A method includes performing by a processor: estimating a total cathode space current for a thermionic vacuum tube having at least one grid and a plate, such that at least one amplification factor associated with the at least one grid is determined by a polynomial based on a variable that represents at plurality of voltages associated with the at least one grid and the plate, the variable being heuristically determine. Transitions between positive and negative grid operation may experience a step change in estimated current value caused by the inclusion or elimination of grid current. A part of the grid current may be added back into the plate current during transition. This small contribution to plate current may gradually diminish as tube operation moves farther away from the transition boundary.

A method includes performing by a processor: estimating a total cathode space current for a thermionic vacuum tube having at least one grid and a plate, such that at least one amplification factor associated with the at least one grid is determined by a polynomial based on a variable that represents at plurality of voltages associated with the at least one grid and the plate, the variable being heuristically determine. Transitions between positive and negative grid operation may experience a step change in estimated current value caused by the inclusion or elimination of grid current. A part of the grid current may be added back into the plate current during transition. This small contribution to plate current may gradually diminish as tube operation moves farther away from the transition boundary.