The mathematical model of a cylindrical triode-type system on the basis of the field emitter is under consideration. The internal area of the system is filled of two different dielectrics. Effect of space charge is not considered. The field emitter is modeled by a charged filament of finite length, which located on the system's axis. The modulator has a form of a circular diaphragm. The Poisson equation with the given values of potentials at the electrodes is solved. The variable separation method is used to determine distribution of electrostatic potential. An unknown function of the charge density is approximated by a piecewise constant linear function. The problem of finding unknown coefficients in the potential eigenfunction expansion is reduced to the linear algebraic equations system. Numerical calculations emitter's forms are represented.