Introduction to Transmission Lines

Contents

Preparatory Exercise

Evaluate the inductance per unit length Lo and the capacitance per unit length Co for RG58/U coax cable, consisting of an inner conductor of radius a = 0.81 mm, surrounded by polyethylene (dielectric constant of 2.25), a concentric conducting braid of radius b = 2.9 mm, and outer insulation. Evaluate the following quantities before coming to the laboratory: (LoCo)-1/2 and (Lo/Co)1/2.

Figure 1. Formulas for transmission line calculations.

Note to Instructors
This laboratory exercise is meant to be exploratory. Please refrain from posting formulas related to reflections from improperly terminated transmission lines. Students should record their observations/comments and submit their report at the end of the lab session.

Equipment List

BK Precision 2120 Dual Trace Oscilloscope or equivalent. 100 ns pulser circuit with 50 ohm output impedance. 12 V dc power supply and red/black banana plug patch cords. 500 ft spool of RG58/U coax cable. Additional 100 ft coil of RG58/U coax cable. 3 BNC tees, short bnc-terminated cable, 95 ohm, 75 ohm, 50 ohm, and shorting BNC terminators.

Figure 2. Elements of coaxial cable.

Objectives
Reinforce your understanding of the correct use and operation of oscilloscope.
Develop an appreciation for correct termination of transmission lines (such as Ethernet and television cable).
Exercise critical thinking.

Introduction
The finite speed of transmission of electric signals becomes a factor with high-speed circuits and long cables. Transmission line theory was developed early in this century to deal with the propagation of signals along well-defined paths, which the familiar twin-lead antenna lead, the ever-popular coax cable, and closely-spaced parallel films (such as on a printed-circuit board). Transmission lines are characterized by several parameters, including the characteristic impedance, the phase speed, and the attenuation length. The meaning and importance of these parameters will be illustrated in the following exercises.

Pulser Characteristics
Power pulser circuit by supplying +12 V dc to the red banana jack and connecting the power supply ground to the black jack. Connect the pulser output (BNC jack) to the oscilloscope and adjust controls to obtain steady waveform. (As a demonstration of your laboratory prowess, please attempt to obtain a stable display without help from the lab instructor --- refer to Introduction to the Oscilloscope for additional guidance if needed.) Sketch pulse shape and record the amplitude, pulse width, and period of the waveform. Make sure that you define how you determine the pulse width: full width at half maximum, 10%--90% width, etc. How does the observed pulse width compare to the stated bandwidth of the oscilloscope (20 MHz corresponding to ~15 ns risetime)?

Speed of Pulse Propagation
Split output of pulser with BNC tee and feed signal into one end of the spool of coax cable. Connect other end of cable directly to the other channel of the oscilloscope. Record both waveforms and comment on any changes that occur.

Measure the time between the primary pulses on each channel. Make sure that the sweep setting (time/cm) is in the calibrated position --- remember that x10 magnification of the time base may be obtained by pulling out the calibration knob. Describe the measurement process; i.e., which part of each waveform was used to mark the time: rising edge, trailing edge, peak position, 50% crossing, etc.

Convert the measured delay to a propagation speed for 500 ft of cable. Compare to the speed of light and to the quantity (L_oC_o)^-1/2 from the Preparatory Exercise. Comment!

Signal Attenuation
Connect a tee to the far end of the cable (end far from the pulser) and reconnect to the oscilloscope. Attach a 50 ohm teminator, the BNC connector with a red "cap," and record both waveforms. Record the ratio of amplitudes of input pulse and transmitted pulse (pulse received at far end); express the loss of signal in terms of an attenuation length (the 1/e length). Comment on the suitability for using this type of cable for wiring the entire campus for high-speed computer connections.

Termination of Transmission Lines
Finally, remove the 50 ohm terminator and observe changes in waveforms with and without "correct termination" of the cable. At what times to the "extra pulses" appear? Record the polarity and magnitude of all pulses observed.

Compare the quantity (L_o/C_o)^1/2, the so-called characteristic impedance, with the value of 50 ohm for correct termination. Comment!

Repeat the observations above using a shorting terminator, a "0" ohm terminator, instead of the 50 ohm terminator. Comment on the observed changes in both channels. Repeat with 75 ohm and 93 ohm terminators (metal caps).

Critical Thinking Exercises

• Why does the pulse at the far end of the 500 ft cable apparently double in magnitude when the 50 ohm terminator is removed?
• Why does the the polarity of the first pulse returning to the pulser (the one following the primary pulse on the 'scope channel monitoring the near end of the cable) flip when the cable is shorted at the far end?

Resolution of the Reflected Pulse
Repeat all of the above observations after substituting an additional 100 ft of cable for the terminator. Study the effects of changing the termination condition at the far end of the additional coil. The additional length of cable will temporally separate the out-going pulse and its refection as seen on the last channel, still connected to the far end of the 500 ft spool, and should facilitate your responses to the critical thinking queries.

Courtesy of Elmer Atkins; 1959 The Saturday Evening Post