9.20.3 Example control strings

9.20.4 Lookup algorithm

In lookup mode the function returns the closest point in the specified dimension. When the lookup ordinate is equidistant from two bracketing samples the function snaps away from zero.

9.20.5 Interpolation algorithms

The linear interpolation algorithm provides a simple linear interpolation between the closest sample points on a given isoline. Cubic spline interpolation1 generates a spline for each isoline being interpolated. The extrapolation option specified is taken into account when generating the spline coefficients so as to avoid end point discontinuities in the first order derivative of the interpolated function.

When formulating the cubic spline equations the desired derivative of the interpolation function at both end points must be specified in order to provide the complete set of constraints for the cubic spline equations. It is convenient then that the table model function specifies end point extrapolation behavior. If the user selects linear extrapolation this leads to a natural spline. If constant extrapolation is specified the end point derivative is set to zero thus avoiding a discontinuity in the first order derivative at that end point.

Quadratic splines are similar to cubic splines, offering more efficient evaluation with generally less favorable interpolation results. Again one should attempt to avoid end point discontinuities, though it is not always possible in this case.

As a general rule cubic splines are best applied to smoothly varying samples (such as the DC I-V characteristic of a diode) while linear interpolation is a better option for data with abrupt transitions (such as a transient pulsed waveform).

1Numerical Methods in Scientific Computing, Germund Dahlquist and Åke Björck.

9.20.6 Example

A simple call to the $table_model function is illustrated using the two dimensional sample set given in the above plots and tables. Let’s first assume this data is stored in a file called sample.dat. The data is two dimensional with a single dependent variable. The independent variables were named x and y above. y is the outermost independent variable in the sample set while x is the innermost independent variable.

module example_tb(a, b); electrical a, b; inout a, b;

analog begin

I(a, b) <+ $table_model(0.0, V(a,b),"sample.dat"); end

endmodule

This instance specifies zero for x and uses a module potential to interpolate y. No control string is specified and so the function defaults to performing linear interpolation and linear extrapolation in both dimensions.

It is possible to specify how to perform the interpolation via the control string:

I(a, b) <+ $table_model(0.0, V(a,b),"sample.dat", "1LL,3LL");

Linear interpolation and extrapolation are specified in y and cubic interpolation with linear extrapolation in x.

The data source may also be specified as an array.

module example_tb(a, b); electrical a, b; inout a, b;

real y[0:11], x[0:11],f_xy[0:11]; analog begin

@(initial_step) begin

// y=0.0 isoline

y[0] =0.0; x[0] =1.0; f_xy[0] =0.5; y[1] =0.0; x[1] =2.0; f_xy[1] =1.0; y[2] =0.0; x[2] =3.0; f_xy[2] =1.5; y[3] =0.0; x[3] =4.0; f_xy[3] =2.0; y[4] =0.0; x[4] =5.0; f_xy[4] =2.5; y[5] =0.0; x[5] =6.0; f_xy[5] =3.0; // y=0.5 isoline

y[6] =0.5; x[6] =1.0; f_xy[6] =1.0; y[7] =0.5; x[7] =3.0; f_xy[7] =2.0; y[8] =0.5; x[8] =5.0; f_xy[8] =3.0; // y=1.0 isoline

y[9] =1.0; x[9] =1.0; f_xy[9] =1.5; y[10]=1.0; x[10]=2.0; f_xy[10]=2.0; y[11]=1.0; x[11]=4.0; f_xy[11]=3.0;

end

I(a, b) <+ $table_model(0, V(a,b), y, x, f_xy); end

endmodule

Here the array is specified via array variables. The variables are initialized inside an initial_step block ensuring that they do not change after the first call to $table_model. Arrays may also be specified directly via an array assignment pattern.