Fig. 1

Schematic of the DSR resonator. The distance between resonant ring and feeder line is${{g}_{\text{c}}}$, the width of the resonant ring is w, the gap of DSR is${{g}_{\text{s}}}=$0.5 mm, the radius values of the resonant ring are r2 = 3 mm, r3 = 3.2 mm, r4 = 4.2 mm, and the width of the feeder line is$d=$3.2 mm. Tuning is achieved by adjusting the position of the copper flake on the left side of the resonant ring

Fig. 2

(a) S11 curve simulation corresponding to different w values (${{g}_{\text{c}}}=$0.1 mm), the illustration in the figure shows the influence of w on ${{Q}_{0}}$and Fr. The${{Q}_{0}}$of the resonator is the maximum and Fr is 7.2 GHz when w is 1.5 mm; (b) S11 curve simulation corresponding to different ${{g}_{\text{c}}}$values (w = 1.5 mm), it would be the best coupling when${{g}_{\text{c}}}=$0.1 mm, the illustration in the figure shows the influence of${{g}_{\text{c}}}$on${{Q}_{0}}$

Fig. 3

(a) Distribution of the magnetic field amplitude of the resonator at 7.2 GHz. (b) Distribution of the magnetic field in +z direction. The magnetic field in the +z direction is evenly distributed in the gap area of the resonant ring, and the magnetic field intensity reaches 500 A/m

Fig. 4

Schematic diagram of the ESR system. (1) Radiofrequency microwave source (R&S SMB100A); (2) Circulator (DH701FD); (3) Detector (Keysight 8471E); (4) Lock-in amplifier (Stanford Research SR830); (5) Direct current source (GWINSTEK PSW); (6) Waveform generator (SIGLENT SDG1050); (7) Power amplifier (LC1901); (8) Home-built permanent magnet; (9) Home-built Helmholtz coil

Fig. 5

S11 parameter diagram of the resonator without samples and with samples before and after tuning that is measured by vector network analyzer (VNA, Agilent N5234A); the illustration in the figure is the resonator loaded with powder sample. The microwave reflection at the resonance point is halved after tuning with copper flake

Fig. 6

ESR signal of DPPH powder of different quality (m = 0.42, 0.72, 1.12 and 1.63 mg) at room temperature. The peak-to-peak values (a) and SNR (b) of the four ESR signals are illustrated in the figure. Experimental parameters: microwave power =17 dBm, microwave frequency f = 6.82 GHz, magnetic field modulation frequency = 999 Hz, lock-in time constant = 100 ms, roll-off = 24 dB/oct, ENBW = 0.78 Hz

Fig. 7

(a) S11 curves of the resonator with two different substrate materials and without substrate, illustration (a) shows the measured ESR signal of DPPH covered with Zerodur, illustration (b) shows the measured ESR signal of DPPH covered with Si. The resonant frequency of the resonator changes to 6.57 GHz and 6.35 GHz while Zerodur and Si are loaded. The g values obtained from the two side tests are 1.972 3 and 1.973 1, respectively, with a relative error of 0.041%