10.3 Back EMF, Saturation & Inductor Applications
Key Takeaways
- Back EMF is the self-induced voltage that opposes a change in inductor (or motor winding) current; at switch-off it can produce a large voltage spike
- Magnetic saturation is the region where further increases in magnetising current produce little extra flux; inductance falls and waveforms distort
- LR series time constant τ = L/R (seconds); current rises or falls roughly 63% of the way to its final value in one τ
- Inductors are used for filtering, chokes, energy storage in converters, transformers/mutual devices, and EMI suppression
- Aircraft relevance includes 28 V DC inductive spikes on relays/contactors, 400 Hz magnetics, and the need for suppression diodes or snubbers on switched coils
10.3 Back EMF, Saturation & Inductor Applications
Quick Answer: Back EMF is self-induced voltage opposing current change (e = −L di/dt) — dangerous spikes at switch-off. Saturation flattens flux vs current so effective L drops. τ = L/R sets how fast LR circuits settle. Inductors filter, choke, store energy, and couple magnetically — all relevant to aircraft DC and 400 Hz AC systems.
Sections 10.1–10.2 gave Faraday, L, M, and Lenz. This section turns those ideas into the behaviours technicians meet on the ramp and in the avionics bay: inductive kick, saturated cores, exponential LR transients, and everyday uses of inductors.
Back EMF
Back EMF (back electromotive force) is the self-induced EMF in an inductor or inductive winding that opposes the change in current, per Lenz’s Law.
| Situation | What back EMF does |
|---|---|
| Current trying to increase (switch-on) | Back EMF opposes the rise — current cannot jump instantly |
| Current trying to decrease (switch-off) | Back EMF opposes the fall — tries to keep current flowing |
| Steady current | di/dt = 0 → back EMF = 0 |
At switch-on across a DC supply, back EMF is large at first (rapid attempted di/dt), so current rises gradually. At switch-off, interrupting current forces a very large |di/dt| if the circuit opens abruptly; e = −L di/dt can produce a high-voltage spike that arcs across switch contacts or damages semiconductors.
Worked magnitude insight. L = 0.5 H; current 2 A interrupted in roughly 0.001 s → average |e| ≈ L ΔI/Δt = 0.5 × 2 / 0.001 = 1000 V. That is why relay coils and contactor coils need suppression (flyback diode, RC snubber, or dedicated suppressor) on aircraft DC buses.
Back EMF in motors (preview)
A rotating DC motor armature also generates a back EMF proportional to speed (generator action inside the motor). Supply voltage minus back EMF drives armature current through resistance. Module 3.12 expands motors; here, note that “back EMF” appears both as inductive self-EMF during current change and as motional EMF in machines — same Faraday family, different context.
Saturation Point
An iron-cored inductor’s flux does not rise forever with current. As domains align (§9.3), the core approaches magnetic saturation:
| Region | Behaviour |
|---|---|
| Linear / unsaturated | Φ roughly ∝ I; L ≈ constant |
| Approaching saturation | Incremental permeability falls |
| Saturated | Extra current buys little extra Φ; effective inductance drops |
Consequences for Module 3:
- Magnetising current becomes non-linear and can show peaks (transformer inrush / saturated choke).
- AC flux waveforms distort if driven too hard.
- Designers add air gaps in some chokes to store more energy and linearise (at the cost of lower L).
- Heat and audible buzz can increase when magnetics are overdriven.
Exam wording. “Saturation point” means the region of the B–H or Φ–I curve where further increase in magnetising force yields little increase in flux density — the inductor no longer behaves as a fixed henry value.
LR Time Constant (Brief)
A series resistor R and inductor L driven by DC obey an exponential transient.
Time constant:
τ = L / R
| Unit check | L in henrys, R in ohms → τ in seconds |
|---|---|
| Meaning | Time to reach about 63% of the total current change toward the final value |
| Rise (switch to V) | i(t) = (V/R)(1 − e^(−t/τ)) toward I_final = V/R |
| Decay (shorted LR) | i(t) = I_0 e^(−t/τ) toward zero |
| After ~5τ | Transient essentially finished (~99%) |
Worked example 1. L = 0.2 H, R = 10 Ω → τ = 0.2/10 = 0.02 s (20 ms).
Worked example 2. L = 2 H, R = 100 Ω → τ = 0.02 s again — large L with large R can match a small L with small R. Current rate of change still limited by L, but the settling time scale is L/R.
Quick contrast with capacitors. RC uses τ = RC; LR uses τ = L/R. Do not swap the formulas on the exam.
Principal Uses of Inductors
| Application | Role of L / M |
|---|---|
| Filter / choke | Opposes AC or ripple; passes steady DC more readily (series choke in power supplies) |
| Smoothing | With capacitors, forms LC or π filters on DC rails |
| Energy storage | ½LI² stored in the magnetic field — used in switch-mode converters and ignition-style pulses |
| Transformers / coupled inductors | Mutual inductance transfers AC energy between windings |
| EMI / RFI suppression | Common-mode chokes and series inductors limit high-frequency noise |
| Tuning / resonance (with C) | Sets resonant frequency f = 1/(2π√(LC)) in radios and filters (Module filter topics expand this) |
| Sensors | Variable reluctance / inductive pickups convert motion to EMF |
Inductive reactance preview (AC): X_L = 2πfL. Higher frequency or larger L → more opposition to AC. That is why a choke that barely notices 28 V DC ripple components can still block higher-frequency noise, and why 400 Hz aircraft magnetics are sized differently from 50/60 Hz ground equipment.
Aircraft Relevance
Aircraft electrical systems make inductance unavoidable:
| Context | Why inductance matters |
|---|---|
| 28 V DC bus with relays, contactors, solenoids | Coil inductance → back-EMF spikes at de-energise; suppression protects contacts and solid-state drivers |
| Starter / large contactors | High L and high I → severe arc if opened without care; follow maintenance procedures |
| 400 Hz AC generation and distribution | Transformers and inductors sized for higher frequency; core losses and reactances scale with f |
| Ignition / high-energy coils | Mutual inductance steps voltage; rapid di/dt produces large secondary EMF |
| Avionics power filtering | Chokes and coupled inductors on power inputs reduce conducted EMI |
| Current transformers / instrument magnetics | Mutual coupling measures AC current safely |
Maintenance mindset. When replacing a relay coil suppressor diode, polarity matters (diode normally reverse-biased across the coil for DC). An open suppressor → contact burning and voltage spikes. A shorted suppressor → coil circuit fault. Understanding back EMF turns that into diagnosis, not superstition.
Energy and Switch-Off Path
Stored magnetic energy W = ½ L I² must go somewhere when current is interrupted:
| Path | Result |
|---|---|
| Arc across opening contacts | Contact wear, EMI |
| Avalanche / breakdown of a transistor | Device failure |
| Flyback diode / snubber / TVS | Controlled dissipation — preferred |
Lenz’s Law says the inductor will try to keep current flowing; give it a designed path.
Formula Drill Summary
| Need | Use |
|---|---|
| Self-induced / back EMF | e = −L di/dt |
| Mutual EMF | e_s = −M di_p/dt |
| Faraday (flux) | e = −N dΦ/dt |
| Inductance definition | L = NΦ/I |
| LR time constant | τ = L/R |
| Stored energy | W = ½LI² |
| Inductive reactance (AC preview) | X_L = 2πfL |
Exam Scenario Set
Scenario A — Switch-off spike. Opening a relay coil without a diode → large back EMF; arcing at the controlling contacts.
Scenario B — Saturated choke. Overcurrent pushes the core into saturation → inductance collapses → ripple filtering worsens.
Scenario C — Time constant. Doubling L doubles τ; doubling R halves τ. Current still heads toward V/R, but the speed of approach changes.
Scenario D — Aircraft 400 Hz. Same L gives larger X_L than at 50 Hz; filter and transformer designs differ from industrial mains gear.
Section Synthesis Table
| Topic | One-line exam takeaway |
|---|---|
| Back EMF | Self-induced opposition to di/dt; spikes at interruption |
| Saturation | Little extra Φ for more I; effective L falls |
| τ = L/R | ~63% of exponential current change per time constant |
| Uses | Chokes, filters, energy storage, transformers, EMI, sensors |
| Aircraft | Suppress inductive loads on DC; respect 400 Hz magnetics |
Together with Faraday’s Law (§10.1) and self/mutual inductance plus Lenz (§10.2), this completes CAAS SAR-66 Module 3 topic 3.11 Inductance/Inductor and prepares you for DC machines, AC theory, RLC circuits, and transformers that follow.
The time constant of a series LR circuit is given by:
When current through an inductor is interrupted suddenly, the back EMF tends to:
At magnetic saturation of an inductor core, which statement is most accurate?
Why are suppression diodes often fitted across aircraft DC relay coils?