hysteresis

NODE

Magnetic saturation with memory: the output depends on where the signal has been, not only where it is.

Parameters

FIELD	WHAT IT DECIDES	RANGE	REQUIRED
drive_db	Drive [dB].	0 〜 48	yes
width	Loop width (0 is almost linear, 1 is the widest).	0 〜 1	yes

{
  "drive_db": 12,
  "type": "hysteresis",
  "width": 0.5
}

How it is computed

He   = H + α·M                                effective field
Man  = Ms · L(He / a)                          anhysteretic magnetisation (Langevin)
dMirr/dH = (Man - M) / (δ·k - α·(Man - M))      δ = sign(dH)
dM/dH = [(1-c)·dMirr/dH + c·dMan/dHe]
        / [1 - α·c·dMan/dHe - α·(1-c)·dMirr/dH]

The Jiles-Atherton model of magnetic hysteresis, the same one used to describe transformer cores and tape. Because the branch depends on whether the input is rising or falling, the node carries state: the same instantaneous value does not always give the same output.

width opens and closes the loop: near zero it is almost linear, at the maximum it is the widest.
Drive is compensated exactly as it is on the waveshaper, so loudness does not move with it. Here the compensation cannot be integrated in closed form, so it is measured by running a reference sine through the model itself, never through your music.
The model is quasi-static: it is written in dM/dH rather than dM/dt, so it does not need to be re-derived per sample rate.

Using it

It needs no DC blocker.
With symmetric excitation the loop is symmetric about the origin, so no DC is produced. That is fixed by a test rather than assumed, which is the difference from the asymmetric waveshaper.
It is the most expensive node.
It is sequential, it branches, and it uses transcendental functions, so it cannot be vectorised. If you are running a long convolution as well, watch the CPU figure before adding several of these.
It is nonlinear, so the chain gains a limiter.
Simulation before it can be heard, the output limiter armed for the session, and a soft start.