Download AC Theory - David Knight. Radio, electrical and electronic articles.

96
transformation rule (33.3) tells us that:
j2πf L = j(NS/NP)² 2πf L'
i.e.,
L = (NS/NP)² L'
This is a remarkable result because, not only does it give us the basis for constructing equivalent
circuits to serve as models for real transformers, it also tells us something about inductors. The
expression can only be true if the inductance of the coil is proportional to the square of the number
of turns in it. We can see why by considering the two 1:N auto-transformer equivalent circuits
shown below:
In the left-hand circuit, the inductance of
the transformer is referred to the primary side,
and for reasons of convention is given the
symbol AL. In the right-hand circuit, the
inductance is referred to the secondary side
and is given the symbol L. From the
foregoing discussion, we can immediately write the relationship between L and AL:
L = N² AL
We can also interpret L as the inductance of the whole coil, and AL as the inductance of one turn of
the coil.
AL is known as the inductance factor, and depends on the physical dimensions of the coil and the
nature of any magnetic core material. It may be interpreted either as the inductance of a one-turn
coil, or as the inductance of an auto-transformer referred across a one-turn tap. AL has the units of
inductance (Henrys), but is more informatively given units of inductance / turn² ("Henrys per turnsquared").
Continuously variable auto-transformer:
One of the drawbacks of ferrite or iron-cored transformers as impedance matching devices is that
the the transformation ratio can only be altered in a
stepwise fashion, by changing windings or tappings
one turn at a time (or half a turn if the core has two
holes). If the turns in the coils are few, as tends to
be the case in radio-frequency applications, then the
steps available can be very coarse indeed. It is
however possible to make a continuously variable
inductor or auto-transformer by rotating a coil about
its axis and tapping into it with a rolling contact, the
coil end-connections being made by slipping
contacts (known, for historical reasons, as
"brushes"). Such a device is known colloquially as a
"roller coaster", and an example is shown in the
photograph on the right.
This is the motor-driven variable impedance transformer from a 1957 vintage Collins 180L-3A
automatic HF antenna tuner. The tuner is designed to match end-fed wire (Marconi) antennas of 14
to 40 metres in length over a frequency range of 2 to 25MHz, and is for use with transmitters with
an output of up to 150W and a preferred load impedance of 52Ω. An interesting feature
of the transformer is that it achieves a continuous transition from step-down to step-up
by having an overwind (see diagram right), i.e., the brush contact at one end of the coil
goes to a centre-tap, and the end of the coil is left unconnected. The coil has 28 turns,
and the input tap is at 14 turns, so a maximum impedance step-up of approximately 4:1
is obtainable.