Variable-capacitance transducers

In Appendix 11A we found that simple manometers, externally mounted level indicators, variable capacitance transducers, and pneumatic valves exhibit inherent second-order dynamic behavior. Design all the systems above so that they exhibit underdamped behavior with a decay ratio equal to. In other words, find the conditions that the values of the physical parameters of these systems should satisfy in order for the device to exhibit underdamped behavior with decay ratio... 

The third way that a variable capacitance transducer can measure displacement is by having a fixed parallel plate capacitor with a slab of dielectric material having a dielectric constant different from that of air that can slide between the plates (Figure 2.1d). The effective dielectric constant for the capacitor will depend on how much of the slab is between the plates and how much of the region between the plates is occupied only by air. This, also, can yield a transducer with linear capacitance as a function of displacement characteristics. 

The electronic circuits used with variable capacitance transducers, are essentially the same as any other circuit used to measure capacitance. As with the inductance transducers, these circuits can take the form of a bridge circuit or specific circuits that measure capacitive reactance. One concern with capacitive sensors is that the sensor should be electrically shielded if there are electrically conductive objects in the vicinity of the sensor. Otherwise stray capacitances may affect the measurement. 

Figure 11A.2 Variable capacitance differential pressure transducer, (a) Differential pressure sensing element, (b) Pressure signal transmission system.

The following two references can be consulted for further details on the variable capacitance differential pressure transducer and the pneumatic control valve ... 

Such sensors are used to measure the pressure of a process or the pressure difference which is employed to compute a liquid level or a flow rate (orifice plate, venturi tube). The variable capacitance differential pressure transducer has become very popular. Figure 11A.2 shows a schematic of such a device. Pressure differences cause small displacements of the sensing diaphragm. The position of the sensing diaphragm... 

The model for a variable capacitance pressure transducer was developed in Appendix 11A and is given by eq. (13.9). It shows that the system is inherently second-order and can exhibit underdamped response. What does this mean for the applicability of such device ... 

Measuring device. This can be a variable capacitance differential pressure transducer (Section 13.3), measuring the pressure of a liquid column of height h. The dynamic response of the sensor is given by eq. (13.9). Let Ap = ah, where a is a constant. Then take... 

The variable capacitance differential pressure transducer is a very popular device which is used to sense and transmit pressure differences. Figure 11A.2 shows a schematic of such a device. A pressure signal is... 

IV.l Consider the flow control loop shown in Figure 13.2a. The following information is also available (1) An orifice plate is used to measure the flow (2) a variable capacitance differential pressure transducer is employed (see Appendix 11 A) to sense and transmit the pressure difference developed around the orifice plate (3) the controller is PI and (4) the control valve is of equal percentage, with the valve flow characteristic curve given by... 

The scheme of such a metal-arch capacitance transducer is shown in Fig. 50. The transducer is about 3 mm thick and has a diameter between 6 and 10 mm. The fixed electrode consists of a sputtered tantalum film on a glass substrate, the dielectric is a reactively sputtered tantalum pentoxide film, and the variable electrode consists of phosphor bronze and is either an arch shaped 15 pm thin foil obtained from a metal strip or a spherical dome shaped foil made by sputtering [245]. A maximum capacitance value of 340 pF could be obtained and short time and long time stability s were better than 0.2 pF min 1 and 0.05 pF hour 1 respectively. The sensitivity of such transducers was between 2000 and 8000 pF mm 1. Q factors have been obtained in... 

Schematic representation of a metal-arch capacitance transducer according to Jones et al. [245]. This capacitance transducer is of the variable-area electrode type. A tantalum/tantalum oxide film structure is deposited onto a flat glass substrate to obtain a suitably flat surface for contact with a flexible electrode which may be a thin metal foil possibly deposited in the shape of a dome or an arch...

Although there are a variety of pressure transducer types available, for most lespiiatory applications the newer solid-state pressure transducers offer the most attractive alternative. Variable-capacitance... 

On the other hand, there may be instances when seemingly unstable fractures are in fact valid stable fractures. The inability to adequately detect stable crack extension results in the appearance of an unstable test and the presumption of an invalid result. A variety of methods have been used to verify stability such as load-point displacement (LPD) as determined from the linear variable differential transducer (LVDT) used to control the test system actuator center-point displacement (CPD) as determined using an LVDT or capacitance extensometer placed in or near the flexure fixture a time record as generated with an XY recorder or strain as monitored with a strain gage centered about the crack plane on the compressive or back-face of the test specimen [12,13]. In addition, laser extensometers have also been used [14]. 

Besides the strain gauge type transducer, other pressure transducers may employ variable capacitance, variable inductance, or piezoelectric crystal sensors to detect pressure changes. The low level output pressure transducer can be used in systems controlling flammable and other hazardous gases if the system has been designed such that the electronic power levels being used to excite the transducer remain very low. They can even be used in Class I, Division II areas if the proper intrinsic safety barriers are used in conjunction. Like the pressure gauge, the transducer may have a... 

Schematic diagram of the Rheometrics RFSII. A dc motor C is controlled in steady rotation by a tachometer B and in sinusoidal or other angular position changes by a rotary variable capacitance transformer (RVCT) A. The sample is surrounded by a temperature ctmtrol bath D. The upper fixture is attached to a rebalance transducer E, described further in Figure 8.2.5. Adapted from Rheometrics (1 ).

Two types of capacitive transducers may be used variable gap or variable area. The most used arrangement. Fig. 4, is a pair of capacitors with a common central moving plate and two fixed plates or vice versa (variable gap). When the central plate moves with the mass relative to the fixed plates, one of the capacities increases and the other decreases. The same happens with the variable area type. An identical sinusoidal or square signal with frequency of several kHz is fed to each capacitor with opposite sign. The signal amplitude at the common point of both capacitors is proportional to the capacitance... 

Seismk Accelerometers, Fig. 4 Schematics of variable capacitance displacement transducers, (a) Variable gap. As the central plate (red) moves right, the gap with the left fixed plate (blue) increases (capacitance of left capacitor, yellow, decreases), and the gap with the right plate (blue) decreases (capacitance of the right capacitor, light blue. 

Seismic Acceierometers, Fig. 5 Normalized sensitivity of capacitive transducers of variable gap blue) and variable area red). A straight line is plotted for reference dotted) with the slope of the variable gap at the origin... 

In a variable area transducer with plate overlap dimensions a x h, the capacitance difference is Unear with the displacement x ... 

The sensitivity of the capacitative transducer with variable separation is... 

Electrical Variables. Included here are those variables which are measured as the product of a process, as in the case of measuring die current and voltage of a generator, and also as part of an instrumentation system. Numerous transducers, of course, yield electrical signals that represent by inference some other variable quantity, such as a temperature or pressure. Variables in this class include electromotive force, electric current, resistance, conductance, inductance, capacitance, and impedance. 

The operation of proximity sensors can be based on a wide range of principles, including capacitance, induction, Hall and magnetic effects variable reluctance, linear variable differential transformer (LVDT), variable resistor mechanical and electromechanical limit switches optical, photoelectric, or fiber-optic sensors laser-based distance, dimension, or thickness sensors air gap sensors ultrasonic and displacement transducers. Their detection ranges vary from micrometers to meters, and their applications include the measurement of position, displacement, proximity, or operational limits in controlling moving components of valves and dampers. Either linear or angular position can be measured ... 

The displacement transducer shown in Fig. 5 is generally one of two types. A linear-variable differential transformer (LVDT) is effectively a transformer where the coupling to the secondary winding(s) is a function of the position of a movable magnetic core. A capacitive displacement transducer (CDT) is a capacitor where the... 

The two capacitive techniques described above are used variable gap between plates and variable area. The first is quite nonlinear and usually requires electrostatic feedback to linearize the transducer response. Recently, electromagnetic feedback has also been proposed for MEMS accelerometers (Dwyer 2011). On the other hand, the variable area technique is more linear, and some devices using it operate in open-loop mode (e.g., Homeijer et al. 2011). Figure 10 shows a possible arrangement for a MEMS accelerometer. 

---