1.6 Inductors: Construction, Factors Affecting Inductance and Combinations

1.6 Inductors: Construction, Factors Affecting Inductance and Combinations

ACMA Exam Focus: Syllabus items 4.13-4.15. Recall that the unit of inductance is the henry, that an inductor is normally a coil of wire storing energy in its magnetic field, and that inductance rises with more turns, larger coil diameter and closer turn spacing. You must also apply the series, parallel and series-parallel formulas — and the syllabus note is your friend here: "Calculations will only involve inductors of the same value."

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1. The Inductor and the Henry

An inductor is normally nothing more elaborate than a coil formed by a number of turns of wire. When current flows, a magnetic field builds up around and through the coil, which stores energy in that magnetic field. The ability to store and then use that energy is called inductance, symbol $L$.

The unit is the henry (H), named after the physicist Joseph Henry. A coil has an inductance of one henry when a current changing at one ampere per second induces one volt across it:

$V = L\frac{\Delta I}{\Delta t}$

One henry is a very large inductance, so amateur work almost always uses sub-multiples.

Note that last row: every piece of wire has some inductance. At VHF the few nanohenries in a component lead change how a circuit behaves, which is why RF layouts use short, direct connections.

2. Stored Energy and Back-EMF

The energy held in the magnetic field is:

$E = \frac{1}{2}LI^2$

with $E$ in joules, $L$ in henries and $I$ in amperes.

Worked example. A 10 mH RF choke carries 3 A of direct current:

$E = \frac{1}{2} \times 0.010 \times 3^2 = 0.045\ \text{J} = 45\ \text{mJ}$

That energy must go somewhere when the current stops. As the field collapses it induces a voltage — the back-EMF — which opposes the change that produced it. Hence the key behavioural fact: an inductor opposes a change in current, not current itself.

• Switch on: current rises gradually rather than instantly.
• Steady direct current: the coil looks like nothing more than its own DC resistance.
• Switch off: the field collapses fast, so the back-EMF can reach hundreds of volts. This burns switch and relay contacts, and is why a flyback diode is fitted across relay coils.
• Alternating current: the current is always changing, so the coil always opposes it. That opposition is inductive reactance, $X_L = 2\pi f L$, which rises with frequency.

3. The Four Factors That Set Inductance

Syllabus 4.14 requires you to recall that "the inductance of a coil increases with increasing number of turns, increasing coil diameter and decreasing spacing between turns". Core material is the fourth factor, the most powerful of all.

All four appear in the solenoid approximation $L = \dfrac{\mu N^2 A}{l}$, where $\mu$ is the core permeability, $N$ the turns, $A$ the cross-sectional area and $l$ the coil length. You are not required to calculate with it, but it explains every row: turns are squared, area is on top and length is on the bottom — so stretching a coil out lengthens $l$ and reduces inductance.

That is how amateurs trim an air-cored VHF coil: squeeze the turns together to raise inductance, spread them apart to lower it. Slug-tuned coils do it from the inside — a ferrite slug raises inductance, a brass slug lowers it.

4. Cores: Air, Powdered Iron and Ferrite

• Air-cored. Relative permeability about 1. No core losses, nothing to saturate, very stable. Used for high-power transmitter tank circuits and VHF/UHF coils.
• Powdered iron. Iron particles bonded in an insulating binder, giving a distributed air gap. Moderate permeability, high Q and good stability, suiting tuned circuits, antenna traps and low-pass filters.
• Ferrite. A ceramic of iron oxide with nickel-zinc or manganese-zinc. Permeability is very high, so few turns give a large inductance. Used for broadband transformers, baluns, RF chokes and clip-on suppression sleeves (syllabus 8.6).

Toroids deserve special mention. A ring-shaped core gives the flux a closed path, so almost all of it stays inside the core. Two things follow: more inductance per turn, and very little stray field radiated or picked up. Toroids can therefore sit close together in a crowded transceiver, while open solenoid coils must be spaced apart and are often mounted at right angles to minimise unwanted coupling.

An RF choke is an inductor with a high reactance at the operating frequency that still passes direct current, letting you feed DC to an amplifier stage without RF escaping into the supply rail.

5. Mutual Inductance and Coupling

When two coils share magnetic flux, a changing current in one induces a voltage in the other. That shared property is mutual inductance, symbol $M$, also measured in henries, and the coupling coefficient $k$ says how much flux is shared, from 0 (none) to 1 (all). It is the basis of the transformer (syllabus 4.24) and of coupled tuned circuits, and also the cause of unwanted coupling between stages. Examination calculations always treat inductors as uncoupled.

6. Combining Inductors (Syllabus 4.15)

Inductors combine using exactly the same pair of formulas as resistors.

In series the inductances simply add:

$L_T = L_1 + L_2 + \cdots + L_n \qquad\text{equal values:}\qquad L_T = nL$

In parallel take the reciprocal of the sum of the reciprocals:

$\frac{1}{L_T} = \frac{1}{L_1} + \frac{1}{L_2} + \cdots + \frac{1}{L_n} \qquad\text{equal values:}\qquad L_T = \frac{L}{n}$

Because the syllabus restricts calculations to equal values, those two shortcuts answer every combination question on the paper: multiply by the number in series, divide by the number in parallel.

Worked example 1. Four identical 60 uH RF chokes.

• All four in series: $4 \times 60 = 240$ uH.
• All four in parallel: $60 \div 4 = 15$ uH.

Worked example 2 — a series-parallel network. Wire those same four chokes as two branches of two in series, the branches then in parallel. Collapse the network one step at a time.

• Step 1, each series branch: $2 \times 60 = 120$ uH.
• Step 2, the two equal branches in parallel: $120 \div 2 = 60$ uH.

The whole network therefore behaves as a single 60 uH inductor.

Two sanity checks catch most mistakes: a series total is always larger than the largest single inductor, and a parallel total is always smaller than the smallest. Fail either test and you have used the wrong formula.

7. The Classic Trap: Capacitors Behave the Opposite Way

Syllabus 4.5, 4.12 and 4.15 all ask for combination calculations, and only one of the three components behaves differently.

The reason is physical: capacitors in parallel effectively increase the total plate area, raising capacitance, while capacitors in series increase the plate separation, reducing it.

8. Quick Recap

• The unit of inductance is the henry; expect mH, uH and nH in practice.
• An inductor stores energy in its magnetic field, $E = \frac{1}{2}LI^2$.
• Back-EMF means an inductor opposes a change in current.
• Inductance rises with more turns, larger diameter, closer turns and a higher-permeability core.
• Series: multiply by $n$. Parallel: divide by $n$. Capacitors do it the other way round.