Transmission Lines and TDR Overview This is the procedure for lab 2a. This is a one- week lab. The prelab should be done BEFORE going to the lab session. In this lab, the characteristics of different transmission lines will be analyzed. Reference materials for this and other labs are on the lab website. For help, contact TAs or instructor. Lab 2a Objectives Learn about different types of transmission lines including coaxial cable, two wire lines, and microstrip. Measure the effect of external materials on capacitance, and therefore impedance, of a line. Background: Students should understand before the lab: Lumped element (RLGC) model for transmission lines (TL) and how to calculate the RLGC parameters for a variety of transmission lines. Prelab Equipment: Matlab software is needed to complete this pre-lab. For more information: Contact the teaching assistants or class instructor. See website for details: www.ece.utah.edu/~ece3300 1
1. RLGC Model of Transmission Lines: Write a Matlab TM code that will calculate the values of R, L, G, C, α, β, velocity of propagation, and Zo for a coaxial transmission line, two wire line, and parallel plate transmission line. The following information is from [1]. 2
2 Test your code on the following transmission lines, and bring the code to lab with you: RG58 Coaxial Line (cable type is printed on the side of the cable) The inner radius a = 0.445 mm, and the outer radius b = 1.765 mm. The conductor is copper (σ c = 5.8 x 10 7 S/m, µ r = 1.0). The insulation between the coaxial lines is polyethylene (PE, ε r = 2.25, σ = 0.0001 S/m). Unless a material is clearly magnetic (ferrite materials), assume µ r = 1.0. Answers for coax: R = 3.6947 ohms/m L = 2.7557e-007 H/m G = 4.5602e-004 mohs/m C = 9.1164e-011 F/m alpha = 0.0461 Np/m beta = 31.4923 rad/m u p = 1.9951e+008 m/s Zo = 54.9796-0.0368i ohms Parallel Plate Line The polyethylene substrate has a thickness of 1mm. The top and bottom are made of copper. The width of the line is 6mm. Twin Lead The radius of the wires is 2mm, and the distance between the wires is 6mm. Assume they are seperated by polyethylene. Answers for twin lead line: R = 1.3131 ohms/m L = 3.8497e-007 H/m G = 3.2643e-004 mohs/m C = 6.5256e-011 F/m alpha = 0.0211 Np/m beta = 31.4923 rad/m u p = 1.9951e+008 m/s Zo = 76.8071+ 0.0097i ohms 3
Lab Procedure Overview: This is the lab 2a procedure. It should be read before coming to the lab but the procedure is to be done during the lab visit. Different types of transmission lines are studied, including coaxial cable, two wire lines, and microstrip. Also, the impedance and other parameters are measured and analyzed. Equipment List: Capacitance meter RG58 50 ohm coax (several lengths, read wire type off side of cable) Two wire transmission line (lamp cord), adjust length by cutting it Box of sand I. Transmission Lines 1. Using the capacitance meter, measure the capacitance of the RG58 coax and two wire (lamp cord) transmission lines. Perform these measurements at 10 khz frequency. Record the capacitance of each line and measure its length. What is the capacitance C per meter? Compare the measured data to your prelab calculations. Give percent error. 2. Plot the capacitance versus distance of the coaxial and two wire transmission lines on a single graph. Properly label the axes, include a legend, and write a caption for this graph. Want to find out more? Capacitance can be used to determine the location of a broken wire, and inductance can be used to determine the location of a short circuit. Several very inexpensive (and simple!) circuits can be used to make this measurement. See 1, available on the lab website. 3. For one of the transmission lines and at the longest distance, measure the capacitance at three different frequencies. Does the capacitance per unit length change with frequency? Should it? 4. Measure the capacitance of the two-wire line buried in sand. How does burying it affect the capacitance and therefore the impedance? The inductance stays constant when the twowire line is buried. 5. Measure the resistance total R of the inner conductor of the longest RG58 coaxial cable using the LCR meter or DMM. Using the TDR, measure the impedance on the line Z o at two locations down the length of the line and average. What was your calculated value of Zo for RG58? How does it compare to the measured value? How can an approximately Z o = 1 Y. Chung, N. Amarnath, C. Furse, J.Mahoney, Capacitance and Inductance Sensors for Location of Open and Short Circuited Wires, IEEE Transactions on Instrumentation and Measurement 58, 2495-2502 (2009) 4
50 ohm cable have almost R=0 resistance? Explain the difference between R and the characteristic impedance Z 0. 6. Measure the capacitance of the microstrip line. Consider any additional capacitance that may affect your measurement and how to correct for it in order to isolate the capacitance of just the microstip. How does this compare to the calculated C of the parallel plate line? Should they be the same? References [1] F. Ulaby, Fundamentals of Applied Electromagnetics, 6th ed., 2010, ch. 2. [2] Agilent Application Note 1304-2 on TDR Theory (available on the Lab website). [3] Step function response see your basic circuits book. 5