Periodic signal generators include an oscillator circuit, which is configured to generate a first periodic signal at an output thereof, and a piezoelectric-based microelectromechanical resonator. The resonator is configured to generate a second periodic signal at a first electrode thereof, which is electrically coupled to the oscillator circuit. A variable impedance circuit is provided, which is electrically coupled to a second electrode of the piezoelectric-based microelectromechanical resonator. The variable impedance circuit is configured to passively modify a frequency of the second periodic signal by changing an induced electromechanical stiffness in at least a portion of the piezoelectric-based microelectromechanical resonator.