To address the issue that the induction coil of existing magnetic-field-based time-grating angular displacement sensors couples with different magnetic-field characteristics at different air-gap heights, resulting in low utilization of the effective time-varying magnetic-field area, weak magnetic-field pickup capability, small induced-signal amplitude, and consequently increased residual errors within a pole pitch, this study proposes a time-grating angular displacement sensor featuring a three-layer complementary coil-shape assembly. A mathematical model is established to analyze the spatial distribution of the excitation magnetic field in the air gap. Based on this, a stratified coupling theory is developed, enabling the air-gap magnetic field to be categorized into three types. Based on this theory, a measurement model of the proposed sensor is constructed. The excitation coil adopts a double-layer complementary winding structure that enables mutual compensation of magnetic-field constraints at the ends of the winding, resulting in a more uniform excitation field. The induction unit employs a three-layer complementary coil-shape assembly, in which coils of different geometries are placed at different air-gap heights to couple with their corresponding air-gap magnetic-field types. This design significantly improves the amplitude and stability of the induced signal. The principle of magnetic field coupling of planar induction coils and the sensor signal processing method are analyzed: two channels of excitation signals are applied to the excitation coil, the measured traveling wave signal is obtained from the induction coil, and the angular displacement is calculated through phase discrimination. The error analysis and structural parameter optimization of the sensor are carried out through electromagnetic simulation, and the sensor prototype was made by PCB process for experimental verification. The simulation and experimental results show that compared with the traditional single-layer coupling structure, the measurement accuracy of the sensor is improved by 12.6%, the harmonic error introduced by the space air gap magnetic field is reduced, the amplitude and stability of the induced signal are improved, and the signal-to-noise ratio is improved. The optimal installation gap of the sensor is 0.6 mm, and the measurement accuracy of the sensor is ±83″.