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Ratio ZL/Zo = 1 ZL/Zo < 1 ZL/Zo > 1
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The step-function (or pulse) response of the transmission line leads to a powerful means of analyzing the line, and its load, on an oscilloscope Figure 3-7A shows (in schematic form) the test set-up for time domain reflectometry (TDR) measurements An oscilloscope and a pulse (or square-wave) generator are connected in parallel across the input end of the transmission line Figure 3-7B shows a pulse test jig built by the author for testing lines at HF The small shielded box contains a TTL square-wave oscillator circuit Although a crystal oscillator can be used, an RC timed circuit running close to 1000 kHz is sufficient In Fig 3-7B, you can see the test pulse generator box is connected in parallel with the cable under test and the input of the oscilloscope A closer look is seen in Fig 3-7C A BNC tee connector and a double male BNC adapter are used to interconnect the box with the scope If a periodic waveform is supplied by the generator, then the display on the oscilloscope will represent the sum of reflected and incident pulses The duration of the pulse (ie, pulse width), or one-half the period of the square wave, is adjusted so that the returning reflected pulse arrives approximately in the center of the incident pulse Figure 3-8 shows a TDR display under several circumstances Approximately 30 m of coaxial cable, with a velocity factor of 066, was used in a test setup similar to Fig 3-7 The pulse width was approximately 09 microseconds ( s) The hori-
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76 Transmission lines
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Oscilloscope
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3-7A Time domain reflectometry setup
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3-7B Test setup for impromptu time domain reflectometry
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Transmission line responses 77
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3-7C Close-up of RF connections
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3-8A Idealized TDR pulse Small pip on top is reflected signal interfering with forward pulse 09 s
zontal sweep time on the scope was adjusted to show only one pulse which, in this case, represented one-half of a 550-kHz square wave (Fig 3-8B) The displayed trace in Fig 3-8B shows the pattern when the load is matched to the line (ZL = Zo) A slight discontinuity exists on the high side of the pulse, and this represents a small reflected wave Even though the load and line were supposedly matched, the connectors at the end of the line presented a slight impedance discontinuity that shows up on the scope as a reflected wave In general, any discontinuity in the line, any damage to the line, any too-sharp bend, or other anomaly, causes a slight impedance variation, and hence a reflection
78 Transmission lines
3-8B TDR pulse with no significant reflection
Notice that the anomaly occurs approximately one-third of the 09- s duration (or 03 s) after the onset of the pulse This fact tells us that the reflected wave arrives back at the source 03 s after the incident wave leaves Because this time period represents a round-trip, you can conclude that the wave required 03 s/2, or 015 s to propagate the length of the line Knowing that the velocity factor is 066 for that type of line, you can calculate its approximate length: Length = cvT = (3 10 m/s) (066) (15 10 7 s) s
[317]
= 297 m which agrees within experimental accuracy with the 30 m actual length prepared for the experiment ahead of time Thus, the TDR setup (or a TDR instrument) can be used to measure the length of a transmission line A general equation is cvTd 2
Lmeters =
[318]
where L is the length in meters c is the velocity of light (3 108 m/s) v is the velocity factor of the transmission line Td is the round-trip time between the onset of the pulse, and the first reflection Figures 3-8C through 3-8H show the behavior of the transmission line to the stepfunction when the load impedance is mismatched to the transmission line (ZL not equal to Zo) Figure 3-8C shows what happens when the load impedance is less than the line impedance (in this case, 05Zo) The reflected wave is inverted, and
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