Transformers Reference
Transformer fundamentals — turns ratio, impedance reflection, losses, and typical applications.
Reference
Ideal equations
- V_p / V_s
- = N_p / N_s (turns ratio)
- I_p / I_s
- = N_s / N_p (inverse of voltage ratio)
- Power in = Power out
- V_p · I_p = V_s · I_s (ideal)
- Reflected impedance
- Z_p = Z_s · (N_p / N_s)²
Types by core
| Core | Use |
|---|---|
| Laminated silicon steel (EI) | 50/60 Hz mains |
| Toroidal silicon steel | Mains — lower stray field |
| Ferrite | SMPS (10 kHz – 1 MHz) |
| Powdered iron | RF chokes, DC-biased inductors |
| Air core | RF > 10 MHz |
| Nanocrystalline | Current sensors, high-frequency EMI filters |
Loss mechanisms
- Copper loss
- I² · R in windings — dominant at heavy load
- Core (iron) loss
- Hysteresis + eddy currents — present even at no load
- Leakage inductance
- Causes voltage regulation drop
- Magnetizing current
- Excites core even with no load
Common uses
- Step down: mains to low voltage for linear supplies.
- Isolation: 1:1 transformer breaks ground loops, provides safety isolation.
- Impedance matching: audio output (8 Ω speaker → tube amp), RF (50 Ω antenna → 300 Ω dipole).
- Current sensing: CT (current transformer) steps down AC for measurement.
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