Based on the generalized transformation for a nonmagnetic cylindrical concentrator, we present nonlinear coordinate transformations to realize excellent concentrating performance with minimized scattering. By matching the impedance at both the inner and outer boundaries and utilizing nonlinear optimization techniques, the best parameters of the nonlinear transformation can be determined. Results show that the concentrating power is sensitive to the impedance at the inner interface. In addition, an alternating layered system consisting of nonmagnetic isotropic materials is applied to experimentally mimic the concentrator, and excellent concentrating performances have been observed.