The generation regimes of an all-fiber passively mode-locked ytterbium laser with intra-cavity photonic crystal fiber have been studied with the aim to provide recipes for obtaining chirp-free sub-picosecond pulses directly from the cavity. Small-beam area photonic-crystal fiber is used for dispersion compensation of the intra-cavity normal dispersion of b-doped and single-mode fibers as well as for spectrum expanding due to enhanced nonlinearity. Regions of the gain and fiber parameters near the generation threshold were found in both cases of normal and anomalous net intra-cavity dispersion, which provide a stable generation of ultra-short sub-picosecond pulses directly from the cavity. Laser parameters of a transition to the multi-pulsed generation regimes were also found.