Multi-turn split-conductor transmission-line resonators (MSTR) can be designed to operate over a wide range of NMR operating frequencies without lumped tuning capacitors. This architecture constitutes an alternative solution to recent designs proposed for high-Q, thin-film, high-temperature superconducting NMR probes. An advantage is that the resonant frequency can be calculated in a relatively simple manner in terms of coil turns or total coil length, coil width, substrate thickness, and dielectric constant. Analytical calculation of the resonant frequency is provided. Also, a series of MSTRs was constructed on a double copper-clad substrate, and their resonant frequencies are noted. The results obtained were in good agreement with the predicted values.

A split-conductor parallel-plate transmission line resonator is a simple structure made from bending a strip of double-face copper-clad printed-circuit board into a loop with alternate electrical discontinuities (gaps) on opposite sides. Its natural resonant frequency (Fn) is determined by the transmission line characteristic impedance, the loop diameter or strip length, and the number (Ng) of gaps. It is easy to design high frequency resonators simply by increasing Ng. We propose here a single-gap multiturn resonator for low frequency operation as well as a simplified expression for the determination of Fn. A design procedure of this type of resonator is outlined and illustrative examples with parallel-plate as well as ordinary 50 Ω coaxial transmission lines are given. Also, for a given cable length, numerical calculation shows that the minimum resonator frequency can be attained with a form factor of the order of 2.