Theoretical and experimental investigations of frequency transient process caused in crystal plates under local heating

Summary form only given. It is known that nonuniformly heating produces an additional frequency shift in anisotropic crystal plates. This affect is most pronounced when the crystal is spot heated. Temperature gradients appearing along the plate cause mechanical stresses that lead to frequency change. Theoretical investigations of the local heating effect on resonator frequency are carried out. Dependence of frequency control efficiency was investigated in relation to size of heater, number of excited harmonics, cut angle, piezoelement thickness and coefficient of heat exchange with the environment. Using MATLAB and MATCAD software, maps of heat and stress fields were calculated for different heating conditions. The corresponding frequency shift was calculated. This process is essential for many practical applications such as frequency control in low-noise PLL system. It is shown that the form of transient process depends on the ambient temperature and has two time constants. Most of the parameters of local heating controlled oscillator are shown: frequency setting process; control characteristics; phase noise. The obtained theoretical results are close to experimental ones