Why does range drop when the battery weakens, and how does sleep mode extend battery life?

As the supply voltage falls, the output power and modulation quality of the power stage degrade; that is why the complaint the remote works but the range has halved is a typical symptom of a battery about to die. Sleep mode, on the other hand, drops the transmitter to a current in the microamp range as long as no button is pressed; since only a very small part of the total time is spent transmitting, it is this sleep current that really determines battery life.

The link between range and battery is direct. A 6 dB drop in output power halves the theoretical range exactly. A weak battery both lowers the output power and degrades the modulation, reducing the receiver's decoding success. That is why a weak battery usually shows itself first in range and only much later as complete failure to work.

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