An integrated circuit includes first and second coils, a first pad connected to the first coil and to a resonator, a second pad connected to the second coil and to the resonator, and first and second output terminals. The first pad is arranged to provide signals between the resonator and the first coil. The second pad is arranged to provide signals between the resonator and the second coil. A distance between the first pad and the first coil is less than a distance between the first coil and the first output terminal and a distance between the first coil and the second output terminal. A distance between the second pad and the second coil is less than a distance between the second coil and the first output terminal and a distance between the second coil and the second output terminal.

An integrated circuit includes first and second coils, a first pad connected to the first coil and to a resonator, a second pad connected to the second coil and to the resonator, and first and second output terminals. The first pad is arranged to provide signals between the resonator and the first coil. The second pad is arranged to provide signals between the resonator and the second coil. A distance between the first pad and the first coil is less than a distance between the first coil and the first output terminal and a distance between the first coil and the second output terminal. A distance between the second pad and the second coil is less than a distance between the second coil and the first output terminal and a distance between the second coil and the second output terminal.

A method for determining a quality factor of an electrostatically actuated oscillator, the oscillator having a resonance frequency, the method including generating an excitation voltage defined as being the sum of a sinusoidal voltage and a voltage pulse; applying the excitation voltage at the input of the oscillator; acquiring in the time domain a response voltage present at the output of the oscillator after having ceased applying the excitation voltage at the input of the oscillator; determining the quality factor of the oscillator from the response voltage acquired at the output of the oscillator.

A method for determining a quality factor of an electrostatically actuated oscillator, the oscillator having a resonance frequency, the method including generating an excitation voltage defined as being the sum of a sinusoidal voltage and a voltage pulse; applying the excitation voltage at the input of the oscillator; acquiring in the time domain a response voltage present at the output of the oscillator after having ceased applying the excitation voltage at the input of the oscillator; determining the quality factor of the oscillator from the response voltage acquired at the output of the oscillator.

An electronic apparatus for testing an integrated circuit (IC) that includes a ring oscillator is provided. The apparatus configures the ring oscillator to produce oscillation at a first frequency and configures the ring oscillator to produce oscillation at a second frequency. The apparatus then compares the second frequency with an integer multiple of the first frequency to determine a resistive voltage drop between a voltage applied to the IC and a local voltage at the ring oscillator. The ring oscillator has a chain of inverting elements forming a long ring and a short ring. The ring oscillator also has an oscillation selection circuit that is configured to disable the short ring so that the ring oscillator produces a fundamental oscillation based on signal propagation through the long ring and enable the short ring so that the ring oscillator produces a harmonic oscillation based on a signal propagation through the short ring and the long ring.

An electronic apparatus for testing an integrated circuit (IC) that includes a ring oscillator is provided. The apparatus configures the ring oscillator to produce oscillation at a first frequency and configures the ring oscillator to produce oscillation at a second frequency. The apparatus then compares the second frequency with an integer multiple of the first frequency to determine a resistive voltage drop between a voltage applied to the IC and a local voltage at the ring oscillator. The ring oscillator has a chain of inverting elements forming a long ring and a short ring. The ring oscillator also has an oscillation selection circuit that is configured to disable the short ring so that the ring oscillator produces a fundamental oscillation based on signal propagation through the long ring and enable the short ring so that the ring oscillator produces a harmonic oscillation based on a signal propagation through the short ring and the long ring.

A resonant member of a MEMS resonator oscillates in a mechanical resonance mode that produces non-uniform regional stresses such that a first level of mechanical stress in a first region of the resonant member is higher than a second level of mechanical stress in a second region of the resonant member. A plurality of openings within a surface of the resonant member are disposed more densely within the first region than the second region and at least partly filled with a compensating material that reduces temperature dependence of the resonant frequency corresponding to the mechanical resonance mode.

A resonant member of a MEMS resonator oscillates in a mechanical resonance mode that produces non-uniform regional stresses such that a first level of mechanical stress in a first region of the resonant member is higher than a second level of mechanical stress in a second region of the resonant member. A plurality of openings within a surface of the resonant member are disposed more densely within the first region than the second region and at least partly filled with a compensating material that reduces temperature dependence of the resonant frequency corresponding to the mechanical resonance mode.

Provided are micromechanical resonators and resonator systems including the micromechanical resonators. The micromechanical resonators may each include a supporting beam including a fixed end fixed on a supporting member and a loose end configured to vibrate, and a lumped mass arranged on the loose end, wherein the loose end has a width greater than a width of the fixed end, and a width of the lumped mass is greater than that the width of the fixed end.

Provided are micromechanical resonators and resonator systems including the micromechanical resonators. The micromechanical resonators may each include a supporting beam including a fixed end fixed on a supporting member and a loose end configured to vibrate, and a lumped mass arranged on the loose end, wherein the loose end has a width greater than a width of the fixed end, and a width of the lumped mass is greater than that the width of the fixed end.