mdtable_examples

mdtable_examples — multi-dimensional $table_model (Enhancement-17)

Demonstrates multi-dimensional $table_model (2-D bilinear), using version11's own openvaf-r and ngspice-46. Enhancement-17 generalises the 1-D lookup tables of Enhancement-16 to any number of dimensions (1-D / 2-D / 3-D) via multilinear interpolation — still differentiable, so every partial derivative feeds the Jacobian.

mos_table.va is a table-based MOSFET: its drain current is a 2-D lookup table I(Vgs, Vds) read from mos_iv.tbl, interpolated bilinearly:

I(d, s) <+ $table_model(V(g, s), V(d, s), "mos_iv.tbl", "1L");

File	Purpose
mos_iv.tbl	Self-describing 2-D grid: ndim, axis sizes, axis coordinates, then row-major values.
mos_table.va	The table-based MOSFET.
verify_mdtable.py	Checks DC current and the AC gm/gds against a bilinear reference.
plot_mdtable.py	Output characteristics + the interpolated I(Vgs, Vds) surface → mdtable_iv.png.

Run

python3 verify_mdtable.py     # DC + AC checks
python3 plot_mdtable.py       # writes mdtable_iv.png

Expected:

DC: 2-D I(Vgs,Vds) vs bilinear reference       max err ~1e-19 A  PASS
AC: gm, gds vs bilinear partials               max err ~1e-16 S  PASS

The AC check is the important one: the two partial derivatives of the bilinear surface — transconductance gm = dId/dVgs and output conductance gds = dId/dVds — both come out exact, i.e. the full 2-D Jacobian is correct.

The grid file format

For 2-D and 3-D, the data is a self-describing grid file (whitespace-separated tokens; blank lines and #////* comments ignored):

2                 # number of dimensions
6 6               # grid size along each axis
0 0.4 ... 2.0     # axis-0 (Vgs) coordinates, ascending
0 0.4 ... 2.0     # axis-1 (Vds) coordinates, ascending
<v ...>           # size0*size1 values, row-major (axis-0 slowest)

Notes

• Interpolation is multilinear (bilinear in 2-D, trilinear in 3-D), built as recursive 1-D interpolation, and fully differentiable — usable directly in V(...) <+ / I(...) <+ contributions across DC, AC and transient.
• Extrapolation outside the grid is per-axis constant (clamp) by default, or linear with a control string containing L (as here).
• 1-D still takes an inline '{x0,y0,...} array or a two-column data file (Enhancement-16); 2-D/3-D take one coordinate per dimension and a grid file.
• Supported dimensionality is 1-D, 2-D and 3-D — the practical range for compact-model tables. Higher-degree (spline) interpolation remains future work.