Lp
Workbench / Output Stage

Transformer Bandwidth

Primary & leakage inductance frequency limits.

Circuit

Triode ≈ 0.5–3k, pentode ≫ load (unless NFB)

Transformer Parasitics

rp3 kΩLp20 HLleak10 mHCw500 pFRL5 kΩ
Primary-referred transformer model
TRANSFORMER FREQUENCY RESPONSE1101001k10k100k-30-25-20-15-10-505FREQUENCY (Hz)dBfL 14.9 HzfH 71.2 kHz
Response (0 dB = midband)
Low −3 dB
14.9 Hz
Leakage corner
127 kHz
HF resonance
71.2 kHz
Peaking
+0.2 dB
Engineering Notes

How it works

A real output transformer is an ideal transformer surrounded by parasitic elements. Referred to the primary, the simplest useful model has three:

  • Primary inductance Lp: in parallel with the load. At low frequencies its reactance falls and shunts the signal away.
  • Leakage inductance: flux that fails to couple both windings, in series with the load. At high frequencies it chokes off the signal.
  • Winding capacitance: resonates with the leakage inductance, producing a peak (and ringing) near the top of the band.
fL = (rp ∥ RL) / (2π·Lp) fH ≈ (rp + RL) / (2π·Lleak) f₀ = 1/(2π√(Lleak·Cw))

Notice that the source impedance matters: a low-rp triode (or heavy negative feedback) extends the bass because rp ∥ RL is small. A pentode without feedback has a very high rp, so the bass corner is set by RL alone, another reason pentode amplifiers rely on feedback. The curve is computed with a full complex nodal analysis of the model.

Primary inductance also drops at high signal levels and with DC in the core (single-ended), so real-world bass at full power is usually worse than the small-signal figure.