Diagram of the structure principle of differential transformer

There are two types of transformers: air-gap type and differential transformer. Currently, the solenoid type differential transformer is mostly used.
Its basic components include armature, primary coil, secondary coil and coil frame. The primary coil is used as the excitation of the differential transformer, which is equivalent to the primary side of the transformer, while the secondary coil is composed of two coils with the same structural size and parameters connected in series in reverse phase, which is equivalent to the secondary side of the transformer. The solenoid type differential transformer has two-section, three-section, four-section and five-section types according to the different arrangements of the primary and secondary.

(a) Air gap type (b) Solenoid type
1 Primary coil; 2.3 Secondary coil; 4 Armature

The three-section type has a smaller zero-point potential, the two-section type has higher sensitivity and a larger linear range than the three-section type, and the four-section and five-section types improve the linearity of the sensor.
Differential transformer coil arrangements
1 Primary coil; 2 Secondary coil; 3 Armature
Under ideal conditions (ignoring coil parasitic capacitance and armature loss), the equivalent circuit of the differential transformer is shown in the figure.
The complex current value of the primary coil is

The voltages e21 and e22 are induced in the secondary coil, and their values ​​are