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<h1>Inductors</h1>
<p>Inductors are the third fundamental passive component, after resistors and capacitors. They store energy in a magnetic field and resist changes in current — where a capacitor fights changes in voltage, an inductor fights changes in current. This complementary behaviour makes them natural partners for filtering, and their energy-storage property makes them the heart of every switching power supply.</p>

<h2>How They Work</h2>
<p>An inductor is a coil of wire. Run current through it and it creates a magnetic field. Change the current and the magnetic field changes, inducing a voltage that opposes the change — this is Faraday's law of electromagnetic induction, and Lenz's Law gives the direction. The key relationship:</p>
<pre>
V = L × (dI/dt)

V — voltage across the inductor (volts)
L — inductance (henrys, H)
dI/dt — rate of change of current (A/s)
</pre>
<p>If current isn't changing, voltage across an ideal inductor is zero — it looks like a short circuit to steady DC. Rapidly changing current produces a large voltage. This is why you can never just switch off an inductive load (motor, relay coil, solenoid) without handling the stored energy — the collapsing magnetic field generates a voltage spike that can exceed the supply voltage by 10× or more and destroy switching transistors instantly.</p>

<h2>Inductance Units</h2>

<table>
  <thead><tr><th>Unit</th><th>Symbol</th><th>Value</th><th>Typical use</th></tr></thead>
  <tbody>
    <tr><td>Henry</td><td>H</td><td>1 H</td><td>Mains-frequency chokes, audio crossovers</td></tr>
    <tr><td>Millihenry</td><td>mH</td><td>0.001 H</td><td>Audio inductors, power line filters</td></tr>
    <tr><td>Microhenry</td><td>µH</td><td>10⁻⁶ H</td><td>Switching supply inductors (typical: 4.7–470 µH)</td></tr>
    <tr><td>Nanohenry</td><td>nH</td><td>10⁻⁹ H</td><td>RF circuits, PCB trace inductance</td></tr>
  </tbody>
</table>

<h2>Types</h2>

<table>
  <thead><tr><th>Type</th><th>Core material</th><th>Inductance range</th><th>Frequency range</th><th>Best use</th></tr></thead>
  <tbody>
    <tr><td>Air core</td><td>None</td><td>nH – µH</td><td>RF, VHF, UHF</td><td>RF inductors, VCOs, filters above 1 MHz. No saturation, lowest loss.</td></tr>
    <tr><td>Ferrite core</td><td>Ferrite</td><td>nH – mH</td><td>kHz – MHz</td><td>EMI chokes, switching supply inductors, RF transformers</td></tr>
    <tr><td>Powdered iron toroid</td><td>Iron powder</td><td>µH – mH</td><td>DC – MHz</td><td>Switching supplies — handles high DC current without saturating</td></tr>
    <tr><td>Laminated iron</td><td>Silicon steel</td><td>mH – H</td><td>DC – kHz</td><td>Mains-frequency transformers, audio output transformers</td></tr>
    <tr><td>Multilayer chip</td><td>Ferrite (SMD)</td><td>nH – µH</td><td>MHz – GHz</td><td>Surface-mount RF, decoupling beads</td></tr>
  </tbody>
</table>

<h2>RL Time Constant</h2>
<p>Like the RC time constant for capacitors, the RL time constant τ = L/R determines how fast current rises in an inductor circuit:</p>
<pre>
Energising: I(t) = (V/R) × (1 - e^(-t/τ))
De-energising: I(t) = I₀ × e^(-t/τ)

τ = L / R   (seconds, when L is in henrys and R in ohms)
</pre>

<table>
  <thead><tr><th>Time elapsed</th><th>Current (% of final value, energising)</th></tr></thead>
  <tbody>
    <tr><td>1τ</td><td>63.2%</td></tr>
    <tr><td>2τ</td><td>86.5%</td></tr>
    <tr><td>3τ</td><td>95.0%</td></tr>
    <tr><td>5τ</td><td>99.3% — considered fully energised</td></tr>
  </tbody>
</table>

<pre>
Example: L = 10 mH, R = 100Ω
τ = 0.01 / 100 = 0.0001 s = 100 µs
Fully energised in ~500 µs (5τ)
</pre>

<h2>Combining Inductors</h2>
<pre>
Series (assuming no mutual coupling):
  L_total = L1 + L2 + L3 ...    (same rules as resistors)

Parallel:
  1/L_total = 1/L1 + 1/L2 + ...  (same rules as resistors in parallel)

Two in parallel: L_total = (L1 × L2) / (L1 + L2)
</pre>
<p>If inductors are physically close, their magnetic fields can couple — the effective inductance changes depending on whether the fields aid or oppose. PCB layout matters: inductors near each other can interact in ways that are hard to predict without measurement.</p>

<h2>Key Specifications</h2>

<table>
  <thead><tr><th>Spec</th><th>What it means</th><th>Why it matters</th></tr></thead>
  <tbody>
    <tr><td>Inductance (L)</td><td>Nominal value, usually ±10–20%</td><td>Sets filter frequency, energy storage</td></tr>
    <tr><td>DCR (DC resistance)</td><td>Resistance of the wire winding</td><td>Causes voltage drop and power loss at high current — pick low DCR for power supplies</td></tr>
    <tr><td>Saturation current (Isat)</td><td>Current at which inductance drops by 20–30%</td><td>Exceed it and the inductor stops working — in a switching supply this can be destructive</td></tr>
    <tr><td>RMS current rating</td><td>Max continuous current for thermal limit</td><td>Copper heating limit — different from Isat</td></tr>
    <tr><td>SRF (self-resonant frequency)</td><td>Frequency at which parasitic capacitance resonates with L</td><td>Above SRF the component behaves capacitively — use below SRF</td></tr>
    <tr><td>Q factor</td><td>Ratio of reactance to resistance at a given frequency</td><td>High Q = low loss, important for RF and oscillator circuits</td></tr>
  </tbody>
</table>

<h2>Common Applications</h2>

<h3>Switching Power Supplies (Buck Converter)</h3>
<pre>
       Switch (MOSFET)     Inductor
Vin ──────[  SW  ]────────[  L  ]────── Vout
                |                  |
              [Diode]             [C]   ← output cap
                |                  |
               GND                GND

Operation:
  ON:  switch closes → current ramps up through L → energy stored
  OFF: switch opens → inductor maintains current through diode → energy released to output

Inductor value (approximate for buck converter):
  L = (Vin - Vout) × D / (f × ΔI)

  D = duty cycle = Vout/Vin
  f = switching frequency
  ΔI = desired ripple current (typically 20-40% of I_out)
</pre>

<h3>EMI Filtering</h3>
<p>A choke (inductor in series with the power line) presents high impedance to high-frequency noise, blocking it from entering the circuit. Ferrite beads are a single-turn version — very effective for suppressing high-frequency noise on power rails and signal lines. The common-mode choke on PC power cords and USB cables prevents conducted emissions.</p>

<h3>LC Resonant Circuit</h3>
<pre>
Resonant frequency: f₀ = 1 / (2π√LC)

Example: L = 100 µH, C = 100 pF
f₀ = 1 / (2π × √(0.0001 × 0.0000000001))
f₀ = 1 / (2π × 10⁻⁷) ≈ 1.59 MHz  ← RF tuning range
</pre>

<h2>Inductive Kickback — Why It Matters</h2>
<p>Every inductive load needs a flyback diode (also called a freewheeling or snubber diode) across it when switched with a transistor:</p>
<pre>
VCC ──────────────┬── relay/motor (+)
                [D] ← flyback diode (cathode to VCC)
                  │
               [Coil]
                  │
             Transistor drain/collector
             Transistor source/emitter
                  │
                 GND

Without the diode: when transistor turns off, coil produces spike of
-50V, -100V, or more, destroying the transistor in microseconds.
With the diode: spike clamped to one diode drop above VCC (safe).
</pre>
<p>This applies to any relay, motor, solenoid, or contactor coil. It's one of those things you learn once the hard way and never forget.</p>

<h2>References</h2>
<ul>
  <li>Horowitz &amp; Hill — <em>The Art of Electronics</em>, 3rd ed. Chapters 1, 9</li>
  <li>Erickson &amp; Maksimovic — <em>Fundamentals of Power Electronics</em></li>
  <li><a href="https://www.coilcraft.com/en-us/edu/series/a-glossary-of-inductor-terms/" target="_blank" rel="noopener">Coilcraft — Inductor Terms Glossary ↗</a></li>
  <li><a href="https://www.electronics-tutorials.ws/inductor/inductor.html" target="_blank" rel="noopener">Electronics-Tutorials — Inductors ↗</a></li>
</ul>
