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1. Introduction
In designing measurement systems, there are a number of steps that need to be considered:
1. Identification of the nature of the measurement required.
For example, what is the variable to be measured, its nominal value, the range of values that might have to be measured, the accuracy required, the required speed of measurement, the reliability required, the environmental conditions under which the measurement is to be made, etc.
2. Identification of possible sensors.
This means taking into account such factors as their range, accuracy, linearity, speed of response, reliability, maintainability, life, power supply requirements, ruggedness, availability, cost. The sensor needs to fit the requirements arrived at in 1 and also be capable, with suitable signal processing, to give the required output for use in a control system and/or display.
3. Selection of appropriate signal processing.
This element needs to take the output signal from the sensor and modify it in such a way as to enable it to drive the required display or be suitable for control of some device. For example, control applications might require a 4 to 20 mA current to drive an actuator.
4. Identification of the required display.
This means considering the form of display that is required. Is it to be an indicator or recorder? What is the purpose of the display? This chapter is a consideration of some examples of instrumentation systems and the selection of the elements in such systems.
2. Case studies
The following gives case studies of instrumentation systems.
2.1 A temperature measurement
Requirement: Determination of temperature of a liquid in the range 0 C to 100 C where only rough accuracy is required. The situation might be the determination of the temperature of the cooling water for a car engine and its display as a pointer moving across a scale marked to indicate safe and unsafe operating temperatures.
Sensor: A solution might be to use a thermistor as a sensor. It is cheap and robust. This is the commonly used solution with car engine coolant.
Signal processing: The resistance change of the thermistor has to be converted into a voltage which can then be applied across a meter and so converted to a current through it and hence a reading on the meter related to the temperature. FIG. 1 shows a possible solution involving a potential divider circuit to convert the resistance change into a voltage change. Suppose we use a 4.7 k-Ohm, bead thermistor. This has a resistance of 4.7 k-Ohm at 25°C, 15.28 k-Ohm at 0 C and 0.33 k-Ohm at 100 C. The variable resistor might be 0 to 10 k-Ohm. It enables the sensitivity of the arrangement to be altered.
However, if the variable resistor was set to zero resistance then, without a protective resistor, we could possibly have a large current passed through the thermistor. The protective resistor is there to prevent this occurring. The maximum power that the thermistor can withstand is specified as 250 mW. Thus, with a 6 V supply, the variable resistor set to zero resistance, the protective resistance of R1, and the thermistor at 100°C, the current I through the thermistor is given by V=IR as 6 = 7(0 + R + 330), and so:
I = 6/R+330
FIG. 1 Temperature measurement
The power dissipated by the thermistor I^2 x 330 and so if we want this to be significantly below the maximum possible, say 100 mW, then we have:
0.100 (6/R+330)^2 x 330
Hence R needs to be about 15 ohm.
Display: When the temperature of the thermistor is 0 C its resistance is 15.28 k-Ohm. If we set the variable resistor as, say, 5 k-Ohm and the protective resistor as 15 ohm then the voltage output when the supply is 6 V is:
output voltage = 1.48 V
When the temperature rises to 100°C the output voltage becomes:
output voltage = 5.63 V
Thus, over the required temperature range, the voltage output varies from 1.48 V to 5.63 V. A voltmeter to cover this range could be used to display the output.
In general, calibration of thermometers is by determining their response at temperatures which are specified as the standard values for freezing points and boiling points for pure materials.
Alternatively, calibration at these and other temperatures within the range can be obtained by comparison with the readings given by a standard thermometer.
2.2 An absolute pressure measurement
FIG. 2 Diaphragm pressure gauge: (a) basic form of sensor, (b) possible
arrangement of strain gauges on diaphragm, (c) the Wheatstone bridge signal
processor
Requirement: Measurement of the manifold absolute pressure in a car engine as part of the electronic control of engine power.
Sensor: A sensor that is used for such a purpose is a diaphragm pressure gauge. FIG. 2(a) shows the basic form of a diaphragm pressure gauge which is often used in such circumstances. The diaphragm is made of silicon with the strain gauges diffused directly into its surface. Four strain gauges are used and so arranged that when two are in tension the other two are in compression (FIG. 2(b)). Signal processing: The four gauges are so connected as to form the arms of a Wheatstone bridge (FIG. 2(c)). This gives temperature compensation since a change in temperature affects all the gauges equally. Thus the output from the sensor with its signal processing is a voltage which is a measure of the pressure.
Display: If required, the output voltage could be displayed on a meter, possibly following some amplification. Calibration of pressure gauges is usually with a dead-weight pressure system. FIG. 3 shows the basic form of such a system. The calibration pressures are generated by adding standard weights to the piston tray, the pressure then being W/A, where W is the total weight of the piston, tray and standard weights and A the cross-sectional area of the piston. After the weights have been placed on the tray, the screw-driven plunger is screwed up to force the oil to lift the piston-weight assembly.
Then the oil is under the pressure given by the piston-weight assembly since it is able to support that weight. By adding weights to the piston tray a gauge can be calibrated over its range.
FIG. 3 Dead-weight pressure gauge calibration
FIG. 4 Rotary potentiometer
2.3 Detection of the angular position of a shaft
Requirement: Detection of the angular position of the throttle shaft of a car to give an indication of the throttle opening, and hence the driver's power demand on the engine, as part of a car engine management system.
Sensor: A rotary potentiometer (FIG. 4) is generally used with the potentiometer wiper being rotated over the potentiometer track.
Signal processing: For a 5 V d.c. voltage connected across the potentiometer, with the throttle closed and the engine idling the wiper can be at a position close to the 0 V terminal and so give a small voltage output, typically about 0.5 V. As the throttle is opened, the shaft rotates and the wiper moves over the track so that at wide-open throttle the wiper is nearly at the end of its track and the output voltage has risen to about 4.3 V. The engine management system uses an operational amplifier to compare the output from the potentiometer with a fixed voltage of 0.5 V so that the op-amp gives a high output when the potentiometer output is 0.5 V or lower and a low output when higher. This high-low signal, together with signals from other sensors, is fed to a microprocessor which then can give an output to control the engine idle speed.
2.4 Air flow rate determination
Requirement: Measurement of the flow rate for the inflow of air in a car manifold in an electronic controlled engine. A simple, and cheap, measurement of the mass rate of flow of air is required with the output being an electrical signal which can be used for control purposes.
Sensor: One method that is used with cars is the hot-wire anemometer.
This sensor consists of a platinum wire which is heated by an electrical current passing through it to about 100 to 200°C. The temperature of the wire will depend on the cooling generated by the flow of air over the wire. Thus, since the electrical resistance of the wire will depend on its temperature, the resistance is a measure of the rate of flow of air over the heated wire. FIG. 5(a) shows the basic form of such a sensor.
FIG. 5 Hot-wire anemometer and its signal processing
Signal processing: The resistance change is transformed into a voltage change by incorporating the sensor as one of the arms of a Wheatstone bridge (FIG. 5(b)). The bridge is balanced at zero rate of flow and then the out-of-balance voltage is a measure of the rate of flow. This voltage is fairly small and so has generally to be amplified.
An alternative arrangement which is used is: Sensor: The vortex flow sensor with the vortex frequency measured by means of a semiconductor pressure sensor.
Signal processing: The output of the pressure sensor is typically a frequency of about 100 Hz when the engine is idling and rising to about 2000 Hz at high engine speed. Signal conditioning is used to transform this output into a square-wave signal which varies between 0.6 V and 4.8 V and can then be processed by the engine control unit.
2.5 Fluid level monitoring
FIG. 6 Liquid level monitoring
Requirement: Monitoring the level of a liquid to indicate when the level falls below some critical value.
Sensor: One method would be to use a magnetic float (FIG. 6) which rises with the liquid level and opens a reed switch (see Section 2.2.8) when the level falls too low.
Signal conditioning: The reed switch is in series with a 39 ohm resistor so that this is switched in parallel with a 1 k-Ohm resistor by the action of the reed switch. Opening the reed switch thus increases the resistance from about 37 ohm to 1 k-ohm. Such a resistance change can be further transformed by signal conditioning to give suitable light on-off signals.
2.6 Measurement of relative humidity
Requirement: Direct measurement of relative humidity without the need for using the operator to use tables to convert temperature values to relative humidity. The traditional method of measuring relative humidity involves two thermometers, one with its bulb directly exposed to the air and giving the 'dry temperature' and the other with its bulb covered with muslin which dips into water. The rate of evaporation from the wet muslin depends on the amount of water vapor present in the air; when the air is far from being saturated then the water evaporates quickly, when saturated there is not net evaporation. This rate of evaporation affects the temperature indicated by the thermometer, so giving the 'wet temperature'. Tables are then used to convert these readings into the humidity.
Sensor: Rather than use a 'wet' thermometer element, a capacitive humidity sensor can be used. The sensor (FIG. 7(a)) consists of an aluminum substrate with its top surface oxidized to form a porous layer of aluminum oxide. On top of the oxide a very thin gold layer is deposited, this being permeable to water vapor.
Electrical connections are made to the gold layer and the aluminum substrate, the arrangement being a capacitor with an aluminum oxide dielectric. Water vapor enters the pores of the aluminum oxide and changes its dielectric constant and hence the capacitance of the capacitor. The capacitance thus gives a measure of the amount of water vapor present in the air.
Signal processing: FIG. 7(b) shows the type of system that might be used with such a sensor. For the capacitive sensor, signal conditioning is used to transform the change in capacitance to a suitable size voltage signal. A temperature sensor is also required since the maximum amount of water vapor that air can hold depends on the temperature and thus to compute the humidity the microprocessor needs to know the temperature, this also requiring signal conditioning to get a signal of the right size. An ADC is then used to convert the signals to digital for processing by a microprocessor system; a microcontroller is likely to be used with an integrated ADC, microprocessor and memory on a single chip, there then being a number of input connections for analogue signals to the system. The microprocessor takes the values for the two inputs and can use a 'look-up' table in its memory to determine the value of the relative humidity. This is then outputted to a digital meter.
FIG. 7 Relative humidity measurement
FIG. 8 LVDT output
2.7 Dimension checking
Requirement: A method by which the dimensions of components can be checked.
Sensor: LVDT displacement sensors can be used.
Signal processing: The e.m.f induced in a secondary coil by a changing current I in the primary coil is given by e = M di/dt, where M is the mutual inductance, its value depending on the number of turns on the coils and the magnetic linkage between the coils, thus the material in the core of the coils. Thus, for a sinusoidal input current to the primary coil of an LVDT, alternating e.m.f s are induced in the two secondary coils A and B. The two outputs are in series so that their difference is the output. FIG. 8 shows how the size and phase of the alternating output changes with the displacement of the core. The same amplitude output voltage is produced for two different displacements. To give an output voltage which distinguishes between these two situations, a phase sensitive demodulator, with a low pass filter, is used to convert the output into a d.c. voltage which gives a unique value for each displacement (FIG. 9).
The coils with simple LVDT sensors and parallel-sided coils exhibit non-linearities as the ferrite core approaches the ends of the coils. This can be corrected for by using stepped windings or, more cheaply, by using a microprocessor system and programming it to compensate for such non-linearities. Such a microprocessor system could also be used to receive the inputs from a number of such LVDT sensors and compare the outputs with the required dimensions of the components and give outputs indicating divergence.
2.8 Temperature of a furnace
Requirement: To monitor the temperature of a furnace operating from room temperature up to 500°C with an accuracy of plus or minus a few degrees.
Sensor: A Chromel-aluminum thermocouple (see Table 1), with a sensitivity of 41 mV/°C and range -1890 to 1260°C, can be used.
Signal processing: Cold junction compensation and amplification are required for the output to be displayed on a meter. Calibration can be against the fixed temperature points or a secondary standard thermometer.
FIG. 9 LVDT d.c. output
3. Data acquisition systems
Frequently, modem instrumentation systems involve the use of PCs*and the term data acquisition is used.
Data acquisition is the process by which data from sensors is transformed into electrical signals that are converted into digital form for processing and analysis by a computer.
A data acquisition system (DAQ) will thus include:
1. Sensors
2. Signal processing to get the signal into the required form and size for the data acquisition hardware.
3. Data acquisition hardware to collect and convert analogue signals to digital format and digital signals for transfer to the computer. Allow for signals from the computer to control the process.
4. A computer which is loaded with data acquisition software to enable analysis and display of the data.
FIG. 10 Basic elements of a digital acquisition card
Personal computer-based systems frequently use plug-in boards for the interface between the computer and the sensors. These boards carry the components for the data acquisition so that the computer can store data, carry out data processing, control the data acquisition process and issue signals for use in control systems. The plug-in board is controlled by the computer and the digitized data transferred from the board to the memory of the computer. The processing of the data is then carried out within the computer according to how it is programmed.
Data acquisition boards are available for many computers and offer, on a plug-in board, various combinations of analog, digital and timing/counting inputs and outputs for interfacing sensors with computers. The board is a printed circuit board that is inserted into an expansion slot in the computer, so connecting it into the computer bus system. FIG. 10 shows the basic elements of a simple data acquisition board. Analogue inputs from the sensors are accessed through a multiplexer. A multiplexer is essentially an electronic switching device which enables a number of inputs to be sampled and each in turn fed to the rest of the system. An analogue-to-digital converter then converts the amplified sampled signal to a digital signal. The control element can be set up to control the multiplexer so that each of the inputs is sequentially sampled or perhaps samples are taken at regular time intervals or perhaps just a single sensor signal is used. The other main element is the bus interface element which contains two registers, the control and status register and the data register. The term register is used for memory locations within a microprocessor.
Consider now what happens when the computer is programmed to take a sample of the voltage input from a particular sensor. The computer first activates the board by writing a control word into the control and status register. This word indicates the type of operation that is to be carried out. The result of this is that the multiplexer is switched to the appropriate channel for the sensor concerned and the signal from that sensor passed, after amplification at an instrumentation amplifier, to the analogue-to-digital converter. The outcome from the ADC is then passed to the data register and the word in the control and status register changed to indicate that the conversion is complete. Following that signal, the computer sets the address bus to select the address of where the data is stored and then issues the signal on the control bus to read the data and so take it into storage in the computer for processing. In order to avoid the computer having to wait and do nothing while the board carries out the acquisition, an interrupt system can be used whereby the board signals the computer when the acquisition is complete and then the computer microprocessor can interrupt any program it was carrying out and jump from that program to a subroutine which stores its current position in the program, reads the data from the board and then jumps back to its original program at the point where it left it.
With the above system, the acquired data moves from the board to the microprocessor which has to interrupt what it is doing, set the memory address and then direct the data to that address in the memory. The microprocessor thus controls the movement. A faster system is to transfer the acquired data directly from the board to memory without involving the microprocessor. This is termed direct memory access (DMA). To carry this out, a DMA controller is connected to the bus. This controller supplies the memory address locations where the data is to be put and so enables the data to be routed direct to memory.
FIG. 11 Graphical programming
FIG. 12 Using a data logger
3.1 LabVIEW
The software for use with a data-acquisition system can be specially written for the data acquisition hardware concerned, developed using off-the-shelf software that is provided with the hardware used, or developed using a general package which provides a graphical interface for programming, e.g. LabVIEW. LabVIEW is a programming language and set of subroutines developed by National Instruments for data acquisition and scientific programming. It is a graphical programming language which has each subprogram and program structure represented by icons. All the programming is then done graphically by drawing lines between connection points on the various icons. The resulting picture shows the data flow. FIG. 11 illustrates this for the simple program of getting input A, getting input B, adding A and B and then displaying the result.
Programs that use one or more LabVIEW functions are called virtual instruments. Each virtual instrument has a front panel and a diagram.
The front panel may be thought of as representing the front panel of an instrument with the instrument controls and display. The diagram contains the actual program and is thus basically of the form shown in FIG. 11.
3.2 Data loggers
Because sensors have often to be located some distance from the computer in which the data processing occurs, instead of running long wires from the sensors to the computer with degradation of the signal en-route, signal conditioning modules are often located close to the sensors and provide digital signal outputs which can then be fed to the computer over a common bus (FIG. 12) or transferred to it on a portable memory card. Such modules are termed data loggers. Loggers are intelligent devices which, as well as data acquisition, are able to be programmed to make decisions based on system conditions.
3.3 Data transfer
Digital data can be communicated between devices by serial or parallel communication. With serial communication each word is sent in a sequence of bits along the same wire, with parallel communication a number of wires are used and each of the bits of a word is sent simultaneously along their own wires. For anything other than very short distances, parallel communication is too expensive and so serial communication is used. A communication link can be established using one of the serial interface standards such as RS-232 or RS-422. The standard interface most commonly used for parallel communication is the general purpose instrument bus (GPIB) IEEE-488. Such standards define the electrical and mechanical details of the communication link.
4. Testing
In order to ensure that when a measurement system is installed it will correctly function, testing is required. Testing a measurement system on installation can be considered to fall into three stages:
1. Pre-installation testing
This is the testing of each instrument and element for correct calibration and operation prior to it being installed as part of a measurement system.
2. Cabling and piping testing
Cables and/or piping will be used to connect together the elements of measurement systems. The display might, for example, be in a control room. All the instrument cables should be checked for continuity and insulation resistance prior to the connection of any instruments or elements of the system. When the system involves pneumatic lines the testing involves blowing through with clear, dry, air prior to connection and pressure testing to ensure the lines are leak free.
3. Pre-commissioning
This involves testing that the measurement system installation is complete, all the instrument and other components are in full operational order when interconnected and all control room panels or displays function.
4.1 Maintenance
When the system is in operation, maintenance will be required to ensure it continues to operate correctly.
If you own a car or motorcycle, then you will be involved with maintenance and testing, whether you carry out the procedures yourself or a garage does it for you. The function of maintenance is to keep the car/motorcycle in a serviceable condition to that it can continue to carry out its function of transporting you from one place to another.
Maintenance is likely to take two forms. One form is breakdown or corrective maintenance in which repairs are only made when the car/motorcycle fails to work. Thus breakdown maintenance might be used with the exhaust with it only being replaced when it fails. The other form is preventative maintenance which involves anticipating failure and replacing or adjusting items before failure occurs. Preventative maintenance involves inspection and servicing. The inspection is intended to diagnose impending breakdown so that maintenance can prevent it. Servicing is an attempt to reduce the chance of breakdown occurring. Thus preventative maintenance might be used with the regular replacement of engine oil, whether it needs it or not at that time.
Inspection of the brakes might be carried out to ascertain when new brake linings are going to be required so that they can be replaced before they wear out. In carrying out maintenance, testing will be involved.
Testing might involve checking the coolant level, brake fluid level, etc. and diagnosis tests in the case of faults to establish where the fault is.
In carrying out the maintenance of a measurement system, the most important aid is the maintenance manual. This includes such information as:
1. A description of the measurement system with an explanation of its use.
2. A specification of its performance.
3. Details of the system such as block diagrams illustrating how the elements are linked; photographs, drawings, exploded views, etc. giving the mechanical layout; circuit diagrams of individual elements; etc.
4. Preventative maintenance details, e.g. lubrication, replacement of parts, cleaning of parts and the frequency with which such tasks should be carried out.
5. Breakdown/corrective maintenance details, e.g. methods for dismantling, fault diagnosis procedures, test instruments, test instructions, safety precautions necessary to protect the service staff and precautions to be observed to protect sensitive components.
With electrical systems the most commonly used test instruments are multirange meters, cathode ray oscilloscopes and signal generators to provide suitable test signals for injections into the system.
6. Spare parts list.
Maintenance can involve such activities as:
1. Inspection to determine where potential problems might occur or where problems have occurred. This might involve looking to see if wear has occurred or a liquid level is at the right level.
2. Adjustment, e.g. of contacts to prescribed separations or liquid levels to prescribed values.
3. Replacement, e.g. routine replacement of items as part of preventative maintenance and replacement of worn or defective parts.
4. Cleaning as part of preventative maintenance, e.g. of electrical contacts.
5. Calibration. For example, the calibration of an instrument might drift with time and so recalibration becomes necessary.
A record should be maintained of all maintenance activities, i.e. a maintenance activity log. With preventative maintenance this could take the form of a checklist with items being ticked as they are completed.
Such a preventative maintenance record is necessary to ensure that such maintenance is carried out at the requisite times. The maintenance log should also include details of any adjustments made, recalibrations necessary or parts replaced. This can help in the diagnosis of future problems.
4.2 Common faults
The following are some of the commonly encountered tests and maintenance points that can occur with measurement systems:
1. Sensors
A test is to substitute a sensor with a new one and see what effect this has on the results given by the measurement system. If the results change then it is likely that the original sensor was faulty. If the results do not change then the sensor was not at fault and the fault is elsewhere in the system. Where a sensor is giving incorrect results it might be because it is not correctly mounted or used under the conditions specified by the manufacturer's data sheet. In the case of electrical sensors their output can be directly measured and checked to see if the correct voltages/currents are given. They can also be checked to see whether there is electrical continuity in connecting wires.
2. Switches and relays
A common source of incorrect functioning of mechanical switches and relay is dirt and particles of waste material between the switch contacts. A voltmeter used across a switch should indicate the applied voltage when the contacts are open and very nearly zero when they are closed. If visual inspection of a relay discloses evidence of arcing or contact welding then it might function incorrectly and so should be replaced. If a relay fails to operate checks can be made to see if the correct voltage is across the relay coil and, if the correct voltage is present, that there is electrical continuity within the coil with an ohmmeter.
3. Hydraulic and pneumatic systems
A common cause of faults with hydraulic and pneumatic systems is dirt. Small particles of dirt can damage seals, block orifices, and cause moving parts to jam. Thus, as part of preventative maintenance, filters need to be regularly checked and cleaned. Also oil should be regularly checked and changed. Testing with hydraulic and pneumatic systems can involve the measurement of the pressure at a number of points in a system to check that the pressure is the right value. Leaks in hoses, pipes and fittings are common faults.
Also, damage to seals can result in hydraulic and pneumatic cylinders leaking, beyond that which is normal, and result in a drop in system pressure.
Problems
Questions 1 to 6 have four answer options: A, B, C and D. Choose the correct answer from the answer options.
1. Decide whether each of these statements is True (T) or False (F).
As part of the electronic control system for a car engine, a thermistor is to be used to monitor the air temperature. The signal processing circuit that could be used with the thermistor in order to give an electrical voltage output is: (i) A Wheatstone bridge, (ii) A potential divider circuit.
A (i)T (ii)T
B (i)T(ii)F
C (i)F(ii)T
D (i)F (ii)F
2. Decide whether each of these statements is True (T) or False (F). It is proposed to monitor the exhaust temperature of a diesel engine by using a thermocouple. In order to give an output which is a few volts in size and which is independent of the temperature of the surrounding air temperature, the output from the thermocouple: (i) Requires amplification, (ii) Requires cold junction compensation.
A (i)T (ii)T
B (i)T(ii)F
C (i)F(ii)T
D (i)F (ii)F
3. Decide whether each of these statements is True (T) or False (F). It is proposed to monitor the transmission oil pressure in a car by using a diaphragm pressure gauge with the movement of the diaphragm monitored by means of a linear variable differential transformer (LVDT). (i) The output from the LVDT will be a resistance change which can be converted into a voltage change by a Wheatstone bridge, (ii) The input to the LVDT is the displacement of the diaphragm.
A (i)T (ii)T
B (i)T(ii)F
C (i)F(ii)T
D (i)F (ii)F
4. Decide whether each of these statements is True (T) or False (F). The signal processing needed for a system where the output from a thermocouple is to be fed into a microprocessor/computer includes: (i) A digital-to-analog converter, (ii) Amplification.
A (i)T (ii)T
B (i)T(ii)F
C (i)F(ii)T
D (i)F (ii)F
5. Decide whether each of these statements is True (T) or False (F). The signal processing needed for a system where the output from an optical encoder is to be fed into a microprocessor/computer includes: (i) An analogue-to-digital converter, (ii) A resistance-to-voltage converter.
A (i)T (ii)T
B (i)T(ii)F
C (i)F(ii)T
D (i)F (ii)F
6. Decide whether each of these statements is True (T) or False (F). The term preventative maintenance is used when: (i) Systems are inspected to diagnose possible points of failure before failure occurs.
(ii) Systems are regularly maintained with such things as items being lubricated and cleaned.
A (i)T (ii)T
B (i)T (ii)F
C (i)F (ii)T
D (i)F (ii)F
7. A driverless vehicle is being designed for operation in a factory where it has to move along prescribed routes transporting materials between machines. Suggest a system that could be used to direct the vehicle along a route.
8. Identify the requirements of the measurement system and hence possible functional elements that could be used to form such a system for the measurement of:
(a) The production of an electrical signal when a package on a conveyor belt has reached a particular position.
(b) The air temperature for an electrical meter intended to indicate when the temperature drops below freezing point.
(c) The production of an electrical signal which can be displayed on a meter and indicate the height of water in a large storage tank.
9. A data acquisition board has a 12-bit analogue-to-digital converter and is set for input signals in the range 0 to 10 V with the amplifier gain at 10. What is the resolution in volts?
10. A load cell has a sensitivity of 25 mV/ k-Ohm and is connected to a digital acquisition board which has a 0 to 10 V, 12-bit analog-to-digital converter. What amplifier gain should be used if the cell is to give an output for forces in the range 0.1 k-Ohm to 10 k-Ohm?
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