We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the kth input carrying a phase delay of (k-1)Δφ. The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay Δφ; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., l={-1},{-1,+1},{-1,0,+1}, or {-2,-1,+1,+2}); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own Δφ value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% for l=-1), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for l={-1} to 122 nm for l={-2,-1,+1,+2}), and (c) increased crosstalk within the C-band (from -23.7 to -13.2dB when the tunable range increases from 2 to 4).