Capacitors frequency variation

The remarkable stability of the capacitance of the SIKO against variations in bias, temperature, frequency and time of operation is a consequence of the superior properties of its ONO dielectric. In contrast to aluminum and tantalum capacitors, the SIKO is a symmetrical device. It shows no significant voltage dependence of the capacitance, as the high s ceramic capacitors do. Only polymeric capacitors show a lower dependence of capacitance on bias than a SIKO. 

One assumes that the double layer admittance is that of a pure capacitor. Thus its value should be independent of frequency. The graphical variation of Y with Y" is shown schematically in Fig. 11.9. More details may be found in Ref. 9. 

Electrochemical impedance spectroscopy (EIS) analysis of such electrodes is shown in Figure 7.2. At high frequencies, the imaginary part of the impedance tends to zero, whereas at low frequencies it increases sharply, thus approaching the variation of impedance with the frequency expected for a pure capacitor (see Chapter 1). In the intermediate frequencies, a semicircle can be observed, the amplitude of the loop varying with the nature of the activated material. This semicircle can be... 

For applications requiring a large sensing surface area, such as those measuring permittivity and conductivity of tissue, an interdigital capacitor was introduced as the capacitive element in an LC circuit. The change in capacitance resulted in a variation of the impedance and resonant frequency of the LC sensor, which can be interpreted as alterations in the permittivity and conductivity of tissue. The sensor was implanted into the phantom tissue and a saturation depth was achieved such that data were only collected from the tissue layer of interest (Yvanoff and Venkataraman 2009). 

For sensing moisture content, a parallel-plate capacitor may be used [78-80]. Capacitance measurements are taken at frequencies of 1.0-4.5 MHz with a Hewlett-Packard 4192 LF Impedance Analyzer equipped with the 16096A test fixture and a specially constructed electrode assembly. Variations in kernel shape and thickness cause capacitance variations. For these reasons, the thickness, mass, and projected area of individual kernels must also be measured [80]. 

The impedance plot shown in Figure 2.1a vs. or the Nyquist plot) corresponds to an electrochemical cell (electrode/NaCl solution/electrode) and the equivalent circuit consists of a resistance (R) in parallel with a capacitor (C), which is represented as RQ, while Figure 2.1b shows the variation of the phase angle 4) = arc tan(Zi g/Z,e ) with frequency (4) vs./), but other typical impedance representations correspond to the variation of Z, and -Zj g with frequency (Bode plots), as indicated in Figure 2.1c and 2.1d. This latter representation allows the determination of the interval of frequency associated with a given relaxation process, between KT and 10 Hz, with a maximum frequency around 2 x 10 Hz, for the NaCl solution... 

Compensation for temperature-related frequency shifts can be accomplished by connecting a reactance (e.g., a variable voltage capacitor called a varactor) in series with the resonator. The effect of this reactance is to puU the frequency to cancel the effect of frequency drift caused by temperature changes. An example of a frequency vs. temperature characteristic both before and after compensation is shown in Fig. 3.8. Notice that the general form for the characteristic before compensation follows the cubic variation given earlier in this section. 

The resulting graphs of simulation (dotted blue line) and real measurement (solid red line) are shown in Fig. 4. As can be seen on the Bode and Nyquist plot, the two resulting curves match very well. However, the simulation cannot take any voltage and frequency depending capacity variations into account which are naturally present in ceramic capacitors. Therefore, a small inductance in series was added to influence the simulative results and give a good fit between simulation and measurement. 

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