An analysis of oscillation frequency characteristics in a CMOS oscillating circuit using a coupling quartz crystal resonator

Oscillation frequency characteristics in a CMOS oscillating circuit using a coupling quartz crystal resonator are described. A miniaturized GT cut quartz crystal resonator consisting of the vibrational portion and the supporting portions which is formed by an etching method is used. The relationship of the resonator´s frequency temperature behavior versus load capacitance (CL) is clarified. The oscillating circuit is shown as an electric equivalent circuit. An amplitude continuation condition and an oscillation condition are theoretically derived. The coupling between both vibrations of a coupling quartz crystal resonator is regarded as a capacitive coupling. From the equivalent circuit of the coupling quartz crystal resonator, an imaginary part is easily calculated. As a result, a frequency equation which is given as a function of CL is readily derived from the oscillation condition and the imaginary part of the coupling resonator. It is shown that by suitably choosing CL, the frequency deviation in this CMOS oscillating circuit is less than 1 p.p.m. over a wide temperature range of -30°C to +70°C without any temperature compensation