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Characteristic Impedance
17 questions By Tony R. Kuphaldt
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Question 4 of 17
What does the “50 ohm” rating of an RG-58/U coaxial cable represent? Explain how a simple cable, with no continuity between its two conductors, could possibly be rated in ohms.
Hint: this “50 ohm” rating is commonly referred to as the characteristic impedance of the cable. Another term for this parameter is surge impedance, which I think is more descriptive.
Reveal answerA cable with a characteristic, or surge, impedance of 50 ohms behaves as a 50-ohm resistor to any voltage surges impressed at either end, at least until the surge has had enough time to propagate down the cable’s full length and back again.
Notes:This concept will seem very strange to students who are only familiar with resistance in the context of resistors and other simple electrical components, where resistance does not change appreciably over time. In this example, though, the “resistance” of the cable is extremely time-dependent, and the time spans involved are typically very short - so short that measurements made with ohmmeters will not reveal it at all!
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Question 5 of 17
Given the following test circuit, with an oscilloscope used to record current from the battery to the cable (measuring voltage dropped across a shunt resistor), what sort of waveform or pulse would the oscilloscope register after switch closure?
Reveal answerThe oscilloscope would register a square-edged pulse of voltage approximately equal to 480 μV, which of course corresponds to a current of approximately 480 mA:
The pulse duration should range somewhere between 162.67 microseconds and 170.42 microseconds (based on two different figures I obtained for RG-58/U cable velocity factors).
Notes:Answering this question requires several steps, and the combining of multiple concepts. It should be apparent from the answer that Ohm’s Law (I = E/R) is sufficient for calculating pulse current, but the time delay figure given in the answer may confuse some students. For those students who calculate a time figure that is half as much as the one given in the answer, encourage them to think of why their (incorrect) answer might have been off by 50%. The existence of a 2:1 ratio such as this implies a simple conceptual misunderstanding.
For the RG-58/U cable velocity factor, I obtained two different figures: 0.63 and 0.66, which accounts for the two time delay answers given.
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Question 6 of 17
Given the following test circuit, with an oscilloscope used to record current from the battery to the cable (measuring voltage dropped across a shunt resistor), what sort of waveform or pulse would the oscilloscope register after switch closure?
Reveal answerThe oscilloscope would register a continuous current of 480 mA any time the switch is closed.
Notes:Challenge your students to think of another electrical component (besides an RG-58/U cable of infinite length) that would behave like this, drawing 480 mA of current from a 24 volt source any time the switch is closed. Hint: you don’t have to think very hard!
