This paper presents the analysis and effects of frequency diversity on finite uniform circular array for generation of range dependent Orbital Angular Momentum (OAM) modes. The analysis reveals that the array factor expression in terms of Bessel's function for a circular array with finite no. of elements possess a phase error in the azimuthal domain at any transverse plane due to which the range dependency of OAM modes is affected. In this report a detailed analysis of the phase distribution on concentric circles for an exact array factor expression without considering any assumption or approximation has been carried out. Effect of changing parameters such as total number of elements and frequency increment value is analyzed and compared with the approximated array factor expression. Fourier analysis in the azimuthal domain reflects the presence of desired modes at a specific range for finite array cases. Generated phase and amplitude profile validate the occurrence of range dependent OAM modes at specified distance. Analysis of phase error for different frequency increment for finite no. of elements is also done. A prior knowledge of the available modes at a specified distance away from the antenna is crucial for improving the spectral efficiency of a communication system or radar.