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Sometimes it seems my bluetooth speaker is particularly sensitive to the distance from my smartphone, sometimes it seems completely indifferent. The variable seems to the battery charge.

My question is: Is my bluetooth range impacted by the remaining battery on my smartphone as a scale or ratio?

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Not in a well defined way, no. Although it is feasible to scale transmit power with remaining battery, this isn't generally a useful feature since it causes confusion for customers, and doesn't necessarily provide better performance.

What is possible is that the circuit designs are sufficiently marginal (or cost-reduced, depending if you are buying or selling) that as the battery voltage drops and the switching current increases for the various voltage regulators, both the regulation and noise characteristics of the design get worse. Similarly, you might find your cell reception is degraded by having a charger connected (yet a charging lead plugged in but not powered might improve reception).

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