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Audio Transformer Turns Ratio

Calculate audio transformer turns ratio for impedance matching between source and load, plus secondary voltage and current.

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Formula

n = √(Z₁/Z₂), V₂ = V₁/n, I₂ = I₁ × n

n— Turns ratio
Z— Impedance (Ω)

How It Works

Audio transformers provide galvanic isolation and impedance matching between signal sources and loads. The turns ratio n = N₁/N₂ determines the voltage transformation: V₂ = V₁/n. Current transforms inversely: I₂ = I₁ × n. Impedance transforms as the square of the turns ratio: Z₂ = Z₁ / n². For impedance matching, we need n = √(Z₁/Z₂). Classic audio uses 600 Ω balanced line impedances for maximum power transfer, with 600:600 transformers (1:1 ratio) for isolation, or 600:10 kΩ transformers (n ≈ 0.245, or 1:4.08 step-up) for mic/line bridging. DI (direct injection) boxes use transformers to convert high-impedance instrument signals (~500 kΩ) to balanced 200–600 Ω microphone-level outputs. Audio transformers also block DC and provide common-mode noise rejection (CMRR), making them ideal for eliminating ground loops.

Worked Example

Match a 600 Ω balanced line output to an 8 Ω speaker (hypothetical). Turns ratio: n = √(600 / 8) = √75 = 8.66 : 1 This means the primary has 8.66× more turns than the secondary. With a 1 V RMS primary voltage: Secondary voltage = 1 / 8.66 = 0.115 V RMS With 1 mA RMS primary current: Secondary current = 1 mA × 8.66 = 8.66 mA RMS Power transferred (ideal transformer): P = 1 V × 1 mA = 1 mW Verify: P = 0.115 V × 8.66 mA = 1 mW ✓ For a DI box (250 kΩ instrument → 150 Ω mic input): n = √(250000 / 150) = √1667 = 40.8 : 1 step-down

Practical Tips

  • ✓Use audio transformers for hum elimination in balanced/unbalanced conversions — they provide 40–60 dB of common-mode rejection, breaking ground loops that cause 50/60 Hz hum in long cable runs.
  • ✓When calculating turns ratio for a DI box, ensure the transformer's insertion loss is accounted for in the gain budget. A well-designed active DI often outperforms a passive transformer DI at extreme impedance ratios.
  • ✓For microphone input transformers, the magnetising inductance must be high enough to pass 20 Hz at the rated input impedance. Check: f_low = R_load / (2π × L_mag); for 150 Ω input and 20 Hz, L_mag ≥ 150 / (2π × 20) ≈ 1.2 H.

Common Mistakes

  • ✗Confusing impedance ratio with turns ratio — the impedance ratio equals the square of the turns ratio (n²), not n itself. A 4:1 turns ratio gives a 16:1 impedance ratio.
  • ✗Expecting perfect impedance matching to maximise power — in audio (voltage-source systems), maximum power transfer is less important than maximum voltage transfer. Bridging (load impedance much higher than source) is preferred in audio to avoid loading the source.
  • ✗Neglecting transformer frequency response — audio transformers have bandwidth limits determined by magnetising inductance (low-frequency rolloff) and leakage inductance plus winding capacitance (high-frequency rolloff). Cheap transformers roll off below 50 Hz or above 10 kHz.

Frequently Asked Questions

A 1:1 isolation transformer passes the signal unchanged in level but galvanically isolates the source from the load, breaking ground loops. Signal transformers (non-unity ratio) both isolate and change the impedance and voltage level. All audio transformers provide isolation; the ratio determines the transformation.
Yes. Connecting the balanced output across the primary and taking the secondary as a single-ended (unbalanced) output converts the signal. The transformer rejects common-mode noise present on the balanced line, providing a clean unbalanced signal with the CMRR of the transformer's winding balance (typically 60–80 dB).
600 Ω was the original telephone and broadcast standard because it gave maximum power transfer over the copper wire impedances common in early telephone networks. Modern audio equipment uses 600 Ω primarily for compatibility with legacy equipment and for the balanced line standard, even though most modern equipment uses voltage-bridging (high input impedance) rather than impedance matching.

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