Determination of the frequency of oscillations in the autodyne sensor under regular and casual temperature mode variations

The sensor is mounted in an orifice of the reactor wall. The antenna is inward to the reactor; its conductivity depends on the permittivity of a high-temperature working body and transforms to an autodyne frequency. Heating of the sensor is realized by the working body through the antenna surface. The largest part of the sensor´s body is outside the reactor and cools through the sidewalls. Variations of resonator length, permittivities, and also capacity of the diode mainly influence the frequency of generation. The error that is most difficult to compensate for is caused by the regular temperature variations at the starting time. Theoretical estimations of this magnitude are presented. The investigation of a casual error is continued. The working body of the sensor (with a resonator), which is represented by a linear narrow-band quadrupole, carries out a temperature transformation into a frequency shift. Its properties are based on the well-known thermophysics regularities. Heat exchange between the working body and antenna occurs by radiation. The rough heat causes temperature waves in the working body of the sensor, which propagate with strong attenuation and with velocities that depend on frequency. The mathematical investigations include: (i) approximation of a temperature curve of growth in the reactor T(t) and its Fourier-expansion; (ii) determination of an impulse characteristic of “quadripole”, h(t) in any cross-section of the sensor; (iii) convolution of functions T(t) and h(t-τ); (iv) integration by the sensor´s (resonator) length along a coordinate x∈O,L; (v) translation into the frequency change. The investigated examples have shown that the compensation of the error under the primary and secondary processing is hampered. A solution for this problem is the development of a computer model, which takes into account all obtained correlations