Here you see an example of an implant transmitter. We wrap the implants with silicone, You see an C - 1 / ER 1750 [Imp] implant model with 2,5 Ah battery capacity. Weight and dimensions changes with the battery in use, as well as lifetime of course. Implants lifetimes are, in most cases, wanted to last for longer periods so that very small batteries don´t make sense and size reduction is limited by this. Additionaly the internal coil antenna also takes some place but even when the antenna can´t radiate optimal inside of an animals body, you still can expect a useful range.
