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<h1>Transformers</h1>
<p>A transformer transfers electrical energy between circuits through electromagnetic induction. Two coils wound around a shared magnetic core — AC into one, AC out the other, with voltage ratio set by the turns ratio. No moving parts, high efficiency, and the ability to provide galvanic isolation. Transformers are the reason AC won over DC for power distribution: they make efficient long-distance power transmission possible, and remain in virtually every mains-powered device built today.</p>

<h2>How They Work</h2>
<p>AC in the primary winding creates a changing magnetic flux in the core. That changing flux induces a voltage in the secondary winding — Faraday's law. The ratio of voltages equals the ratio of turns, and power is conserved (ideally):</p>
<pre>
Voltage ratio:  V_p / V_s = N_p / N_s

Current ratio:  I_p / I_s = N_s / N_p   (inverse of voltage)

Power:          V_p × I_p = V_s × I_s   (conservation, ideal transformer)
</pre>
<p>Step up voltage, step down current — and vice versa. 10× voltage step-up means 10× current step-down. This is what makes long-distance transmission practical: high voltage = low current = low I²R resistive losses in the wires.</p>

<h2>Turns Ratio and Voltage Calculations</h2>

<table>
  <thead><tr><th>Turns ratio (N_p:N_s)</th><th>Effect</th><th>V_s from 120V primary</th><th>I_s from 1A primary</th></tr></thead>
  <tbody>
    <tr><td>10:1 (step-down)</td><td>Voltage ÷10, current ×10</td><td>12V</td><td>10A</td></tr>
    <tr><td>2:1 (step-down)</td><td>Voltage ÷2, current ×2</td><td>60V</td><td>2A</td></tr>
    <tr><td>1:1 (isolation)</td><td>No voltage change, isolated</td><td>120V</td><td>1A</td></tr>
    <tr><td>1:2 (step-up)</td><td>Voltage ×2, current ÷2</td><td>240V</td><td>0.5A</td></tr>
    <tr><td>1:10 (step-up)</td><td>Voltage ×10, current ÷10</td><td>1200V</td><td>0.1A</td></tr>
  </tbody>
</table>

<pre>
Example — power supply transformer:
Primary: 120V AC, 200 turns
Secondary: 100 turns

V_s = 120 × (100/200) = 60V RMS
V_peak = 60 × √2 = 84.9V

If secondary draws 2A:
Primary current = 2 × (100/200) = 1A
VA = 120 × 1 = 60VA = 60 × 2 = 120VA  ← doesn't balance?

Wait — it does: 60V × 2A = 120VA = 120V × 1A ✓
</pre>

<h2>Types of Transformers</h2>

<table>
  <thead><tr><th>Type</th><th>N_p:N_s</th><th>Isolation</th><th>Typical use</th></tr></thead>
  <tbody>
    <tr><td>Step-down</td><td>N_p &gt; N_s</td><td>Yes</td><td>Mains to low-voltage supplies, wall warts</td></tr>
    <tr><td>Step-up</td><td>N_p &lt; N_s</td><td>Yes</td><td>CRT HV supply, neon signs, ignition coils, grid transmission</td></tr>
    <tr><td>Isolation (1:1)</td><td>1:1</td><td>Yes</td><td>Medical equipment, lab safety, ground loop elimination</td></tr>
    <tr><td>Autotransformer</td><td>Variable tap</td><td>No</td><td>Motor starting, voltage adjustment (Variac), induction heating</td></tr>
    <tr><td>Toroidal</td><td>Any</td><td>Yes</td><td>Low leakage flux, lower EMI — preferred for audio and precision supplies</td></tr>
    <tr><td>Flyback (switching)</td><td>Varies</td><td>Yes</td><td>SMPS isolated offline supplies — stores then releases energy (not classic transformer)</td></tr>
    <tr><td>Current transformer (CT)</td><td>1:N (high ratio)</td><td>Yes</td><td>AC current measurement — primary is the conductor passing through the ring</td></tr>
    <tr><td>Audio output transformer</td><td>High:low</td><td>Yes</td><td>Impedance matching in valve/tube amplifiers, balanced audio lines</td></tr>
    <tr><td>RF transformer / balun</td><td>Any</td><td>Sometimes</td><td>Antenna matching, balanced-to-unbalanced conversion</td></tr>
  </tbody>
</table>

<h2>Core Materials</h2>

<table>
  <thead><tr><th>Core material</th><th>Frequency range</th><th>Properties</th><th>Use</th></tr></thead>
  <tbody>
    <tr><td>Laminated silicon steel</td><td>DC – 1 kHz</td><td>High permeability, low cost, eddy current limited by lamination</td><td>Mains-frequency power transformers</td></tr>
    <tr><td>Ferrite (MnZn)</td><td>1 kHz – 1 MHz</td><td>High resistivity (low eddy current), lower permeability than steel</td><td>Switching supply transformers, EMI chokes</td></tr>
    <tr><td>Ferrite (NiZn)</td><td>1 MHz – GHz</td><td>Higher resistivity than MnZn, lower permeability</td><td>RF transformers, EMI suppression beads</td></tr>
    <tr><td>Powdered iron</td><td>DC – 200 MHz</td><td>Lower permeability, handles DC bias well</td><td>Inductor cores, broadband RF transformers</td></tr>
    <tr><td>Air core</td><td>MHz – GHz</td><td>No core losses, lowest inductance per turn</td><td>RF, VHF/UHF transformers and baluns</td></tr>
  </tbody>
</table>

<h2>Real Transformer Non-Idealities</h2>

<table>
  <thead><tr><th>Loss/imperfection</th><th>Cause</th><th>Effect</th><th>How to minimise</th></tr></thead>
  <tbody>
    <tr><td>Copper loss (I²R)</td><td>Winding resistance</td><td>Heat; voltage drop under load</td><td>Larger wire gauge, shorter winding length</td></tr>
    <tr><td>Core hysteresis loss</td><td>Magnetic domains re-aligning each cycle</td><td>Heat; increases with frequency</td><td>Low-loss core material; grain-oriented silicon steel</td></tr>
    <tr><td>Eddy current loss</td><td>Induced currents circulating in solid core</td><td>Heat; increases as f²</td><td>Laminated or powdered core (insulates eddy current paths)</td></tr>
    <tr><td>Leakage inductance</td><td>Flux that doesn't couple primary to secondary</td><td>Voltage regulation issues; spikes in switching supplies</td><td>Interleave windings, use toroidal geometry</td></tr>
    <tr><td>Magnetising current</td><td>Current needed to maintain core flux (no load)</td><td>Non-zero primary current even with no load</td><td>High-permeability core; reduce number of turns per volt</td></tr>
  </tbody>
</table>

<p>Overall efficiency for a well-designed mains power transformer: 95–99%. Audio and RF transformers are optimised for frequency response and phase linearity rather than efficiency.</p>

<h2>Impedance Transformation</h2>
<p>A transformer transforms impedance by the square of the turns ratio — this is one of its most useful properties in audio and RF work:</p>
<pre>
Z_primary = Z_secondary × (N_p / N_s)²

Example: 8Ω speaker, valve amp output impedance 3.2kΩ
Required turns ratio: N_p/N_s = √(3200/8) = √400 = 20:1

A 20:1 step-down transformer makes the 8Ω speaker look like 3.2kΩ to the amp.
The amplifier "sees" its ideal load impedance and delivers maximum power.
</pre>

<h2>VA Rating</h2>
<p>Transformers are rated in VA (volt-amperes), not watts, because the current is limited by heating in the windings regardless of power factor:</p>
<pre>
VA_rating = V_secondary × I_secondary_max

Choose a transformer with VA ≥ total load VA, plus 20–30% margin.
Running a transformer at 90–100% of its VA rating shortens its life.

For a PSU delivering 12V at 2A: VA = 12 × 2 = 24VA → use 30VA transformer
</pre>

<h2>Transformers vs. Switching Converters</h2>

<table>
  <thead><tr><th>Application</th><th>Better choice</th><th>Why</th></tr></thead>
  <tbody>
    <tr><td>Mains-isolated 5V/3A supply</td><td>SMPS (flyback)</td><td>Size and efficiency — a mains-frequency transformer for 15W is bulky</td></tr>
    <tr><td>Lab bench supply, 0–30V variable</td><td>Linear with mains transformer</td><td>Noise, stability, simplicity, current limiting is easy</td></tr>
    <tr><td>Hi-fi amplifier supply</td><td>Toroidal linear transformer</td><td>Low EMI, low noise floor — SMPS noise would degrade audio quality</td></tr>
    <tr><td>Medical/lab isolation</td><td>Isolation transformer</td><td>Galvanic isolation is required for safety; autotransformer not acceptable</td></tr>
    <tr><td>PCB voltage conversion (12V→5V)</td><td>Buck converter</td><td>No transformer needed — inductor-based switching is more efficient</td></tr>
  </tbody>
</table>

<h2>References</h2>
<ul>
  <li>Horowitz &amp; Hill — <em>The Art of Electronics</em>, 3rd ed. Chapters 9, 13</li>
  <li>Erickson &amp; Maksimovic — <em>Fundamentals of Power Electronics</em></li>
  <li><a href="https://www.electronics-tutorials.ws/transformer/transformer-basics.html" target="_blank" rel="noopener">Electronics-Tutorials — Transformer Basics ↗</a></li>
  <li><a href="https://www.murata.com/en-us/products/power/transformer" target="_blank" rel="noopener">Murata — Power Transformers ↗</a></li>
</ul>
