Page 292 - Analog and Digital Filter Design

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Selecting Components for Analog Filters

Inductors in the filter would be adjusted at room temperature to give the
required response. If the filter were then used in a hostile environment (hot or
cold) the filter would go out of tune and perhaps attenuate the wanted signals
(or let in the unwanted signals).

Inductors

Inductors can be a source of many problems. High-value inductors are bulky-
This is because they are usually made up from hundreds of turns of enameled
copper wire that is wound on a bobbin and enclosed by a ferrite core. The wind-
ings capacitively couple to each other, which effectively introduces a parallel
capacitor across the coil. This capacitance causes the inductor to resonate at
some frequency. Above the self-resonant frequency, the impedance of the induc-
tor falls due to the capacitive reactance dominating.

Inductors also possess some series resistance due to the intrinsic resistance of
the copper wire used. This resistance limits the magnification of an applied
voltage at resonance. A resonant circuit is a series or parallel combination of an
inductor and a capacitor. Energy is stored, either in the magnetic flux or in the
electric flux. At resonance this energy passes from one form to the other and
large currents or voltages can be detected.

The voltage or current magnification is known as the “Q” of the circuit. If a
resistance is in series with the inductor the current flow is restricted, which
lowers the Q. This can have an effect on a flter because one with a sharp cutoff
requires components with a high Q; in general, the inductor Q must be at least
ten times the Q of the filter. Low Q inductors cause the filter’s response to
become rounded, in a graphical sense, close to the cutoff frequency. Resistance
can also lead to an insertion loss (even at DC) due to the potential divider action
of the inductor’s resistance and the load resistance.
Resistance also occurs due to the “skin effect.” This is produced by inductance
inside the wire forcing the electrons to travel down the outside surface (hence
“skin” effect). This can be a serious problem for inductors working at a few
hundred kHz and is alleviated by the use of cotton covered Litz wire. This is
the type of wire used to make ferrite rod antennas for radios working in the
low and medium frequency range (LF and MF). It comprises several strands of
enameled copper wire inside a cotton braid. This wire has a lower skin effect
because the current is shared down each of the strands; the surface area of all
the strands combined is considerably larger than the equivalent diameter solid
copper wire.

An inductor that is made from a coil of wire, wound on a bobbin, and SUT-
rounded by a ferrite core is known as a pot-core. The ferrite core is cylindrical