An FPGA-Based DDS-Synchronized Quadrature Lock-In Module for Sweep-Field Demodulation in a Single-Beam SERF Magnetometer

Sweep-field operation in a single-beam spin-exchange relaxation-free (SERF) magnetometer requires stable extraction of the dispersion zero-crossing. A frequency mismatch between the modulation signal and the demodulation references, or an unsuitable low-pass filter, can shift this zero-crossing and affect working-point determination. This paper presents a zero-crossing-stability-oriented FPGA quadrature lock-in module for SERF sweep-field demodulation. The module is designed around two requirements of sweep-field operation: maintaining a common frequency basis between the modulation output and the demodulation references, and preserving the dispersion zero-crossing when the low-pass-filter cutoff frequency is adjusted. A shared direct digital synthesizer generates both the sinusoidal modulation output and the I/Q references, keeping the excitation and demodulation signals on the same frequency basis. After quadrature multiplication, CIC decimation and a reloadable Kaiser-window FIR filter are used for low-pass processing. Board-level tests show a 1000.054 Hz spectral peak for a 1000 Hz setting and a loopback amplitude of 0.496 V, close to the ideal 0.500 V baseband amplitude. On the SERF platform, I/Q rotation reduces the quadrature residual ratio from 32.1% to 0.10%. When the FIR cutoff frequency is changed from 3 to 15 Hz, the maximum zero-crossing difference is about 0.58 ms, corresponding to 0.12% of the 2 Hz sweep period. These results show that the module supports stable zero-crossing extraction and working-point determination during sweep-field operation in a single-beam SERF magnetometer.