resulting in cancellation.
The opposite of differential mode is called common mode. In
common mode, all conductors have currents flowing in the same
direction. Even when a circuit is designed to operate in differential
mode, it may not have exactly equal currents in the two conduc-
tors withI 1 +I 2 = 0, meaning that current is leaking off to ground at
one end of the circuit or the other. Although paired cables are rel-
atively immune to differential-mode interference, they do not have
any automatic protection from common-mode interference.
Figure g shows a device for reducing common-mode interference
called a ferrite bead, which surrounds the cable like a bead on
a string. Ferrite is a magnetically permeable alloy. In this appli-
cation, the ohmic properties of the ferrite actually turn put to be
advantageous.
Let’s consider common-mode transmission of interference. The
bare cable has some DC resistance, but is also surrounded by a
magnetic field, so it has inductance as well. This means that it
behaves like a series L-R circuit, with an impedance that varies
asR+iωL, where bothRandLare very small. When we add the
ferrite bead, the inductance is increased by orders of magnitude,
but so is the resistance. NeitherRnorLis actually constant with
respect to frequency, but both are much greater than for the bare
cable.
Suppose, for example, that a signal is being transmitted from a
digital camera to a computer via a USB cable. The camera has
an internal impedance that is on the order of 10Ω, the computer’s
input also has a∼ 10 Ωimpedance, and in differential mode the
ferrite bead has no effect, so the cable’s impedance has its low,
designed value (probably also about 10Ω, for good impedance
matching). The signal is transmitted unattenuated from the cam-
era to the computer, and there is almost no radiation from the
cable.
But in reality there will be a certain amount of common-mode
current as well. With respect to common mode, the ferrite bead
has a large impedance, with the exact value depending on fre-
quency, but typically on the order of 100 Ωfor frequencies in
the MHz range. We now have a series circuit consisting of three
impedances: 10, 100, and 10Ω. For a given emf applied by an
external radio wave, the current induced in the circuit has been
attenuated by an order of magnitude, relative to its value without
the ferrite bead.
Why is the ferrite is necessary at all? Why not just insert ordinary
air-core inductors in the circuit? We could, for example, have two
solenoidal coils, one in the outgoing line and one in the return line,
interwound with one another with their windings oriented so that
Section 11.7 Electromagnetic properties of materials 739