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The photometric, electrical, and thermal features of LED systems are highly dependent on one another. By considering all these factors together, it is possible to optimize the design of LED systems. This paper presents a general theory that links the photometric, electrical, and thermal behaviors of an LED system together. The theory shows that the thermal design is an indispensable part of the electrical circuit design and will strongly influence the peak luminous output of LED systems. It can be used to explain why the optimal operating power, at which maximum luminous flux is generated, may not occur at the rated power of the LEDs. This theory can be used to determine the optimal operating point for an LED system so that the maximum luminous flux can be achieved for a given thermal design. The general theory has been verified favorably by experiments using high-brightness LEDs.