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Yb-doped double-cladding photonic crystal fibers have become key components for power scaling in fiber laser systems, by providing many advantages, especially an ultra large effective area. The single-mode regime, which is a mandatory requirement for high quality laser beams, can be obtained in such large core active fibers only through a careful design. In this paper the cut-off properties of 19-cell photonic crystal fibers have been thoroughly investigated with the avoided-crossing approach, in order to find guidelines for the design of single-mode fibers. The air-hole diameter and the core refractive index have been changed, as well as the number of air-hole rings in the fiber inner cladding. Simulation results have shown that, regardless of the air-hole ring number, the guided-mode cut-off properties are strongly influenced by the main design parameters, especially by the core refractive index. In particular, a wider single-mode wavelength range can be obtained in 19-cell fibers with small air-holes and low core refractive index. Moreover, double-cladding photonic crystal fibers with larger inner-cladding provide better guided-mode cut-off properties, which can have positive effects on the amplification process in practical applications.