**Young Cheol Kim 1, Hyun Deok Kim 2,\*, Byoung-Ju Yun <sup>2</sup> and Sheikh Faisal Ahmad 1,\***


Received: 13 January 2020; Accepted: 25 March 2020; Published: 26 March 2020

**Abstract:** A novel analytical solution for the designing of the birdcage RF coil has been demonstrated in this paper. A new concept of dominant resonance path has been introduced in this paper which is used to identify the specific closed current loop in the birdcage RF coil which is responsible for the dominant resonance frequency mode. This concept is used to determine the precise numerical values of the lumped capacitance deployed in the legs and/or end-rings of the birdcage RF coil for its proper operation at the desired resonance frequency. The analytical solution presented in this paper has been established by performing the two-port network based equivalent circuit modeling of the birdcage RF coil. The proposed analytical solution uses T-matrix theory and develops a relationship between the input impedance of the birdcage coil and the impedances of its leg and end-ring segments. The proposed analytical solution provides the information about the resonance frequency spectrum of the birdcage RF coil and solves the issue of its interfacing with external circuits without affecting its resonance characteristics. Based upon the proposed analysis and designing strategy presented in this paper, the low pass, high pass and band pass configurations of the birdcage RF coil were successfully implemented with FPCB (Flexible Printed Circuit board) technique for small volume NMR imaging applications at 1.5 T and 3.0 T MRI system. The results obtained for the implemented birdcage coils using the proposed analysis and designing technique are in closed agreement with already established methods.

**Keywords:** MRI system; birdcage coil; birdcage configurations; coil capacitance; analytical solution; equivalent circuit modelling; T-matrix theory; 3D-EM simulation; small volume RF coil
