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Commit d8f555e8 authored by Erik Strand's avatar Erik Strand
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Redo 7.1

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......@@ -8,22 +8,43 @@ title: Problem Set 5
Cables designed to carry signals with minimum pickup of interference often consist of a twisted pair
of conductors surrounded by a grounded shield. Why the twist? Why the shield?
Twisted pairs are used for differential signaling, i.e. where we listen to the difference between
the voltages on the wires as opposed to either absolute value. Noise can be imparted to our
conductors by external electric or magnetic fields. In particular, we need to worry about changing
fields (since static electric fields won't affect our current, and static magnetic fields will
induce a [Hall effect](https://en.wikipedia.org/wiki/Hall_effect) but not overlay a different
signal.)
If they were weren't twisted, a close noise source would add more noise to the closer wire, thus
distorting the voltage difference. Twisting distributes noise on average evenly across the two
wires, helping preserve the differential signal.
A shield helps prevent noise sources from interacting with the conductors at all. As we've seen,
oscillating electric fields can only penetrate so far. So the shield effectively provides a low pass
filter for the sorts of noise that can reach the conducting pair, with the cutoff frequency
determined by the shield's thickness. Grounding it ensures that built up static charge has a place
to go, though not all shields are grounded.
Let's answer this from the ground up. The simplest way to transfer a signal is to use a single wire,
where a voltage is applied at one end and measured at the other. In practice this requires at least
some current flow, so there must be a return path which for now I'll assume is literal ground. The
voltage we measure will be different than the voltage we apply if and only if the path integral of
the electric field along our wire is nonzero.
A stationary electric field won't have any effect, since it will quickly induce a charge
distribution that cancels itself (i.e. the field inside a conductor is zero). But a quickly changing
one can induce a voltage, since the rate of charge transfer within the conductor is finite. This is
capacitive coupling.
Similarly, a stationary magnetic field will only apply a net force on electrons perpendicular to the
current. This induces a [Hall effect](https://en.wikipedia.org/wiki/Hall_effect) but won't impact
our measurement. But a varying magnetic field (or moving the wire through a fixed one) can induce a
voltage because it causes curl in the electric field. This is inductive coupling.
How can we mitigate these effects? If we surround our signal wire with another conductor, the
capacitively induced voltages will mostly appear there. This is a shield. The effectiveness of the
shield depends on its conductivity, its thickness, and the frequency of the interference (recall
that oscillating electric fields penetrate conductors up to a skin depth). It doesn't necessarily
need to be grounded to do its job, but doing so ensures it can source enough charge to counteract
even the strongest external fields, and dissipate static buildup.
The inductive coupling is minimized by minimizing the magnetic flux between our signal wire and the
current return path. So if we use a second wire for our return path, and keep it next to the first,
there's much less area for flux to penetrate. By twisting the pair of wires, we create alternating
regions where the flux will have opposite sign. This causes inductively coupled signals to cancel
themselves out. If we want to take this even further, we could use
[star quad](https://en.wikipedia.org/wiki/Star_quad_cable) wire.
Continuing with the theme of noise cancellation, if the drive, line, and load impedances are matched
in the two wires, then any noise signals that do couple will tend to cause equal voltage
fluctuations. This is why differential signaling is common. Note that this works even if we don't
put equal and opposite voltages on the wires: we just need matching electrical characteristics (and
the assumption of equal noise patterns). But applying equal and opposite voltages to the wires does
help in another way: it causes the fields generated by our wires to cancel each other out except at
small distances, so it helps our wires not induce noise in any other signal lines.
## (7.2)
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