Color rendering and luminous efficacy of trichromatic and tetrachromatic LED-based white LEDs

White light-emitting diode (LED) spectra for general lighting should be designed for high luminous efficacy as well as good color rendering, which are generally in a trade-off relationship. White LEDs have uncountable metameres, they have different luminous efficacy and color rendering. Appropriate designed trichromatic and tetrachromatic LED-based white LEDs are presented that have acceptable color rendering as well as good luminous efficacy. Triachromatic white LEDs, with a wavelength combination of 460, 540, and 615 nm, offer high general color rendering index exceeding 89, and luminous efficacy 336 lm/W. The general color rendering index of tetrachromatic LED-based white LEDs combined from 460, 525, 590, and 640 nm is 95, the luminous efficacy is 306 lm/W. Further analysis shows the changing trends of the luminous efficacy, color rendering and the chromaticity coordinate of the optimized trichromatic and tetrachromatic white LEDs depending on the wavelength shift of the primary LEDs. For the optimized trichromatic white LEDs, both the luminous efficacy and color rendering change more with the wavelength shifts of the primary red LEDs than with the wavelength shifts of the blue and green LEDs. For the optimized tetrachromatic white LEDs, the changes of the luminous efficacy caused by the wavelength shifts of one red LED are smaller than the changes of trichromatic white LEDs. And the wavelength shifts of the red primary LED that have shorter wavelength affect the color rendering more than the other primary LEDs. The wavelength shifts of the blue primary LED change the chromaticity coordinate of the white LEDs more. The small changes of the chromaticity coordinate of the white LED do not mean small changes of the k and R_a.