> Soviet agents stationed across the street from Spaso House would turn the device “on” by focusing a radio signal on it, which then bounced back to their radio receiver. When the ambassador or anyone else in the study spoke, the sound waves caused the membrane to resonate and alter the signal that returned to the Soviets, allowing them to hear the conversation.

It could contain more detail but sounds like it was altering a radio signal that was completely external to the device and therefore had no battery at all.