Semiconductor solar cells absorb photons of energy greater than their band-gap and convert the photon energy to electrical energy less than the band-gap. Consequently, small gap solar cells can absorb a large part of the solar spectrum, but deliver little energy per photon absorbed. Large gap solar cells deliver more energy per photon, but can absorb only the high energy part of the spectrum. Splitting the solar spectrum into multiple segments with diffractive elements that separate the incident radiation spatially and focusing it on solar cells optimized for the narrower bands facilitates the energy conversion. Here, we explore limitations to this approach imposed by inevitable parasitic effects. Specifically, we introduce series and parallel resistances into an ideal solar cell model. Resistance of the cell material and the contacts, and current leakage through the junction, due to defects, can be captured by this model. Subsequently, current density characteristics, maximum power density, and efficiency are determined. Highly conductive, low band-gap cells show performance degradation due to series resistance, while highly resistive, large gap cells are sensitive to junction leakage. As a specific case, we consider a three-cell solar cell array fabricated from InxGa1-xN of varying composition.