Energising Transient & Flyback

Closing the switch on a field coil, the current creeps up with time constant L/R. Opening it is the dangerous part: the stored energy must go somewhere, and without a path it leaps the switch contacts as a spark of thousands of volts.

Parameters

Inductance

L

Coil resistance

R

Supply voltage

V

Switch-off suppression

Fig. 10The suppression element sits across the coil and carries the decaying current once the switch S opens.

Switching

Time constant

\tau = L/R

4 ms

Final current

I_0

66.7 mA

To 99 %

4.6\tau

18.4 ms

Stored energy

W

13.3 mJ

Coil kick

V_{pk}

700 mV

Switch stress101 V

Decay time

t_{off}

19.9 ms

☞ Switch must withstand 101 V. Field decays to zero in 19.9 ms.

Coil current: switch closes at t = 0, opens at 5τ

How it works

Theory · assumptions · formulas

Energising

Kirchhoff's voltage law around the loop gives $V = iR + L\,\tfrac{di}{dt}$ , whose solution from rest is

i(t) = \frac{V}{R}\left(1 - e^{-t/\tau}\right), \qquad \tau = \frac{L}{R}

After one time constant the current reaches 63.2 %; after $4.6\tau$ , 99 %. Field-coil speakers take a noticeable fraction of a second to come up to full sensitivity, the source of the familiar "swelling" at switch-on in old radios.

De-energising

An inductor resists any change of current: $v = L\,di/dt$ . Interrupting $I_0$ instantly would require infinite voltage. In practice the voltage rises until something conducts: the winding's own capacitance, the switch gap, or the insulation. The stored energy is

W = \tfrac12 L I_0^2

With stray capacitance $C$ alone, energy sloshes into it and the peak becomes $V_{pk} = I_0\sqrt{L/C}$ .

Suppression options

Diode: clamps to about 0.7 V; the coil's own resistance dissipates the energy. Decay: $i = (I_0 + \tfrac{V_D}{R})e^{-t/\tau} - \tfrac{V_D}{R}$ . Safe but slow; bad for relays, fine for speaker fields.
Resistor $R_s$ : kick of $I_0R_s$ , faster decay with $\tau' = L/(R + R_s)$ . Costs $V^2/R_s$ continuously unless in series with a diode.
Diode + Zener: clamps at $V_C = V_Z + V_D$ , current falls almost linearly and stops after $t = \tau\ln(1 + I_0R/V_C)$ . Fastest decay for a given voltage rating.

Historical noteRadios with series fields never needed suppression: the rectifier, filter capacitors and valve heaters' slow warm-up made the transient gentle. A field coil switched directly from a bench supply is another matter. Always fit a diode.