Design Technique for Analog Temperature Compensation of Crystal Oscillators

For decades, the quartz crystal has been used for precise frequency control. In the increasingly popular field of wireless communications, available frequency spectrum is becoming very limited, and therefore regulatory agencies have imposed tight frequency stability requirements. There are generally two techniques for controlling the stability of a crystal oscillator with temperature variations of the environment. They are temperature control and temperature compensation. Temperature control involves placing the sensitive components of an oscillator in a temperature stable chamber. Usually referred to as an oven-controlled crystal oscillator (OCXO), this technique can achieve very good stability over wide temperature ranges. Nevertheless, its use in miniature battery powered electronic devices is significantly limited by drawbacks such as cost, power consumption, and size. Temperature compensation, on the other hand, entails using temperature dependent circuit elements to compensate for shifts in frequency due to changes in ambient temperature. A crystal oscillator that uses this frequency stabilization technique is referred to as a temperature-compensated crystal oscillator (TCXO). With little added cost, size, and power consumption, a TCXO is well suited for use in portable devices. This paper presents the theory of temperature compensation, and a procedure for designing a TCXO and predicting its performance over temperature. The equivalent electrical circuit model and frequency stability characteristics for the AT-cut quartz crystal are developed. An oscillator circuit topology is introduced such that the crystal is operated in parallel resonance with an external capacitance, and equations are derived that express the frequency stability of the crystal oscillator as a function of the crystal's capacitive load. This relationship leads to the development of the theory of temperature compensation by a crystal's external load capacitance. An example of the TCXO design process is demonstrated with the aid of a MATLAB script.