6.9 : Node Analysis for AC Circuits

Consider an angioplasty system featuring a catheter equipped with a turbine, a critical tool for removing plaque deposits from coronary arteries. This intricate medical device operates using a circuit model reminiscent of a dual-node RLC circuit powered by a current-controlled voltage source.

To unravel the complexities of this system, nodal analysis is employed, a powerful technique founded on Kirchhoff's current law (KCL), which remains valid for phasors. AC circuits can effectively be analyzed using nodal analysis.

The process begins with gathering information about the input source voltage, inductance, and capacitance values. These data points can calculate the driving voltage for the catheter's shaft. Leveraging angular frequency, inductance, and capacitance values, the impedance across the inductor and capacitor is determined, mapping out a frequency domain circuit.

KCL and Ohm's law are applied at both nodes, yielding equations that describe the system's behavior. When simplified and integrated, these equations reveal that the shaft voltage precisely equals the source voltage.

This comprehensive analysis provides essential insights into the electrical operation of the angioplasty system. The voltage data can then be converted into the time domain, allowing for assessing and optimizing the system's performance for effective plaque removal in medical procedures.