The RF output amplitude of the Low Level Radio Frequency (LLRF) system in Shanghai Soft X-ray Free-electron Laser (SXFEL) exhibits oscillations during the search for the maximum accelerating phase, compromisingthe stability of the entire device.

This study aims to develope a multi-variable estimation-based calibration technology for the Vector Modulator (VM) to stabilize the RF output amplitude and reduce the crosstalk between the amplitude and phase loops in closed-loop control.

A non-ideal model of the VM was analyzed and established to address output amplitude stabilization in the LLRF system's microwave power source. The parameters of this model were estimated using real input and output data from the VM. A calibration algorithm was then designed and implemented to mitigate the adverse effects caused by non-ideal factors.

Experimental results demonstrate that the proposed method reduces the impact of phase setpoint changes on the VM's output amplitude from 4.0% Root Mean Square (RMS) to 0.19% RMS after calibration. Furthermore, the error between the phase setpoint and measured phase was reduced to within 0.18° RMS.

This proposed method improvesisolation between amplitude and phase, effectively eliminating phase differences between the output and sampled waveforms.