Multiband Permittivity Measurement of Metallized-Bulk Substrate With Negative Group Delay-Based Ring Resonator

This article explores an original research work on multiband frequency metallized- dielectric permittivity measurement method for copper-plated substrates based on bandpass (BP) negative group delay (NGD) ring circuit. The B P-N GD topology is modeled by S-parameter. The unfamiliar specifications of the B P-N GD function are recalled. The extraction formula of permittivity within multiband frequency is established from NGD center frequency harmonics. The B P-N GD function specifications are defined. The B P-N GD ring resonator (RR) proof-of-concept (PoC) consists of linearly coupled loops implemented in microstrip technology. The multiband permittivity measurement NGD-method validity is proved by well-agreed full-wave simulations and measurements of the NGD RR prototype. An application of the multiband permittivity measurement NGD method using Rogers(Registered trademark.) material-based commercial substrate is presented. The test results of the dielectric sample are validated at 1–10 GHz. Furthermore, uncertainty analyses under the maximum processing error are performed. The effectiveness of the NGD method is confirmed by showing a relative permittivity measurement error of less than 0.5%.