Polynomial source - pspice

The symbol for a polynomial or nonlinear source is POLY (n), where n is the number of dimensions of the polynomial .The default value of n is 1.The dimensions depend on the number of controlling sources. The general form is
POLY (n) {(controlling) nodes} {(coefficients) values}
The out put sources of the controlling sources can be voltage or currents.
For voltage controlled sources, the number of controlling nodes must be twice the number of dimensions.
For current controlled sources, the number of controlling sources must be equal to the number of dimensions.
The number of dimensions and the number of coefficients are arbitrary.


Let us call A,B, and C are the three controlling variables, and Y is the output source.
The following figure shows that is controlled by A,B, and C. The output source takes
The form of Y = f(A,B,C…..)
Where Y can be Voltage or Current
A,B,C can be Voltage or Current or any combination
For a Polynomial of n=1 with A as the only controlling variable, the source function takes
The form of Y=P0+P1A+P2A2+P3A3+P4A4+……………..PnAn
Where P0,P1,P2,P3,P4……………..Pn are the coefficient values. this is written in PSpice as
POLY NC1+ NC1- P0 P1 P2 P3 P4……………..Pn
Where NC1+ NC1- are the positive and negative nodes, respectively, of the controlling source A.
For a Polynomial of degree n=2 with A & B as the controlling sources, the source function takes the form of
Y=P0+P1A+P2B2+P3A2+P4AB+P5B2+ P6A3+ P7A2B+ P8AB2+ P9B3+……..
This is described in PSpice as
POLY (2)NC1+ NC1- NC2+ NC2- P0 P1 P2 P3 P4………….Pn
Where NC1+, NC2+,and NC1-, NC2- are the positive and negative nodes, respectively, of the controlling sources.

For a Polynomial of degree n=3 with A , B & C as the controlling sources, the source function takes the form of
Y=P0+P1A+P2B+P3C+P4A2+P5AB+ P6AC+ P7B2+ P8BC+ P9C2+P10A3+P11A2B+P12A2C+P13AB2+P14ABC+P15AC2+
P16B3+P17B2C+P18BC2+P19C3+P20A4+……………………
This is described in PSpice as
POLY (3)NC1+ NC1- NC2+ NC2-,NC3+ NC3- P0 P1 P2 P3 P4 P5……….Pn
Where NC1+, NC2+, NC3+ and NC1-,NC2-,NC3- are the positive and negative nodes, respectively, of the controlling sources.
Typical Model Statements, for Y=2V(10),The model is POLY 10 0 2.0
For Y=V(5)+2[V(5)]2+3[V(5)]3 +4[V(5)]4,
the model is POLY 5 0 0.0 1.0 2.0 3.0 4.0
For Y=0.5+V(3)+2V(5)+3[V(5)]3 +4[V(3) V(5),the model is
POLY(2) 3 0 5 0 0.5 1.0 2.0 3.0 4.0