Field Coil Inductance

A field coil is also an inductor, often a large one. Its inductance governs how quickly the field builds up, how much energy must be dumped at switch-off, and how well it filters ripple when used as a choke.

Parameters

Construction

Turns

N

Core cross-section

A

cm²

Iron path length

\ell_i

Relative permeability

\mu_r

Air gap (total)

g

DC current

I

Fig. 9Gapped laminated core. The gap, though tiny, usually dominates the reluctance.

Inductance

L

21.9 H

Stored energy

\tfrac12 LI^2

39.3 mJ

Reactance @ 100 Hz

X_L

13.7 kΩ

Reactance @ 120 Hz16.5 kΩ

L per turn²

A_L

874 nH

Core flux density

B

0.656 T

Effective μ

\mu_e

261

☞ Gap carries 87 % of the magnetic reluctance.

Inductance vs. turns (log–log)

How it works

Theory · assumptions · formulas

Inductance from reluctance

Any coil's inductance is the turns squared divided by the reluctance of its flux path, $L = N^2/\mathcal{R}$ . For a core of section $A$ , iron length $\ell_i$ and total gap $g$ :

L = \frac{\mu_0 N^2 A}{g + \ell_i/\mu_r}

Because $\mu_r$ is in the thousands, even a fraction of a millimetre of gap dominates. That is a blessing: the gap makes the inductance predictable and stops DC from saturating the iron. The core flux density at DC is $B = \mu_0 N I/(g + \ell_i/\mu_r)$ .

Air-core coils: Wheeler's formula

For a multilayer coil of mean radius $a$ , length $b$ and winding depth $c$ , H. A. Wheeler (1928) gave the empirical expression, here converted to metres:

L\ [\mu\mathrm{H}] = \frac{31.6\,N^2 a^2}{6a + 9b + 10c}

Why field coils are huge inductors

Thousands of turns on an iron pot with a single narrow gap easily reach several henries. A speaker field of 1500 Ω commonly measures 2–10 H, exactly the region wanted for a power-supply filter choke (Plate XI).

CautionIron-core inductance depends on DC bias and AC level. Measure at the operating current; an LCR meter at zero bias will read high.