To compensate for frequency variation in the quartz oscillator 4, 6 due to temperature variation, a second quartz oscillator 12, 14 forming a thermal sensor is employed. The beat frequency fB (circuit 16) which is counted in the counter 26 for a period of time T.sub.1 gives a measurement corresponding to temperature. The number which is thus counted is raised to its square and by means of the comparator 30 taken away from the pulses counted by the divider 8 with a periodicity T.sub.T. The system may be used to provide temperature compensation for a time keeping quartz time base.

The present invention concerns a low frequency oscillator device including a quartz resonator (1) and an electronic maintenance circuit for maintaining the vibrations of said quartz resonator. According to the present invention, the quartz resonator is arranged to vibrate according to a torsional mode and therefore has a single cutting angle defined by a rotation at a determined angle (.theta.) about the crystallographic axis X of the quartz crystal. This resonator includes in particular at least one undesired fundamental flexural vibrating mode at a first frequency and a desired fundamental torsional vibrating mode at a second frequency higher than said first frequency. Moreover, the electronic maintenance circuit is an inverter circuit (2) whose transconductance value (g.sub.m) is determined such that said device cannot oscillate according to the undesired fundamental flexural vibrating mode but according to the desired fundamental torsional vibrating mode of said resonator. The oscillator device according to the present invention thus has substantially improved thermal characteristics with respect to known oscillator devices using flexural vibrating resonators.

In a method for manufacturing a quartz crystal unit, a quartz crystal tuning fork resonator is formed by etching a quartz crystal wafer to form a quartz crystal tuning fork base, quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, and a groove having stepped portions in at least one of opposite main surfaces of each of the quartz crystal tuning fork tines. A first electrode is disposed on at least one of the stepped portions of each of the grooves and a second electrode is disposed on each of side surfaces of each of the quartz crystal tuning fork tines. A frequency of oscillation of the quartz crystal tuning fork resonator is adjusted at least twice and in different steps. The quartz crystal tuning fork resonator is then mounted in a case and an open end of the case is covered with a lid.

A piezoelectric resonator formed as a thin parallelepipedic quartz plate whose width is arranged along the electric axis X of the crystal, the length along an axis Y' and the thickness along an axis Z', wherein the axes Y' and Z' form an angle approximately equal to 24.degree. with the mechanical axis Y and the optical axis Z of the crystal, respectively, and the ratio w/l of its width to its length is approximately equal to 0.64.

In the method, following an operating point determination of the quartz resonator circuit, a substitution of the equivalent circuit diagram of the quartz resonator by an independent current source is implemented with the initial, previously determined amplitude of the current of the dynamic arm of the quartz resonator. The dynamic equilibrium state is determined for this circuit arrangement with firing methods or methods of harmonic balance. After a resubstitution of the current source by the equivalent circuit diagram of the quartz resonator, a transient analysis is implemented for the dynamic equilibrium state. This method is iteratively implemented as long as the identified growth rate lies above a prescribable barrier.