  This paper shows that pinched hysteresis can be observed in simple nonlinear
resonance circuits containing a single diode that behaves as a
voltage-controlled switch. Mathematical models are derived and numerically
validated for both series and parallel resonator circuits. The lobe area of the
pinched loop is found to increase with increased frequency and multiple
pinch-points are possible with an odd symmetrical nonlinearity such as a cubic
nonlinearity. Experiments have been performed to prove the existence of pinched
hysteresis with a single diode and with two anti-parallel diodes. The formation
of a pinched loop in these circuits confirms that: 1) pinched hysteresis is not
a finger-print of memristors and that 2) the existence of a nonlinearity is
essential for generating this behavior. Finally, an application in a digital
logic circuit is validated.
