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The continuous monitoring of electrical brain activity with implanted depth electrodes is essential for understanding the neural substrates of many physiological and pathological brain functions, such as emotion and epilepsy. Existing instrumentation uses wires to power and record directly from the brain. This article describes the theory involved in every aspect of the design of an inductively powered system with emphasis on the trade-offs involved. A complete inductive powering system consists of two major parts - a drive coil and a pickup coil, and their associated impedance matching networks. The drive coil is designed to maximize the magnetic field within the desired enclosure at the drive frequency. Similarly, the pickup coil is designed to maximize the amount of magnetic flux density converted to power for the implant, while minimizing it's own dimensions. A specific real-world application of inductive powering is detailed, illustrating how many of the design decisions were made to develop a successful system for recording neural signals from awake and freely behaving animals.