Transfer Functions & the Load Ellipse

From flat H(s) to nonlinear, frequency-dependent tube clipping · EL34 vs 6L6
Lesson
Sandbox

Controls

6L6
6L6 · beam tetrode
EL34 · pentode
Beam tetrode: sharp low knee, lower $g_m$, more headroom. Pentode: rounder knee, higher $g_m$.
420 V
3.4 kΩ
Primary load = speaker Z reflected through the OT turns ratio squared.
−36 V
8 $V_\text{pk}$
Peak amplitude of the input sine on the grid.
1.0 kHz
Sets |Z| and load angle $\phi$ from the speaker model (log scale, 40 Hz–8 kHz).
off
load line → load ellipse
Off = resistive load line. On = full complex Z(f): the V–I locus opens into an ellipse.
12
$\mathrm{DF} = R_\text{load}/R_\text{out}$. Low DF (high output Z) lets the speaker resonance bump & ring — boomy bass. High DF clamps it flat. See the green response trace.
410 V
Sets plateau current ceiling.
E-I
E-I · gapped
Toroid · ungapped
E-I: sheared B–H, soft knee, band-limited, DC-tolerant. Toroid: high-$\mu$, sharp knee, wide band, DC-intolerant.
1.00
Flux demand $\propto V_\text{rms}/f$. Push past the knee to saturate the core.
0%
DC flux from SE bias or Class-AB mismatch. The gapped E-I tolerates it; the toroid jams into saturation.
off
fold the iron into the load
Adds the OT's own magnetizing inductance $L_p$ (shunt, sets the bass corner) and leakage $L_l$ (series, sets the treble corner) to the load the tube sees. $L_p$ is saturable — the bass corner climbs with level. Needs Reactive on.

Output & Analysis

Output voltage waveform (one cycle)
Harmonic spectrum (FFT magnitude)
|Z| (pink) · phase $\phi$ (green-dim) · delivered response (green)
Transient: cone ring & decay after a step (set by damping factor)
OT core B–H hysteresis loop · loop area = core loss, dots = remanence $\pm B_r$ (E-I green · toroid pink)
Saturated secondary voltage ($\propto dB/dt$) — soft vs hard flat-top
THD
Load angle $\phi$
|Z| at f
Clipping
Even/Odd ratio
Core flux $B_\text{pk}$
Damping factor
Resonance bump
Cone $Q_\text{ts}$
Ring time (−40 dB)
Core $B_\text{pk}/B_\text{sat}$
OT HF corner
OT LF corner