Voltage controlled temperature compensated crystal oscillator using 2-port crystal resonator

Generally, the frequency-vs.-temperature characteristic of voltage-controlled temperature compensated crystal oscillators (VCTCXO) varies when their oscillation frequency is shifted. In an effort to solve the problem, the authors developed a VCTCXO using a 2-port crystal resonator with a special electrode structure. The VCTCXO with the 2-port crystal resonator can have two load capacitances, i.e., a load capacitance for temperature compensation and a load capacitance for shifting the oscillation frequency. Therefore, the VCTCXO can compensate for temperature changes and shift the oscillation frequency independently. An electric equivalent circuit for the 2-port crystal resonator is introduced, and fundamental equations are derived from the equivalent circuit for determining the extent to which the oscillation frequency varies with the load capacitances, with comparison made between measured and calculated values