A 50-ohm cable?
Early in my explorations of electricity,
I came across a length of coaxial cable with the label "50 ohms"
printed along its outer sheath. Now, coaxial cable is a two-conductor
cable made of a single conductor surrounded by a braided wire jacket,
with a plastic insulating material separating the two. As such, the
outer (braided) conductor completely surrounds the inner (single wire)
conductor, the two conductors insulated from each other for the entire
length of the cable. This type of cabling is often used to conduct weak
(low-amplitude) voltage signals, due to its excellent ability to shield
such signals from external interference.
I was mystified by the "50 ohms" label on
this coaxial cable. How could two conductors, insulated from each other
by a relatively thick layer of plastic, have 50 ohms of resistance
between them? Measuring resistance between the outer and inner
conductors with my ohmmeter, I found it to be infinite (open-circuit),
just as I would have expected from two insulated conductors. Measuring
each of the two conductors' resistances from one end of the cable to the
other indicated nearly zero ohms of resistance: again, exactly what I
would have expected from continuous, unbroken lengths of wire. Nowhere
was I able to measure 50 Ω of resistance on this cable, regardless of
which points I connected my ohmmeter between.
What I didn't understand at the time was
the cable's response to short-duration voltage "pulses" and
high-frequency AC signals. Continuous direct current (DC) -- such as
that used by my ohmmeter to check the cable's resistance -- shows the
two conductors to be completely insulated from each other, with nearly
infinite resistance between the two. However, due to the effects of
capacitance and inductance distributed along the length of the cable,
the cable's response to rapidly-changing voltages is such that it acts
as a finite impedance, drawing current proportional to an applied
voltage. What we would normally dismiss as being just a pair of wires
becomes an important circuit element in the presence of transient and
high-frequency AC signals, with characteristic properties all its own.
When expressing such properties, we refer to the wire pair as a
transmission line.
This chapter explores transmission line
behavior. Many transmission line effects do not appear in significant
measure in AC circuits of powerline frequency (50 or 60 Hz), or in
continuous DC circuits, and so we haven't had to concern ourselves with
them in our study of electric circuits thus far. However, in circuits
involving high frequencies and/or extremely long cable lengths, the
effects are very significant. Practical applications of transmission
line effects abound in radio-frequency ("RF") communication circuitry,
including computer networks, and in low-frequency circuits subject to
voltage transients ("surges") such as lightning strikes on power lines.
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