Example oscillators and oscillator-based apparatus are described. One example oscillator includes: a resonant circuit, configured to generate an oscillator signal; a first cross-coupled transistor, coupled to the resonant circuit; and a power supply circuit, configured to supply a power supply signal for the first cross-coupled transistor based on a first voltage and a second voltage, where the first voltage is a power supply voltage, and the second voltage is a voltage generated by an external sensing circuit. Because an oscillation frequency of the oscillator changes with the power supply signal of the oscillator, the oscillation frequency of the oscillator can be compensated by adjusting the power supply signal.