Nonlinear damping of the LC circuit using antiparallel diodes

We investigate a simple variation of the series RLC circuit in which antiparallel diodes replace the resistor. The result is a damped harmonic oscillator with a nonlinear damping term that is a maximum at zero current and decreases inversely with the current for currents far from zero. Unlike the standard RLC circuit, the behavior of this circuit is amplitude dependent. The transient response makes a transition from underdamped to overdamped behavior, and the resonance response of the steady-state driven oscillator becomes sharper as the source amplitude increases. A set of nonlinear differential equations is derived for the circuit and integrated numerically for comparison with measurements. The equipment is inexpensive and common to upper level physics labs. (C) 2007 American Association of Physics Teachers.