Abstract This study shows that pinched hysteresis can be observed in simple non‐linear 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 non‐linearity such as a cubic non‐linearity. 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 the following: (1) pinched hysteresis is not a fingerprint of memristors, and (2) the existence of a non‐linearity is essential for generating this behaviour. Finally, an application in a digital logic circuit is validated.