Transformers

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.

How They Work

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):

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)

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.

Turns Ratio and Voltage Calculations

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

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 RMS:
Primary current = 2 × (100/200) = 1A
Secondary VA = 60V × 2A = 120VA
Primary VA = 120V × 1A = 120VA

Ideal transformer: primary VA = secondary VA ✓

Transformer VA ratings use RMS voltage × RMS current, because RMS values represent the equivalent heating and power-transfer effect of AC. Multiplying peak voltage by RMS current would not give the VA rating; peak instantaneous power is a different quantity that varies through the AC cycle.

Types of Transformers

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

Core Materials

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

Real Transformer Non-Idealities

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

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.

Impedance Transformation

A transformer transforms impedance by the square of the turns ratio — this is one of its most useful properties in audio and RF work:

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.

VA Rating

Transformers are rated in VA (volt-amperes), not watts, because the current is limited by heating in the windings regardless of power factor:

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

Transformers vs. Switching Converters

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

References

• Horowitz & Hill — The Art of Electronics, 3rd ed. Chapters 9, 13
• Erickson & Maksimovic — Fundamentals of Power Electronics
• Electronics-Tutorials — Transformer Basics ↗
• Murata — Power Transformers ↗