MECH 430 Project Pumping Station, Spring 2017

2 0.918 3 1.17 4 1.52 5 1.87 6.5 2.28 7 2.43 8 2.64 9 2.77 10 3.1 11 3.23 12 3.49 13 3.65 14 3.78 15 3.96 16 4.03 17 4.138 18 4.36 0 2 4 6 8 10 12 0 1 2 3 4 5 f(x) = 0.211092258440047 x + 0.78498646682 capacitor callibration c Column B Linear (C water level (cm) tau 6 8 10 12 14 16 18 20 2258440047 x + 0.784986466821886 or callibration curve olumn B Linear (Column B) water level (cm) BD645, BD647, BD649, BD651 NPN SILICON POWER DARLINGTONS P R O D U C T I N F O R M A T I O N 1 MAY 1993 - REVISED MARCH 1997 Copyright © 1997, Power Innovations Limited, UK Information is current as of publication date. Products conform to specifications in accordance with the terms of Power Innovations standard warranty. Production processing does not necessarily include testing of all parameters. G Designed for Complementary Use with BD646, BD648, BD650 and BD652 G 62.5 W at 25°C Case Temperature G 8 A Continuous Collector Current G Minimum hFE of 750 at 3 V, 3 A B C E TO-220 PACKAGE (TOP VIEW) Pin 2 is in electrical contact with the mounting base. MDTRACA 1 2 3 absolute maximum ratings at 25°C case temperature (unless otherwise noted) NOTES: 1. This value applies for tp ≤ 0.3 ms, duty cycle ≤ 10%. 2. Derate linearly to 150°C case temperature at the rate of 0.4 W/°C. 3. Derate linearly to 150°C free air temperature at the rate of 16 mW/°C. 4. This rating is based on the capability of the transistor to operate safely in a circuit of: L = 20 mH, IB(on) = 5 mA, RBE = 100 Ω, VBE(off) = 0, RS = 0.1 Ω, VCC = 20 V. RATING SYMBOL VALUE UNIT Collector-base voltage (IE = 0) BD645 BD647 BD649 BD651 VCBO 80 100 120 140 V Collector-emitter voltage (IB = 0) BD645 BD647 BD649 BD651 VCEO 60 80 100 120 V Emitter-base voltage VEBO 5 V Continuous collector current IC 8 A Peak collector current (see Note 1) ICM 12 A Continuous base current IB 0.3 A Continuous device dissipation at (or below) 25°C case temperature (see Note 2) Ptot 62.5 W Continuous device dissipation at (or below) 25°C free air temperature (see Note 3) Ptot 2 W Unclamped inductive load energy (see Note 4) ½LIC 2 50 mJ Operating junction temperature range Tj -65 to +150 °C Storage temperature range Tstg -65 to +150 °C Lead temperature 3.2 mm from case for 10 seconds TL 260 °C BD645, BD647, BD649, BD651 NPN SILICON POWER DARLINGTONS 2 MAY 1993 - REVISED MARCH 1997 P R O D U C T I N F O R M A T I O N NOTES: 5. These parameters must be measured using pulse techniques, tp = 300 µs, duty cycle ≤ 2%. 6. These parameters must be measured using voltage-sensing contacts, separate from the current carrying contacts. electrical characteristics at 25°C case temperature (unless otherwise noted) PARAMETER TEST CONDITIONS MIN TYP MAX UNIT V(BR)CEO Collector-emitter breakdown voltage IC = 30 mA IB = 0 (see Note 5) BD645 BD647 BD649 BD651 60 80 100 120 V ICEO Collector-emitter cut-off current VCE = 30 V VCE = 40 V VCE = 50 V VCE = 60 V IB = 0 IB = 0 IB = 0 IB = 0 BD645 BD647 BD649 BD651 0.5 0.5 0.5 0.5 mA ICBO Collector cut-off current VCB = 60 V VCB = 80 V VCB = 100 V VCB = 120 V VCB = 40 V VCB = 50 V VCB = 60 V VCB = 70 V IE = 0 IE = 0 IE = 0 IE = 0 IE = 0 IE = 0 IE = 0 IE = 0 TC = 150°C TC = 150°C TC = 150°C TC = 150°C BD645 BD647 BD649 BD651 BD645 BD647 BD649 BD651 0.2 0.2 0.2 0.2 2.0 2.0 2.0 2.0 mA IEBO Emitter cut-off current VEB = 5 V IC = 0 (see Notes 5 and 6) 5 mA hFE Forward current transfer ratio VCE = 3 V IC = 3 A (see Notes 5 and 6) 750 VCE(sat) Collector-emitter saturation voltage IB = 12 mA IB = 50 mA IC = 3 A IC = 5 A (see Notes 5 and 6) 2 2.5 V VBE(sat) Base-emitter saturation voltage IB = 50 mA IC = 5 A (see Notes 5 and 6) 3 V VBE(on) Base-emitter voltage VCE = 3 V IC = 3 A (see Notes 5 and 6) 2.5 V thermal characteristics PARAMETER MIN TYP MAX UNIT RθJC Junction to case thermal resistance 2.0 °C/W RθJA Junction to free air thermal resistance 62.5 °C/W 3 MAY 1993 - REVISED MARCH 1997 BD645, BD647, BD649, BD651 NPN SILICON POWER DARLINGTONS P R O D U C T I N F O R M A T I O N TYPICAL CHARACTERISTICS Figure 1. Figure 2. Figure 3. TYPICAL DC CURRENT GAIN vs COLLECTOR CURRENT IC - Collector Current - A 0·5 1·0 10 hFE - Typical DC Current Gain 50000 100 1000 10000 TCS130AD TC = -40°C TC = 25°C TC = 100°C VCE = 3 V tp = 300 µs, duty cycle < 2% COLLECTOR-EMITTER SATURATION VOLTAGE vs COLLECTOR CURRENT IC - Collector Current - A 0·5 1·0 10 VCE(sat) - Collector-Emitter Saturation Voltage - V 0·5 1·0 1·5 2·0 TCS130AB TC = -40°C TC = 25°C TC = 100°C tp = 300 µs, duty cycle < 2% IB = IC / 100 BASE-EMITTER SATURATION VOLTAGE vs COLLECTOR CURRENT IC - Collector Current - A 0·5 1·0 10 VBE(sat) - Base-Emitter Saturation Voltage - V 0·5 1·0 1·5 2·0 2·5 3·0 TCS130AC TC = -40°C TC = 25°C TC = 100°C IB = IC / 100 tp = 300 µs, duty cycle < 2% BD645, BD647, BD649, BD651 NPN SILICON POWER DARLINGTONS 4 MAY 1993 - REVISED MARCH 1997 P R O D U C T I N F O R M A T I O N MAXIMUM SAFE OPERATING REGIONS Figure 4. THERMAL INFORMATION Figure 5. MAXIMUM FORWARD-BIAS SAFE OPERATING AREA VCE - Collector-Emitter Voltage - V 1·0 10 100 1000 IC - Collector Current - A 0.01 0·1 1·0 10 SAS130AC BD645 BD647 BD649 BD651 MAXIMUM POWER DISSIPATION vs CASE TEMPERATURE TC - Case Temperature - °C 0 25 50 75 100 125 150 Ptot - Maximum Power Dissipation - W 0 10 20 30 40 50 60 70 80 TIS130AC 5 MAY 1993 - REVISED MARCH 1997 BD645, BD647, BD649, BD651 NPN SILICON POWER DARLINGTONS P R O D U C T I N F O R M A T I O N TO-220 3-pin plastic flange-mount package This single-in-line package consists of a circuit mounted on a lead frame and encapsulated within a plastic compound. The compound will withstand soldering temperature with no deformation, and circuit performance characteristics will remain stable when operated in high humidity conditions. Leads require no additional cleaning or processing when used in soldered assembly. MECHANICAL DATA TO220 ALL LINEAR DIMENSIONS IN MILLIMETERS ø 1,23 1,32 4,20 4,70 1 2 3 0,97 0,61 see Note C see Note B 10,0 10,4 2,54 2,95 6,0 6,6 14,55 15,90 12,7 14,1 3,5 6,1 1,07 1,70 2,34 2,74 4,88 5,28 3,71 3,96 0,41 0,64 2,40 2,90 VERSION 2 VERSION 1 NOTES: A. The centre pin is in electrical contact with the mounting tab. B. Mounting tab corner profile according to package version. C. Typical fixing hole centre stand off height according to package version. Version 1, 18.0 mm. Version 2, 17.6 mm. MDXXBE BD645, BD647, BD649, BD651 NPN SILICON POWER DARLINGTONS 6 MAY 1993 - REVISED MARCH 1997 P R O D U C T I N F O R M A T I O N IMPORTANT NOTICE Power Innovations Limited (PI) reserves the right to make changes to its products or to discontinue any semiconductor product or service without notice, and advises its customers to verify, before placing orders, that the information being relied on is current. PI warrants performance of its semiconductor products to the specifications applicable at the time of sale in accordance with PI's standard warranty. Testing and other quality control techniques are utilized to the extent PI deems necessary to support this warranty. Specific testing of all parameters of each device is not necessarily performed, except as mandated by government requirements. PI accepts no liability for applications assistance, customer product design, software performance, or infringement of patents or services described herein. Nor is any license, either express or implied, granted under any patent right, copyright, design right, or other intellectual property right of PI covering or relating to any combination, machine, or process in which such semiconductor products or services might be or are used. PI SEMICONDUCTOR PRODUCTS ARE NOT DESIGNED, INTENDED, AUTHORIZED, OR WARRANTED TO BE SUITABLE FOR USE IN LIFE-SUPPORT APPLICATIONS, DEVICES OR SYSTEMS. Copyright © 1997, Power Innovations Limited Chapter 2 Capacitive Sensing Technology 2.1 Overview This chapter describes the basic properties of capacitive sensor technologies and their use in various kinds of sensors in industrial applications. Physical properties as well as somelimitationsofcapacitivesensingaredescribedhere.Theuseofcapacitivesensors with hazardous fluids, such as gasoline based fuels, and various configurations of capacitive sensors used in the application of fluid level measurement in dynamic environments are described. In brief, this chapter provides information on capacitive sensing technology and its use in dynamic and hostile environments. 2.2 Characteristics of Capacitors 2.2.1 Overview Capacitors are the basic building blocks of the electronic world. To understand how capacitive sensors operate, it is important to understand the fundamental properties and principles of capacitors. This section provides details on the underlying principles of the capacitor. The physical, geometrical, and the electrical properties of capacitors are discussed in this section. 2.2.2 A Capacitor A capacitor is a device that consists of two electrodes separated by an insulator [1]. Capacitors are generally composed of two conducting plates separated by a non- E. Terzic et al., A Neural Network Approach to Fluid Quantity Measurement in Dynamic Environments, DOI: 10.1007/978-1-4471-4060-3_2, � Springer-Verlag London 2012 11 conducting substance called dielectric (er) [1, 2]. The dielectric may be air, mica, ceramic, fuel, or other suitable insulating material [2]. The electrical energy or charge is stored on these plates. Figure 2.1 illustrates a basic circuit configuration that charges the capacitor as soon as the switch is closed. Once a voltage is applied across the two terminals of the capacitor, the conducting plates will start to store electrical energy until the potential difference across the capacitor matches with the source voltage. The electrical charge remains on the plates after disconnecting the voltage source unless another component consumes this charge or the capacitor loses its charge because of leakage, since no dielectric is a perfect insulator. Capacitors with little leakage can hold their charge for a considerable period of time [2]. The plate connected with the positive terminal stores positive charge (or +Q) on its surface and the plate connected to the negative terminal stores negative charge (or -Q). The time required to fully charge a capacitor is determined by Time Constant (s). The value of the time constant describes the time it takes to charge a capacitor to 63% of its total capacity [1]. The time constant (s) is measured in seconds and can be defined as in Eq. 2.1, where, R is the resistor connected inline with the capacitor having C capacitance. s ¼ RC ð2:1Þ 2.2.3 Capacitance Capacitance is the electrical property of capacitors. It is the measure of the amount of charge that a capacitor can hold at a given voltage [2]. Capacitance is measured in Farad (F) and it can be defined in the unit coulomb per volt as: C ¼ Q V ð2:2Þ where, C is the capacitance in farad (F), Q is the magnitude of charge stored on each plate (coulomb), V is the voltage applied to the plates (volts). Battery Capacitor (C) +Q -Q + - Resistor (R) Fig. 2.1 Capacitor used in a circuit to store electrical charge 12 2 Capacitive Sensing Technology A capacitor with the capacitance of one farad can store one coulomb of charge when the voltage across its terminals is 1 V [2]. Typical capacitance values range from about 1 pF (10-12 F) to about 1,000 lF (10-3 F) [3]. An electric field will exist between the two plates of a capacitor if the voltage is applied to one of the plates [1]. The resulting electric field is due to the difference between the electric charges stored on the surfaces of each plate. The capacitance describes the effects on the electric field due to the space between the two plates. The capacitance depends on the geometry of the conductors and not on an external source of charge or potential difference [2, 4]. The space between the two plates of the capacitor is covered with dielectric material. In general, the capaci- tance value is determined by the dielectric material, distance between the plates, and the area of each plate (illustrated in Fig. 2.2). The capacitance of a capacitor can be expressed in terms of its geometry and dielectric constant as [5]: C ¼ er e0A d ð2:3Þ where, C is the capacitance in farads (F), er is the relative static permittivity (dielectric constant) of the material between the plates, e0 is the permittivity of free space, which is equal to 8:854 � 10�12 F=m; A is the area of each plate, in square meters and d is the separation distance (in meters) of the two plates. The capacitance phenomenon is related to the electric field between the two plates of the capacitor [6]. The electric field strength between the two plates decreases as the distance between the two conducting plates increases [1]. Lower field strength or greater separation distance will lower the capacitance value. The conducting plates with larger surface area are able to store more electrical charge; therefore, a larger capacitance value is obtained with greater surface area. A d (a) A d (b) A d (c) Fig. 2.2 Factors influencing capacitance value. a Normal. b Increased surface area, increased capacitance. c Decreased gap distance, increased capacitance 2.2 Characteristics of Capacitors 13 2.2.4 Capacitance in Parallel and Series Circuits The net capacitance of two or more capacitors, connected next to each other, depends on their connection configurations [3]. If two capacitors are connected in parallel, they both will have the same voltage across them; therefore, their net capacitance will be the sum of the two capacitances. The net capacitance of a parallel combination of capacitors is given as [4]: CT ¼ Q1 V þ Q2 V þ � � � þ Qn V ; or ð2:4Þ CT ¼ C1 þ C2 þ � � � þ Cn ð2:5Þ where, CT is the total capacitance of the capacitors connected in parallel. Figure 2.3 shows the circuit configuration of multiple capacitors having capaci- tances (C1, C2,…, C4). Both circuits (a) and (b) have the equivalent capacitance CT, which is the sum of all capacitances. However, if two or more capacitors are con- nected in series, the voltage across the two terminals may be different for each capacitor; although the electric charge will be the same on all of them [4]. The equivalent capacitance of capacitors connected in series can be stated as (Fig. 2.4): 1 CT ¼ V1 Q þ V2 Q þ � � � þ Vn Q ; or ð2:6Þ 1 CT ¼ 1 C1 þ 1 C2 þ � � � þ 1 Cn ð2:7Þ V C1 C2 C3 C4 V CT (a) (b) Fig. 2.3 Net capacitance of capacitors connected in parallel (a) V C1 C2 C3 (b) V CT Fig. 2.4 Net capacitance of capacitors connected in series 14 2 Capacitive Sensing Technology 2.2.5 Dielectric Constant The gap between the two surfacesofa capacitor is filled with a non-conducting material such as rubber, glass or, wood thatseparates the two electrodes of thecapacitor[4]. This material has a certain dielectric constant. The dielectric constant is the measure of a material’s influence on the electric field. The net capacitance will increase or decrease dependingonthetype of dielectricmaterial.Permittivityrelatestoa material’sabilityto transmit an electric field. In the capacitors, an increased permittivity allows the same charge to be stored with a smaller electric field, leading to an increased capacitance. According to Eq. 2.3, the capacitance is proportional to the amount of dielectric constant. As the dielectric constant between the capacitive plates of a capacitor rises, the capacitance will also increase accordingly. The capacitance can be stated in terms of the dielectric constant, as [4]: C ¼ er � C0 ð2:8Þ where, C is the capacitance in Farads, er is the dielectric constant and C0 is the capacitance in the absence of dielectric constant. Different materials have different magnitudes of dielectric constant. For example, air has a nominal dielectric constant equal to 1.0, and some common oils or fluids such as gasoline have nominal dielectric constant of 2.2. If gasoline is used as dielectric instead of air, the capacitance value using the gasoline as dielectric will increase by a factor of 2.2. This factor is called Relative dielectric constant or Relative electric permittivity [2]. Some commonly used dielectric materials and their corresponding dielectric values are listed in Table 2.1. 2.2.6 Dielectric Strength The electrical insulating properties of any material are dependent on dielectric strength [7]. The dielectric strength of an insulating material describes the Table 2.1 Commonly used dielectric materials and their values [4, 6] Material Dielectric constant Material Dielectric constant Accetone 19.5 Mica 5.7–6.7 Air 1.0 Paper 1.6–2.6 Alcohol 25.8 Petroleum 2.0–2.2 Ammonia 15–25.0 Polystyene 3.0 Carbon dioxide 1.0 Powdered milk 3.5–4.0 Chlorine liquid 2.0 Salt 6.1 Ethanol 24.0 Sugar 3.3 Gasoline 2.2 Transformer oil 2.2 Glycerin 47.0 Turpentine oil 2.2 Hard paper 4.5 Water 80.0 2.2 Characteristics of Capacitors 15 maximum electric field of that material. If the magnitude of the electric field across the dielectric material exceeds the value of the dielectric strength, the insulating properties of the dielectric material will breakdown and the dielectric material will begin to conduct [1]. The breakdown voltage or rated voltage of a capacitor represents the largest voltage that can be applied to the capacitor without exceeding the dielectric strength of the dielectric material [1]. The applied voltage across a capacitor must be less than its rated voltage. The operating voltage across a capacitor can be increased depending on the insulating material or the dielectric constant. Teflon and Polyvinyl chloride have greater dielectric strength. The dielectric constant can be increased by adding high dielectric constant filler material [8]. Table 2.2 lists the dielectric strength values for different types of materials at room temperature. Factors such as thickness of the specimen, operating temperature, frequency, and humidity can affect the strength of the dielectric materials. 2.3 Capacitive Sensor Applications 2.3.1 Overview A capacitive sensor converts a change in position, or properties of the dielectric material into an electrical signal [9]. According to the Eq. 2.3 in Sect. 2.2.3, capacitive sensors are realized by varying any of the three parameters of a capacitor: distance (d), area of capacitive plates (A), and dielectric constant (er); therefore: C ¼ fðd; A; erÞ ð2:9Þ A wide variety of different kinds of sensors have been developed that are primarily based on the capacitive principle described in Eq. 2.3. These sensors’ functionalities range from humidity sensing, through level sensing, to Table 2.2 Approximate dielectric strengths of various materials [4] Material Dielectric strength (106 V/m) Material Dielectric strength (106 V/m) Air (dry) 3 Polystyrene 24 Bakelite 24 Polyvinyl chloride 40 Fused quartz 8 Porcelain 12 Mylar 7 Pyrex glass 14 Neoprene rubber 12 Silicone oil 15 Nylon 14 Strontium titanate 8 Paper 16 Teflon 60 Paraffin-impregnated paper 11 16 2 Capacitive Sensing Technology displacement sensing [10]. A number of different kinds of capacitance based sensors used in a variety of industrial and automotive applications are discussed in this section. 2.3.2 Proximity Sensing A proximity sensor is a transducer that is able to detect the presence of nearby objects without any physical contact. Normally a proximity sensor emits an electromagnetic or electrostatic field, or a beam of electromagnetic radiation (e.g. infrared), and detects any change in the field or return signal. Capacitive type proximity sensors consist of an oscillator whose frequency is determined by an inductance–capacitance (LC) circuit to which a metal plate is connected. When a conducting or partially conducting object comes near the plate, the mutual capacitance changes the oscillator frequency. This change is detected and sent to the controller unit [11]. The object being sensed is often referred to as the prox- imity sensor’s target. Figure 2.5 shows an example of the capacitive proximity sensor. As the distance between the proximity sensor and the target object gets smaller, the electric field distributed around the capacitor experiences a change, which is detected by the controller unit. The maximum distance that a proximity sensor can detect is defined as ‘nominal range’. Some sensors have adjustments of the nominal range or ways to report a graduated detection distance. A proximity sensor adjusted to a very short range is often used as a touch switch. Capacitive proximity detectors have a range twice that of inductive sensors, while they detect not only metal objects but also dielectrics such as paper, glass, wood, and plastics [12]. They can even detect through a wall or cardboard box [12]. Because the human body behaves as an electric conductor at low frequencies, capacitive sensors have been used for human tremor measurement and in intrusion alarms [12]. Capacitive type proximity sensors have a high reliability and long functional life because of the absence of mechanical parts and lack of physical contact between sensor and the sensed object. An example of a proximity sensor is a limit switch, which is a mechanical push- button switch that is mounted in such a way that it is activated when a mechanical part or lever arm gets to the end of its intended travel [13]. It can be implemented Capacitive Proximity Sensor Target Object Electric Field Fig. 2.5 Capacitance based proximity sensor 2.3 Capacitive Sensor Applications 17 in an automatic garage door opener; where the controller needs to know if the door is all the way open or all the way closed [13]. Other applications of the capacitive proximity sensors are: • Spacing—If a metal object is near a capacitor electrode, the mutual capacitance is a very sensitive measure of spacing [14]. • Thickness measurement—Two plates in contact with an insulator will measure the insulator thickness if its dielectric constant is known, or the dielectric constant if the thickness is known [14]. • Pressure sensing—A diaphragm with stable deflection properties can measure pressure with a spacing-sensitive detector [14]. 2.3.3 Position Sensing A position sensor is a device that allows position measurement. Position can be either an absolutepositionorarelativeone[15].Linearaswellasangularpositioncanbemeasured using position sensors. Position sensors are used in many industrial applications such as fluid level measurement, shaft angle measurement, gear position sensing, digital encoders and counters, and touch screen coordinate systems. Traditionally, resistive type potentiometers were used to determine rotary and linear position. However, the limited functional life of these sensors caused by mechanical wear has made resistive sensors less attractive for industrial applications. Capacitive type position sensors are normally non-mechanical devices that determine the position based on the physical parameters of the capacitor. Position measurement using a capacitive position sensor can be performed by varying the three capacitive parameters: Area of the capacitive plate, Dielectric constant,and Distance betweenthe plates.The following applicationsare some examples of the utilization of capacitive position sensors in: • Liquid level sensing—Capacitive liquid level detectors sense the liquid level in a reservoir by measuring changes in capacitance between conducting plates which are immersed in the liquid, or applied to the outside of a non-conducting tank [14]. • Shaft angle or linear position—Capacitive sensors can measure angle or position with a multi-plate scheme giving high accuracy and digital output, or with an analogue output with less absolute accuracy but faster response and simpler circuitry. • X–Y tablet—Capacitive graphic input tablets of different sizes can replace the computer mouse as an x–y coordinate input device. Finger-touch-sensitive devices such as iPhone [16], z-axis-sensitive and stylus-activated devices are available. • Flow meter—Many types offlow meters convert flow to pressure or displacement, using an orifice for volume flow or Coriolis Effect force for mass flow. Capacitive sensors can then measure the displacement. 18 2 Capacitive Sensing Technology 2.3.4 Humidity Sensing The dielectric constant of air is affected by humidity. As humidity increases the dielectric increases [17]. The permittivities of atmospheric air, of some gases, and of many solid materials are functions of moisture content and temperature [10]. Capacitive humidity devices are based on the changes in the permittivity of the dielectric material between plates of capacitors [10]. Capacitive humidity sensors commonly contain layers of hydrophilic inorganic oxides which act as a dielectric [18]. Absorption of polar water molecules has a strong effect on the dielectric constant of the material [18]. The magnitude of this effect increases with a large inner surface which can accept large amounts of water [18]. The ability of the capacitive humidity sensors to function accurately and reliably extends over a wide range of temperatures and pressures. They also exhibit low hysteresis and high stability with minimal maintenance requirements. These features make capacitive humidity sensors viable for many specific operating conditions and ideally suitable for a system where uncertainty of unaccounted conditions exists during operations. There are many types of capacitive humidity sensors, which are mainly formed with aluminium, tantalum, silicon, and polymer types [10]. 2.3.5 Tilt Sensing In recent years, capacitive-type micro-machined accelerometers are gaining popularity. These accelerometers use the proof mass as one plate of the capacitor and use the other plate as thebase.Whenthesensor is accelerated, theproofmass tendsto move; thus, the voltage across the capacitor changes. This change in voltage corresponds to the applied acceleration. Micromachined accelerometers have found their way into automotive airbags, automotive suspension systems, stabilization systems for video equipment, transportation shock recorders, and activity responsive pacemakers [19]. Capacitive silicon accelerometers are available in a wide range of specifications. A typical lightweight sensor will have a frequency range of 0–1,000 Hz, and a dynamic range of acceleration of ±2 to ±500 g [19]. Analogue Devices, Inc. [20] has introduced integrated accelerometer circuits with a sensitivity of over 1.5 g [14]. With this sensitivity, the device can be used as a tiltmeter [14]. 2.4 Capacitors in Level Sensing 2.4.1 Overview The general properties of the capacitor described in Sect. 2.2.3 can be used to measure the fluid level in a storage tank. In a basic capacitive level sensing system, capacitive sensors have two conducting terminals that establish a capacitor. If the 2.3 Capacitive Sensor Applications 19 gap between the two rods is fixed, the fluid level can be determined by measuring the capacitance between the conductors immersed in the liquid. Since the capac- itance is proportional to the dielectric constant, fluids rising between the two parallel rods will increase the net capacitance of the measuring cell as a function of fluid height. To measure the liquid level, an excitation voltage is applied with a drive electrode and detected with a sense electrode. Figure 2.6 illustrates a basic set-up of a liquid level measurement system. In this section, various aspects and configurations of capacitive fluid level measurement systems have been described in detail. 2.4.2 Sensing Electrodes The sensing electrodes of the capacitive sensor could be shaped into various forms and structures. The geometry of the sensing electrodes influences the electric field between them. For example, the capacitance between two parallel rods will be different from that between two parallel plates because of the nature of electric field distribution around an electrically charged object. A few types of sensing electrodes, such as cylindrical rods, rectangular plates, helixical wires, and tubular shaped capacitors are described in this subsection. 2.4.2.1 Cylindrical Rods Cylindrical rods are made of conductors, where the negative electrode stores the negative charge and the positive electrode stores the positive charge. An electrical field will exist between the two electrodes if a voltage is applied across them. Figure 2.7 illustrates the two cylindrical rods separated by distance d. The capac- itance between the two parallel rods can be determined by the following rule [21]: C ¼ pe0er ln d r L; If d � r ð2:9Þ Drive electrode Sense electrode Fluid Fig. 2.6 Basic liquid level sensing system 20 2 Capacitive Sensing Technology C ¼ pe0er ln d þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2 � 4r2 p 2r ! L; where d � r ð2:10Þ where, C is the capacitance in farads (F), er is the relative static permittivity (dielectric constant) of the material between the plates, e0 is the permittivity of free space, which is equal to 8:854 � 10�12 F=m; L is the rod length in meters, d is the separation distance (in meters) of the two rods, r is the radius of the rod in meters. 2.4.2.2 Cylindrical Tubes Cylindrical tube based electrodes are commonly used in tubular capacitive sensors. Tubular capacitive sensors have a simple design, which makes them easier to manufacture. Maier [22] has used capacitive sensors that are formed as concentric, elongated cylinders for sensing the fuel level in aircraft fuel tanks. The capacitance of the sensor varies as a function of the fraction of the sensor wetted by the fuel and the un-wetted fraction in the airspace above the fuel/air interface [22]. Figure 2.8 shows an illustration of the cylindrical tube capacitor. A cylindrical capacitor can be thought of as having two cylindrical tubes, inner and outer. The inner cylinder can be connected to the positive terminal, whereas the outer cylinder can be connected to the negative terminal. An electric field will exist if a voltage is applied across the two terminals. If ra is the radius of the inner cylinder and rb is the radius of the o