The optimization model of limited luminous efficacy (LLE) for correlated color temperature (CCT) tunable phosphor-coated white light-emitting diodes (pc-W LEDs) consisting of blue chips, green and yellow phosphors, and red chips, including downconversion energy loss, has been developed under the constraint of a designated color-rendering index (CRI) and a special CRI of R9 for strong red. The optimal spectra of pc-W LEDs are obtained with a nonlinear program for maximizing LLE under conditions of both CRI and R9 above 90, 95, and 98 at CCTs of 2700-6500 K. The pc-W LEDs with LLE>301 lm/W for both CRI and R9 above 90, LLE>290 lm/W for both CRI and R9 above 95, and LLE>276 lm/W for both CRI and R9 above 98 could be achieved at CCTs of 2700-6500 K. The recommended peak wavelengths and full widths at half-maximum (FWHMs) for the current LEDs and phosphors and their photometric and colorimetric performances are presented.
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