Systems and methods for digital synthesis of an output signal using a frequency generated from a resonator and computing amplitude values that take into account temperature variations and resonant frequency variations resulting from manufacturing variability are described. A direct frequency synthesizer architecture is leveraged on a high Q resonator, such as a film bulk acoustic resonator (FBAR), a spectral multiband resonator (SMR), and a contour mode resonator (CMR) and is used to generate pristine signals.

Systems and methods for digital synthesis of an output signal using a frequency generated from a resonator and computing amplitude values that take into account temperature variations and resonant frequency variations resulting from manufacturing variability are described. A direct frequency synthesizer architecture is leveraged on a high Q resonator, such as a film bulk acoustic resonator (FBAR), a spectral multiband resonator (SMR), and a contour mode resonator (CMR) and is used to generate pristine signals.

A timepiece reduces power consumption while maintaining required precision. The timepiece has a frequency divider that frequency divides an oscillation signal and outputs a reference signal; nonvolatile memory that stores information related to a temperature characteristic of the oscillation frequency of the crystal oscillator; multiple registers; a temperature measuring circuit; an evaluation circuit; and a temperature compensation circuit. The temperature compensation circuit reads the information from one of the registers and corrects the reference signal based on the read information and the temperature measurement information when the evaluation circuit determines the information stored in the multiple registers is the same; and when the evaluation circuit determines the information stored in the multiple registers is different, reads the information from the nonvolatile memory, stores the read information in the multiple registers, and corrects the reference signal based on the read information and the temperature measurement information.

A timepiece reduces power consumption while maintaining required precision. The timepiece has a frequency divider that frequency divides an oscillation signal and outputs a reference signal; nonvolatile memory that stores information related to a temperature characteristic of the oscillation frequency of the crystal oscillator; multiple registers; a temperature measuring circuit; an evaluation circuit; and a temperature compensation circuit. The temperature compensation circuit reads the information from one of the registers and corrects the reference signal based on the read information and the temperature measurement information when the evaluation circuit determines the information stored in the multiple registers is the same; and when the evaluation circuit determines the information stored in the multiple registers is different, reads the information from the nonvolatile memory, stores the read information in the multiple registers, and corrects the reference signal based on the read information and the temperature measurement information.

Systems and methods for digital synthesis of an output signal using a frequency generated from a resonator and computing amplitude values that take into account temperature variations and resonant frequency variations resulting from manufacturing variability are described. A direct frequency synthesizer architecture is leveraged on a high Q resonator, such as a film bulk acoustic resonator (FBAR), a spectral multiband resonator (SMR), and a contour mode resonator (CMR) and is used to generate pristine signals.

Systems and methods for digital synthesis of an output signal using a frequency generated from a resonator and computing amplitude values that take into account temperature variations and resonant frequency variations resulting from manufacturing variability are described. A direct frequency synthesizer architecture is leveraged on a high Q resonator, such as a film bulk acoustic resonator (FBAR), a spectral multiband resonator (SMR), and a contour mode resonator (CMR) and is used to generate pristine signals.

Systems and methods for digital synthesis of an output signal using a frequency generated from a resonator and computing amplitude values that take into account temperature variations and resonant frequency variations resulting from manufacturing variability are described. A direct frequency synthesizer architecture is leveraged on a high Q resonator, such as a film bulk acoustic resonator (FBAR), a spectral multiband resonator (SMR), and a contour mode resonator (CMR) and is used to generate pristine signals.

Systems and methods for digital synthesis of an output signal using a frequency generated from a resonator and computing amplitude values that take into account temperature variations and resonant frequency variations resulting from manufacturing variability are described. A direct frequency synthesizer architecture is leveraged on a high Q resonator, such as a film bulk acoustic resonator (FBAR), a spectral multiband resonator (SMR), and a contour mode resonator (CMR) and is used to generate pristine signals.

According to some aspects of the present disclosure, an atomic clock and methods of forming and/or using an atomic clock are disclosed. In one embodiment, an atomic clock includes: a light source configured to illuminate a resonance vapor cell; a narrowband optical filter disposed between the light source and the resonance vapor cell and arranged such that light emitted from the light source passes through the narrowband optical filter and illuminates the resonance vapor cell. The resonance vapor cell is configured to emit a signal corresponding to a hyperfine transition frequency in response to illumination from the light source, and a filter cell is disposed between the light source and the resonance vapor cell and configured to generate optical pumping. An optical detector is configured to detect the emitted signal corresponding to the hyperfine transition frequency.

According to some aspects of the present disclosure, an atomic clock and methods of forming and/or using an atomic clock are disclosed. In one embodiment, an atomic clock includes: a light source configured to illuminate a resonance vapor cell; a narrowband optical filter disposed between the light source and the resonance vapor cell and arranged such that light emitted from the light source passes through the narrowband optical filter and illuminates the resonance vapor cell. The resonance vapor cell is configured to emit a signal corresponding to a hyperfine transition frequency in response to illumination from the light source, and a filter cell is disposed between the light source and the resonance vapor cell and configured to generate optical pumping. An optical detector is configured to detect the emitted signal corresponding to the hyperfine transition frequency.