AN ANALYSIS OF THE ERRORS OF METHODS OF MEASURING RESONANCE FREQUENCY RADIO MEASUREMENTS

The factors that affect the errors of analog and digital methods of measuring resonance frequency are considered. Analytical expressions are obtained for the errors of each of these methods, taking the appropriate factors into account. The errors of the digital method are investigated numerically in the Matlab medium. The problem of measuring resonance frequency arises when developing frequency sensors, the sensitive elements of which are different types of resonators (acoustic, electromagnetic, electromechanical, etc.) and in different physical investi- gations, in which such resonators are used. When measuring the parameters of resonators, in particular, the resonance frequency, both analog and digital methods are employed. We will consider remote measurements, carried out on the amplitude-frequency characteristic of the resonator using a resonance frequency measuring instrument. A block diagram of the device consists of a tunable frequency generator (TFG) and signal control and processing units (SCPU) (Fig. 1). The circuit also contains the resonator being investigated in the form of an equivalent LCR-circuit, connected in this measuring system using a communications cable. The measuring instrument operates as follows. The signal from the TFG, the frequency of which is varied over a specified range, is applied to the input of the resonator. From the output of the resonator, a signal is obtained in a form which repeats the amplitude-fre- quency characteristic of the resonator. The signal is then applied to the input of the SCPU, where the maximum of the ampli- tude-frequency characteristic is recorded, and from this maximum one determines the resonance frequency. Moreover, the SCPU generates a controlling signal for the TFG. In analog measuring instruments, the frequency is varied continuously, and the maximum of the amplitude-frequency characteristic is determined by analog methods (1). In digital measuring instruments (2), one uses as the TFG a synthesizer, whose frequency is varied digitally in steps of s ω . The synthesizer is controlled, the ampli- tude-frequency characteristic is processed and the resonance frequency is determined in this case by means of a microprocessor, which forms part of the SCPU. The choice of the analog or digital method of measurement is mainly determined by metrological and economic fac- tors. The advantages of digital measuring instruments are the high accuracy, the possibility of operating with many resonators, and the ability to use different signal processing algorithms. The advantages of the analog method is the relative simplicity of the circuit and the low cost, but as far as all the remaining parameters are concerned, these measuring instruments are infe- rior to digital instruments. We will consider the metrological characteristics of both methods in more detail. The Analog Method of Measuring Resonance Frequency. The main sources of errors of analog measuring instru- ments are transients in the resonator being investigated and noise in the measuring signal. The effect of transients. The error due to transients in the resonator arises when it is excited by a signal with a variable frequency. Hence, at the output of the resonator one obtains a dynamic resonance curve, the maximum of which is shifted