This measurement will be used to compare with the simulated TDR measurement. Part C: SWR Measurements Objective: To investigate standing waves and electrical length on a transmission line In this part of the experiment, the existence of standing waves will be demonstrated by changing the electrical length of the transmission line. The function generator will be changed to produce a sinusoidal signal and the frequency will be varied to change the electrical length. The electrical length of a line is the length measured in units of wavelengths (λ) of the signal that is applied to it. When the source frequency is increased, the wavelength decreases making the cable longer when measured in units of wavelength. With the frequency set to 1kHz, a 100 load resistor will be connected to the end of the line. You will adjust the oscilloscope to view at least one period of the input waveform. Q14. Calculate the electrical length of the transmission line at this frequency. 4

5 Answer: electrical length = d/ = 52.8 ft/(6.6 x 10 8 ft/s/1khz) = 52.8ft/660,000ft) = wavelengths or << 1 The line is electrically short at this frequency so the impedance at the source end of the cable will be the same as the load resistance value of 100 (See Footnote #4). Q15. If the function generator is set to 5Vp-p before the cable is connected, what voltage will appear at the source end of the line when it is connected to the generator? Remember that the function generator has an internal impedance of 50? Answer: [100 /(50+100) ]x5v = 3.33V You will increase the function generator frequency while observing any changes in the source voltage until you reach the largest frequency available (15 MHz). Q16. What would you expect to happen to the source voltage? Remember that there will be a change in the impedance along the line when there is a mismatch between the load impedance and the characteristic impedance of the line. See Footnote #4. Answer: The voltage will change because the source will see a different impedance. (See Footnote #4). Q17. Will the source voltage increase, decrease or both or will it stay the same value? Answer: It will depend on the frequency. It could increase, decrease or stay the same. Q18. How would you be able to determine the source voltage if you knew the generator frequency and the length of the line? Answer: Knowing that the internal source impedance is 50, you can use the voltage divider formula and the reflected impedance to calculate the voltage. The Smith chart can be used to determine the reflected impedance based on the signal wavelength or you can use equation 32 in chapter 7. (See Footnote #4). You will repeat the measurements with a load resistance of 10. The electrical length of the transmission line at the frequency where you have a 10% change in voltage is the frequency where the line is considered electrically long and transmission line theory becomes important. Footnotes: 5

6 1. Electromagnetic (EM) energy (in the form of a voltage and current wave) travels at an extremely fast yet finite speed. The speed is the exact same speed at which light travels, since light is also EM energy. The speed of EM transmission depends on the medium through which it travels, being the fastest in a vacuum or free space. In coaxial cables the speed is less than the free space value of 3x10 8 m/s (also 1x 10 9 ft/s, 186,000 miles/s or 1 ft/ns). The actual speed in the cable can be determined by taking the reciprocal of the square root of the distributed value of inductance and capacitance in the cable. 2. Just like sound and other mechanical waves, EM waves reflect if they encounter a change in the medium in which they are traveling. In a coaxial cable the energy must stay within the cable so it reflects back in the direction it came from. The voltage and current wave "see" a load impedance equal to the characteristic impedance of the cable, which is consistent throughout the cable. If the cable is terminated in an impedance other than this characteristic impedance, there will be a reflection. The reflected energy will cause the voltage and current to change on the transmission line because the voltage and current along the line will be a combination of the waves traveling in each direction, 3. By observing the voltage at the source end of a transmission line we can tell how long it takes for the incident and reflected wave to travel down the line and back to the source. Note that in this part of the experiment we didn't need access to the load end of the line. That is why a TDR (time domain reflectometer) can determine the location of loads, faults or other inconsistencies remotely without digging up the cable if it is buried. Note also that you were able to see whether the load end was terminated in a lower or higher impedance than the characteristic impedance of the line. A similar technique is used with fiber optic cables using an instrument called the OTDR (optical time domain reflectometer) that sends an optical pulse into the fiber. 4. The electrical length of a transmission line depends on two things, its physical length and the frequency of the signal propagating in the line. It is defined for sinusoidal signals and is equal to the physical length of the line divided by the signal wavelength. It is dimensionless (when equal length units are used) and is the length given in units of signal wavelength. The voltage amplitude on a transmission line with standing waves depends on the electrical distance from the termination creating a reflection. The current varies in a similar way except that the maximums for current is the minimum for voltage and visa-versa. Since the impedance on the line is the ratio of voltage to current, it also varies along the line. The impedance on a lossless line as a function of electrical distance from the load is given by the equation, Z s = (Z L + jz 0 tanßs)/(z 0 + jz L tanßs) Z s = line impedance at a given point from the load Z L = load impedance Z 0 = line's characteristic impedance ßs = distance from the load to the point where the line impedance is desired (in electrical degrees) = distance in wavelengths x 360 As the frequency of the source is varied, the electrical length of the transmission line is changed. Using the equation we can predict the voltage at the source end since the generator source impedance and the line impedance at the source end form a voltage divider. Alternately a Smith chart can be used to graphically solve the equation. The Smith chart has other important uses and is more versatile than using the equation which is difficult to use when given the source impedance and finding the load impedance, or when solving for the distance along the line for various load/source impedance conditions. If you ever work in with very high frequency circuits (VHF and higher) you will undoubtedly see Smith chart representations of circuit performance. 6