1" sensitivity resonant frequency shift

In a sensor experiment (e.g., in a typical biochemical experiment) the sensor has been functionalized with a sensitive film, which is in contact with an analyte containing buffer solution. The new resonance frequencies / can be calculated when replacing Ls and Rs by =Ls + Lc + Liiq and R = Rs + Knq, respectively (neglecting Qiq and Guq). Usually frequency shifts are determined and of interest only. Some example data are added to Table 2. Series and parallel resonance frequency shifts vary by a few percent. All the parallel resonance frequencies are very much affected by external capacitance (values in brackets). The same holds for all frequency shifts in a Hquid except /s. Oscillators based on parallel resonance should not be used because stray capacitance is hardly to avoid and hardly to keep constant in an experimental setup. Deviations of/r and/m from s are also ampHfied by external capacitance. 

In our discussion of electromagnetic techniques, we omitted a few available technologies that provide some unique capabilities and, with further development, can attain practical application. One such technique involves the use of a microwave resonance sensor (Kobyashi and Miyahara, 1984) that uses a microwave cavity to measure solids concentration and velocity by monitoring the resonance frequency shift. However, this technique suffers from some shortcomings the frequency shift may be positive or negative, depending on the dielectric properties of the solids, and the cavity is extremely sensitive to changes in moisture content and temperature. 

Figrue BTl 1.1 shows the range of radiolfequencies where resonances may be expected, between 650 and 140 MHz, when Bq = 14.1 T, i.e. when the H resonance frequency is 600 MHz. There is one bar per stable isotope. Its width is the reported chemical shift range (Bl.11.5) for that isotope, and its height corresponds to the log of the sensitivity at the natural abundance of the isotope, covering about six orders of magnitude. The... 

Figure Bl.11.1. Resonance frequencies for different nuclei in a field of 14.1 T. Widths indicate the quoted range of shifts for each nucleus, and heights mdicate relative sensitivities at the natural isotopic abundance, on a log scale covering approximately six orders of magnitude. Nuclei resonatmg below 140 MHz are not shown.

Two methods of further enhancing detection sensitivity rely on the use of multiple resonators or multiple fiber modes. The first will just be mentioned briefly, because although it is absorption based it uses a frequency shift. When two microresonators have resonances that are coincident in frequency, and the second resonator is brought near to the first resonator, which is in contact with the coupling fiber, the... 

Equation (14.5) establishes the linear relationship between the RI sensitivity and the resonant mode s frequency shift for a given number of captured molecules at the OFRR surface. Also, note that the magnitude of the shift is directly proportional to the surface density and the excess polarizability of the bound molecules. Although (14.5) is developed for the OFRR, it is generally applicable to other types of ring resonator sensors, as is shown by Zhu, et al.27... 

If one side of the quartz is coated with material, the spectrum of the resonances is shifted to lower frequencies. It has been observed that the three above mentioned modes have a somewhat differing mass sensitivity and thus experience somewhat different frequency shifts. This difference is utilized to determine the Z value of the material. By using the equations for the individual modes and observing the frequencies for the (100) and the (102) mode, one can calculate the ratio of the two elastic constants Cgg and C55. These two elastic constants are based on the shear motion. The key element in Wajid s theory is the following equation ... 

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