Development of a multi-radian phase detector for a mm-wave interferometer

Abstract

One of the most widely adopted method to determine the electron density in plasmas is interferometery. The signal from a mm-wave source of an interferometer is split into two waves. One wave, the reference wave, is sent to a detector by means of waveguide and the other, the probe wave, is transmitted through a plasma before being brought to the detector. The plasma causes phase shift in the probe wave due to the change in refractive index of the medium resulting in a phase difference between the reference wave and the probe wave at the detector. The phase difference Φ is proportional to the line-integrated density of the plasma. When the phase difference exceeds 2π, the output of a common analog phase detector jumps from 2π to zero. For an appropriate real-time plasma control with density feedback, a reliable real-time phase detection with the ability of measuring multiples of 2π is crucial. With this motivation, the Multi-radian Phase Detector (MPD) based on a DPLL (Digital Phase Locked Loop) circuit was developed. The main idea of MPD is digital tracing of phase changes which are over 2π rad. With the developed MPD, it is possible to measure phase shifts from 0 up to 16×2π rad (16 fringes) continuously with a resolution of about $\frac{1}{100} \times 2\pi $rad. Experiments were performed to verify the ability to detect the phase difference over 2π rad. In the first experiment, the phase differences by the phase shifter which is composed of high-pass filters is given to the phase detector and the output of this phase detector is examined. There are the good agreements between the given phase difference below 2π rad and the corresponding phase detector output. In the next experiments, the phase difference by a real plasma, an AC discharge plasma on KAIST-Tokamak, is made for an examination of the Multi-radian Phase Detector. This experiment verifies that the Multi-radian Phase Detector measures the multiples of 2π radian phase difference continuously.