Page 6 - Complete Wireless Design

Wireless Essentials

Wireless Essentials 5

desired inductance of the coil (Fig. 1.1). This also means that there must be
some frequency that will allow the coil’s inductance to be in parallel resonance
with the distributed capacitance, causing a high impedance peak to form at
that frequency. In fact, the impedance created by this parallel resonance would
be infinite if not for the small value of wire resistance found in series with the
inductor’s structure. The point of resonance is called the self-resonant fre-
quency (SRF) of the inductor and must be much higher than the circuit’s actu-
al frequency of operation if the inductor is to be used in a tuned resonant
circuit (to maintain the tank’s proper impedance). RF inductors for use at the
higher frequencies are built with small form factors in order to decrease this
distributed capacitance effect, and thus increase their SRF (this technique will
also lower the maximum inductance available, however).
An inductor parameter that is especially important for tuned circuits is the Q,
or quality factor, of the inductor. The Q indicates the quality of the inductor at a
certain test frequency; Q equals the inductive reactance divided by the combined
DC series resistance, core losses, and skin effect of the coil. At low frequencies Q
will increase, but at high frequencies the Q of an inductor will begin to decrease
as a result of the skin effect raising the resistance of the wire. (Even while this
is occurring, the distributed capacitance is also decreasing the desired induc-
tance of the coil. Thus, the Q will soon reach zero, which is the value at its SRF).
The coil’s DC series resistance is the amount of physical resistance, measured by
a standard ohmmeter, that is due to the innate resistance within the inductor’s
own wire. The DC series resistance affects not only the Q of a coil as mentioned
above (and can reach relatively high levels in physically small, high-value, high-
frequency inductors), but will also drop a significant amount of DC bias voltage.
This is important in choosing a coil for a circuit that demands that the inductor
must not have an excessive DC voltage drop across it, which can cause erratic cir-
cuit operation because of decreased bias voltages available to the active device.
The last major loss effect that can create problems in high-inductance coils at
high frequencies is created by coil-form losses, which can become substantial
because of hysteresis, eddy currents, and residual losses, so much so that the
only acceptable type of inductor core material is typically that of the air-core type.

Inductor coil design. There are times when the proper value or type of induc-
tor is just not available for a small project or prototype, and one must be
designed and constructed.
For a high-frequency, single-layer air-core coil (a helix), we can calculate
the number of turns required to obtain a desired inductance with the follow-
ing formula.

L [(18d) (40l)]
n
d
where n number of single layer turns required to meet the desired
inductance (L)
L desired inductance of the air coil, h

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