Many implantable medical devices such as pacemakers,

Chapter 8, Problem 62

(choose chapter or problem)

Many implantable medical devices such as pacemakers, retinal implants, deep brain stimulators, and spinal cord stimulators are powered by an in-body battery that can be charged through a transcutaneous inductive device. Optimal battery charge can be obtained when the out-of-body charging circuit is in resonance with the implanted charging circuit (Baker, 2007). Under certain conditions, the coupling of both resonant circuits can be modeled by the feedback system in Figure P8.3 where

G(s) = \(\frac{K s^4}{\left(s^2+2 \zeta \omega_n s+\omega_n^2\right)^2}\)

The gain K is related to the magnetic coupling between the external and in-body circuits. K may vary due to positioning, skin conditions, and other variations. For this problem let \(\zeta\) = 0.5 and \(\omega_n\) = 1.

a. Find the range of K for closed-loop stability.

b. Draw the corresponding root locus.