Verilog-A: Lookup tables for AC analysis

Hello everyone, 

I have a problem performing AC analysis on lookup tables based components.

Basically, on the basis of Pown M. question,  I wanted to extend the validity of that code to AC analysis as well. By reducing the problem to its core, I created a simple voltage dependent differential capacitance and I found out that it does not work properly. I should better say that the error seems to be proportional to the variation of the capacitance (defined in the lookup table) with respect to the polarization point. 

Below I attach the code of a simple nonlinear capacitor described by a lookup table, which gives the capacitor value according to a specific polarization point. 

`include "constants.vams"
`include "disciplines.vams"

module cap_LT(c1,c2);

inout c1,c2;
electrical c1,c2;
real c;
(* desc = "charge" *) real q;

analog begin

c=$table_model( (V(c1,c2)), "vc_C.txt","1LL");

q = c*(V(c1,c2));
I(c1,c2) <+ ddt(q);

end
endmodule

The lookup table has been generated at a fixed frequency and changing the voltage across the capacitor. Hence, the simulation I am performing is an AC analysis at a fixed frequency while the sweep is made on a design variable which correspond to the DC bias of the component. Additionally I have put a very small AC stimulus.

As stated above, the simulation runs without issues but the capacitance I extract from the results is not the same as the one defined by the lookup table. Indeed, the more its changes along the polarization, the more the error increases (the maximum error is more or less twice the capacitance values it should have).

I think it is related to the time derivative ddt but still I can't find any workaround. As far as I know, the simulator performs at each sweep point a DC analysis in order the respective small signal circuit. Hence, even doing single polarization analysis the result does not change.

can somebody help me please? 

many thanks in advance.