Maximal linear range of linear transformer analysis using maple & 1stopt

The output voltage of a linear transformer is considered to be proportional to the rotor´s rotational angle (in radians) in a certain range. In the case of primary and secondary side complete compensation for quadrature armature reaction, the linear transformer´s maximum linear range is considered to extend 60 degrees to 60 degrees if only if the turn ratio equals 0.54 in the circumstance that the linear error is controlled within 0.1%. But it is not the case when checking the linear error formula using the optimum parameters. In this paper, the numerical analysis combining figure demostration was applied to obtain the accurate solution using maple® and lstopt®. The paper´s optimization is instructive for the linear transformer is highly accurate device in the servo system, and provides a feasible mathematic method to dealing with this kind optimal problem.