This paper presents a new type of co-excitation axial reluctance resolver(CARR), and deduces the distribution functions of signal windings in the winding mode of equal turns. According to the flux change law of the upper and lower teeth of the stator, the expression of axial effective coupling length of rotor is obtained. The self-inductance and mutual inductance of two-phase precise machine signal windings and excitation windings are theoretically studied by winding function method. The inductance variation law of each winding of CARR is obtained under the condition of odd pole pairs and even pole pairs. It provides the basis for the theoretical design and optimization of this kind of resolver, and is beneficial to improve the measurement precision of precise machine signal output. Then, the finite element method is used to compare and analyze the inductance variation law of each winding obtained by analytical method, which verifies the correctness of the theoretical research on the inductance of each winding in the winding mode of equal turns.