Second‐Order RLC Circuit Natural Response

Summary

This chapter starts with analyses of two second‐order RLC circuits, series and parallel, directly in terms of resistance R, inductance L, and capacitance C. RLC analyses are then repeated using two different damping variables, damping coefficient alpha and then damping ratio zeta. Second‐order RLC time domain circuit analysis often starts with Kirchhoff's current or voltage law to set up the differential equations. Natural response, also called zero‐input response, depends only upon the initial conditions present in the circuit. The chapter provides natural response graphs, of series RLC current versus time, and the complex plane locations are plotted for four cases or classes of roots. For RLC differential equation analysis, a general notation can be used and applied to both series and parallel RLC. The chapter explores the locations of characteristic roots in terms of zeta, in the complex sigma and j‐omega plane.