Equivalent electrical sensors

Modeling and optimization of chemical sensors can be assisted by creating equivalent electrical circuits in which an ordinary electrical element, such as a resistor, capacitor, diode, and so on, can represent an equivalent nonelectrical physical parameter. The analysis of the electrical circuit then greatly facilitates understanding of the complex behavior of the physical system that it represents. This is a particularly valuable approach in the analysis and interpretation of mass and electrochemical sensors, as shown in subsequent chapters. The basic rules of equivalent circuit analysis are summarized in Appendix D. Table 3.1 shows the equivalency of electrical and thermal parameters that can be used in such equivalent circuit modeling of chemical thermal sensors. 

Rational optimization of performance should be the main goal in development of any chemical sensor. In order to do that, we must have some quantitative tools of determination of key performance parameters. As we have seen already, for electrochemical sensors those parameters are the charge-transfer resistance and the double-layer capacitance. Particularly the former plays a critical role. Here we outline two approaches the Tafel plots, which are simple, inexpensive, but with limited applicability, and the Electrochemical Impedance Spectroscopy (EIS), based on the equivalent electrical circuit model, which is more universal, more accurate, and has a greater didactic value. 

The equivalent electrical circuit approach has already been introduced in connection with analysis of mass sensors (Chapter 4). Its application is older and somewhat... 

Fig. 6.17 Equivalent electrical circuit representing potentiometric sensor with asymmetrically placed membrane (as in Fig. 6.16b). The field-effect transistor input to the voltmeter is added...

Frequency as an experimental variable offers additional design flexibility. This approach has several advantages. The most important one is the lack of polarization of the contacts. The second one is the fact that equivalent electrical circuit analysis can be used that aids in elucidation of the transduction mechanisms. Perhaps the most important distinguishing feature of this class of conductometric sensors is the fact that their impedance is measured in the direction normal to their surface. In fact, there may be no requirement on their DC conductivity and their response can be obtained from their capacitive behavior. In the following section, we examine so-called impedance sensors (or impedimetric sensors see Fig. 8.1b). 

Fig. 8.13 A capacitive impedance sensor. Schematic diagram (a) and equivalent electrical circuit (b) 1-vapor absorbing layer 2-Cr/Ni/Au plate of the capacitor (Cl) 3-Ta plate (C2) 4-top, porous metal plate 5 insulating substrate...

The simplest dielectrometer is a capacitor containing a layer of a material that can more or less reversibly take up chemical vapor of a given dielectric constant. The diagram of such a sensor and its equivalent electrical circuit is shown in Fig. 8.13 (Garverick and Senturia, 1982). 

FIGURE 4.17 Equivalent electrical circuit for electrochemical oxygen sensor a at the absence of polarization and b polarization of the solid electrolyte-electrode interface. (From Zhuiykov, S., In-situ" diagnostics of solid electrolyte sensors measuring oxygen activity in melts by developed impedance method, Meas. Sci. Technol. 17 (2006) 1570-1578. With permission.)... 

The key issue in these sensors is the interface between the ion selective membrane and the contact. The most convenient way to present this problem is in the form of the equivalent electrical circuit in which the resistances and capacitances have their usual electrochemical meaning (Fig.2). It is necessary to include the electrometer (or at least its input stage) in the analysis of these sensors. In most modern instruments the amplifier is an insulated gate field-effect transistor (IGFET) which has the input dc resistance of greater than 10 and the input capacitance on the order of picofarads. 

Murran reported a position sensor based on capacitance sensing methods [5]. The equivalent electrical circuit model of a pair of electrodes (ground electrode and control electrode) with an electrolyte droplet is shown in Fig. 7a. The equivalent capacitance is given by... 

So far various analyses of PZT sensors have been performed. These can be classified into two groups. One employed equivalent electric circuit (Mason 1958) and the other applied solutions of the field equations (Auld 1973). These are based on one-dimensional analysis, and thus results can not be readily extended to three-dimensional (3-D) analysis. This is because the PZT element used in an AE sensor is neither an infinite bar nor an infinite plate. 

A pH sensor, based on a.c. conductivity measurements of a thin polymer film, has been developed. The sensor consists of a planar interdigitated electrode array coated with a polypyrrole multilayer, built-up using the Langmuir-Blodgett technique. Impedance spectroscopy has been used to investigate the complex admittance of the device when exposed to aqueous solutions of different pH. The experimental data have been fitted to the theoretical response of an equivalent electrical network of capacitors and resistors. A response over the pH range 3.5 to 8 has been measured. 

The symbol Xsp(t) denotes the internal set-point composition expressed as an equivalent electrical current signal. This signal is used internally by the controller. Xsp t) is related to the actual composition set point x sp t) by the sensor-transmitter gain Ky (which is the slope of the calibration curve) ... 

Since driver s-side airbags were made mandatory in 1984, it is estimated that they have saved thousands of lives (Figure A). The way they work is relatively simple. A mechanical sensor in the front of the vehicle is set off by any sudden impact equivalent to hitting a brick wall at 10 mph. The sensor sends an electrical signal to a gas generator attached to the airbag. 

The temperature dependence of the fabricated open cavity FP device was evaluated experimentally. The sensor was placed in a programmable electric tubular furnace. The temperature of the furnace was increased from room temperature to 1,100°C at a step of 50°C. The cavity length as a function of the temperature is plotted in Fig. 7.11, where it increased nearly linearly following the increase of temperature. The temperature sensitivity of the particular FP device under test was estimated to be 0.074 nm °C 1 based on the linear fit of the measurement data. The equivalent coefficient of thermal expansion (CTE) of the fiber FP device was 2.4x10 6oC. ... 

The sensor head is lowered into a monitoring well. Upon contact with any fluid, the float ball is raised and a continuous tone emitted from an audible alarm. When the sensor head contacts the interface between LNAPL and groundwater, the change in conductive properties is detected by the electrical conductivity sensor and a beeping tone is emitted. The distances along the tape at which the two changes in the audible alarm occur are recorded as referenced from a presurveyed point on the lip of the monitoring well. The resultant distance is equivalent to the apparent thickness of the LNAPL in the well. 

Figure 15. Equivalent circuit of FET humidity sensor. Reproduced with permission from Ref. 9. Copyright 1985 Institute of Electrical Engineering of Japan.

Whatever the scale or method of culture (T-flask, Schott bottle, spinner flask, or bioreactor), the temperature of the culture medium with which the cells are in contact is always a fundamental state variable, because it interferes with growth and the production process. However, it is a process variable that is easy to monitor and control. On a small scale the culture flask is usually put in a thermostatically controlled incubator, where the measured value of a thermometer sends a sign to turn the heating on or off ( on-off control ). In bioreactors, there are equivalent systems, as will be seen later. Usually, however, a resistance thermometer sensor type is used (resistance temperature detector or RTD), the electric... 

In the previous section we considered the conditions under which mechanical resonances would occur in a TSM resonator. In considering only the mechanical properties of the crystal, however, we neglected consideration of how these resonances would actually be excited or detected. The device uses a piezoelectric substrate material in which the electric field generated between electrodes couples to mechanical displacement. This allows electrical excitation and detection of mechanical resonances. In constructing a practical sensor, changes in resonant frequency of the device are measured electrically. The electrical characteristics of the resonator can be described in terms of an equivalent-circuit model that describes the impedance (ratio of applied voltage to current) or admittance (reciprocal of impedance) over a range of frequencies near resonance. 

For other film characterization techniques, the sensitivity of the AW device to the mechanical or electrical properties of a film is used. The presence of two sensor responses (i.e., velocity and attenuation or, equivalently, the frequency and admittance magnitude) has the significant advantage that the amount of in-... 

As the readers may see, quartz crystal resonator (QCR) sensors are out of the content of this chapter because their fundamentals are far from spectrometric aspects. These acoustic devices, especially applied in direct contact to an aqueous liquid, are commonly known as quartz crystal microbalance (QCM) [104] and used to convert a mass ora mass accumulation on the surface of the quartz crystal or, almost equivalent, the thickness or a thickness increase of a foreign layer on the crystal surface, into a frequency shift — a decrease in the ultrasonic frequency — then converted into an electrical signal. This unspecific response can be made selective, even specific, in the case of QCM immunosensors [105]. Despite non-gravimetric contributions have been attributed to the QCR response, such as the effect of single-film viscoelasticity [106], these contributions are also showed by a shift of the fixed US frequency applied to the resonator so, the spectrum of the system under study is never obtained and the methods developed with the help of these devices cannot be considered spectrometric. Recent studies on acoustic properties of living cells on the sub-second timescale have involved both a QCM and an impedance analyser thus susceptance and conductance spectra are obtained by the latter [107]. 

The measuring cell is equipped with a water jacket for temperature control, which simultaneously holds the measuring capillary and two platinum electrodes, one of which is immersed into the liquid under study. The second is situated exactly opposite to the capillary and controls the size of bubbles. The electric signals from the gas flow rate sensor PSl and pressure transducer PS2, the microphone and the electrodes, as well as the compressor are connected to the PC which operates the apparatus and acquires the data.The value of t, equivalent to the time interval necessary to form a bubble of radius R, can be calculated using Poiseuille s law, as long as the conditions p = const in the system holds (Fainerman 1979, 1990, 1992),... 

Lastly, it may seem somewhat bizarre to associate a safety device with an explosion but this is the method used to inflate air bags (Figure 1.2), If a vehicle is involved in a frontal collision equivalent to hitting a brick wall at more than 12 to 15 miles per hour, then sensors detect the sudden deceleration and trigger an electrical device which detonates a mixture containing about 65 g of sodium azide (NaN3). The azide undergoes a relatively slow type of explosion... 

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