The design of the MESFET transistor requires the solution of the following nonlinear system of equations for :

This system arises when computing the coefficients linked to the derivatives in the Taylor development of the nonlinearities of the capacity appearing in the circuit model for the microwave transistor MESFET. These coefficients are very important when determining the transistor behaviour in the intermodulation distortion and, currently, almost no model takes care of this nonlinearity.This system is converted to an algebraic one by expanding the cosine function and by introducing the new variables:

In this way the algebraic problem is reduced to the resolution of the following polynomial system of 2
The case *n*=2 is very easily solved and the solution is given by the
following:

- 1.
- The simplification of the polynomials
*U*_{i}or*V*_{j}(*s*) would provide a better solution: for example in the previous expression of_{2}*V*(_{0}*s*) the first factor can easily be represented as_{2} - 2.
- The solution of the cases
*n*=3 and*n*=4 requires the manipulation of very big parametric expressions and one possible way of solving this problem could be the simplification question addressed before.