In this paper, an approach to the design of shielded radio-frequency (RF) phased-array coils for magnetic resonance imaging (MRI) is proposed. The target field method is used to find current densities distributed on primary and shield coils. The stream function technique is used to discretize current densities and to obtain the winding patterns of the coils. The corresponding highly ill-conditioned integral equation is solved by the Tikhonov regularization with a penalty function related to the minimum curvature. To balance the simplicity and smoothness with the homogeneity of the magnetic field of the coil's winding pattern, the selection of a penalty factor is discussed in detail.
