Test of gravitational red-shift based on tri-frequency combination of microwave frequency links Xiao Sun, Wen-Bin Shen, Ziyu Shen, Chenghui Cai, Wei Xu and Pengfei Zhang Eur. Phys. J. C, 81 7 (2021) 634 Published online: 20 July 2021 DOI: 10.1140/epjc/s10052-021-09415-y