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10. Signal transmission
Measurement signals often have to be transmitted over quite large distances from the place of measurement to a display unit and/or a process control unit. Methods used for such transmission are:
1. Analog voltage transmission
Analog voltage signals can suffer corruption due to induced noise and the resistance of the connecting cables can result in attenuation of the voltage, the voltage drop across the output being reduced by that across the line resistance (FIG. 84). Such effects can be reduced by the use of signal amplification and shielding with the connecting cables. However, because of these problems, such signals are not generally used for large distance transmission.
2. Current loop transmission
The attenuation which occurs with voltage transmission can be minimized if signals are transmitted as varying current signals. This form of transmission is known as current loop transmission and uses currents in the range 4 mA to 20 mA to represent the levels of the analogue signal. The level of 4 mA, rather than 0 mA, is used to indicate the zero signal level since, otherwise, it would not be possible to distinguish between a zero value signal and a break in the transmission line. FIG. 85 shows the basic arrangement with the signal from the sensor being converted to a current signal by a voltage-to-current converter, e.g. that shown in FIG. 79, transmitted and then converted to a voltage signal at the display.
FIG. 84 Analogue voltage transmission
FIG. 85 Current loop transmission
Digital voltage signals
Digital signals can be transmitted over transmission lines using either serial or parallel communication. With serial communication, the sequence of bits used to describe a value is sent in sequence along a single transmission line. With parallel transmission, each of the bits is sent along a separate parallel transmission line. For long-distance communication, serial communication is used.
In order to transfer data, both the sender and receiver have to agree on the meaning of the transmitted binary digital patterns. The most commonly used character set is the American Standard Code for Information Interchange (ASCII), thus using 7 bits to represent each character (Table 2). The format used for sending such data has to be standardized. For example, with the RS-232 form of serial transmission, a sequence of 10 bits is used, the first bit being a start of message signal, then seven bits for the data, then a pairy bit to identify whether errors have occurred in the transmission, and finally a stop bit to indicate the end of the message.
Digital signal transmission has a great advantage when compared with analogue transmission in that signal corruption effects can be considerably reduced. With digital transmission, error coding is used to detect whether corruption has occurred. These are bits added to the sequence of bits used to represent the value and are check values which are not likely to tally with the received bits if corruption has occurred, the receiver can then request the message be sent again.
For example, the sequence 1010 might be transmitted and corruption result in 1110 being received. In order to detect such errors one form of check uses a parity bit which is added at transmission. With even-parity, the bit is chosen so that the total number of is in the transmission, including the parity bit, is an even number. This 1010 would be transmitted as 10100. If it is corrupted and received as 11100 then the parity bit shows there is an error.
Application The RS-232 is a widely used serial data Interface standard in which the electrical signal characteristics, such as voltage levels, the forms of plug and sockets for interconnections, and the interchange circuits are all specified. Because RS-232 is limited to distances less than about 15 m, another standard such as RS-485 tends to be used in many control systems with distances up to about 1200 m being possible.
FIG. 86 Optical fibers
Pneumatic transmission
Pneumatic transmission involves converting the sensor output to a pneumatic pressure in that range 20 to 100 kPa or 20 to 180 kPa.
The lower limit gives the zero sensor signal and enables the zero value to be distinguished from a break in the circuit. Such pressure signals can then be transmitted though plastic or metal piping, the distances being limited to about 300 m because of the limitations of speed of response at larger distances.
Fiber-optic transmission
An optical fiber is a light conductor in the form of a long fiber along which light can be transmitted by internally being reflected of the sides of the fiber (FIG. 86). The light sources used are LEDs or semiconductor laser diodes. Digital electrical signals are converted into light pulses which travel down the fiber before being detected by a photodiode or phototransistor and converted back into an electrical signal. Fiber optics has the advantages that they are immune to electromagnetic interference, data can be transmitted with much lower losses than with electrical cables, the fibers are smaller and less heavy than copper cables and are more inert in hazardous areas.
10.1 Noise
The term noise is used, in this context, for the unwanted signals that may be picked up by a measurement system and interfere with the signals being measured. There are two basic types of electrical noise:
1. Interference
This is due to the interaction between external electrical and magnetic fields and the measurement system circuits, e.g. the circuit picking up interference from nearby mains power circuits.
2. Random noise
This is due to the random motion of electrons and other charge carriers in components and is determined by the basic physical properties of components in the system.
The three main types of interference are:
1. Inductive coupling
A changing current in a nearby circuit produces a changing magnetic field which can induce e.m.f.s, as a result of electromagnetic induction, in conductors in the measurement system.
2. Capacitive coupling
Nearby power cables, the earth, and conductors in the measurement system are separated from each other by a dielectric, air. There can thus be capacitance between the power cable and conductors, and between the conductors and earth. These capacitors couple the measurement system conductors to the other systems and thus signals in the other systems affecting the charges on these capacitors can result in interference in the measurement system.
3. Multiple earths
If the measurement system has more than one connection to earth, there may be problems since there may be some difference in potential between the earth points. If this occurs, an interference current may arise in the measurement system.
FIG. 87 Twisted pairs
Methods of reducing interference are:
1. Twisted pairs of wires
This involves the elements of the measurement system being connected by twisted wire pairs (FIG. 87). A changing magnetic field will induce e.m.f.s in each loop, but because of the twisting the directions of the e.m.f.s will be in one direction for one loop and in the opposite direction for the next loop and so cancel out.
2. Electrostatic screening
Capacitive coupling can be avoided by completely enclosing the system in an earthed metal screen. Problems may occur if there are multiple earths. Coaxial cable gives screening of connections between elements, however, the cable should only be earthed at one end if multiple earths are to be avoided.
3. Single earth
Multiple earthing problems can be avoided if there is only a single earthing point.
4. Differential amplifiers
A differential amplifier can be used to amplify the difference between two signals. Thus if both signals contain the same interference, then the output from the amplifier will not have amplified any interference signals.
5. Filters
A filter can be selected which transmits the measurement signal but rejects interference signals.
11. Smart systems
It is possible to have a measurement system where the sensor and signal processing such as amplification and analogue-to-digital conversion are carried out with separate components. However, these are often available combined in a single integrated sensor circuit. However, often the output from such a system needs further data processing and the resulting combination of sensor, signal processing and a microprocessor to give 'intelligent' processing of sensor inputs results in what is termed a smart or intelligent sensor. Such a microprocessor-equipped sensor can have the functions to give such functions as compensation for random errors, automatic calculation of measurement accuracy, automatic self calibration, adjustment for non-linearities to give a linear output and self-diagnosis of faults.
Smart sensors have the ability to 'talk', to 'listen', and to interact with data.
This 'intelligent' processing is most likely to be accomplished by the use of a microprocessor.
In a process plant there are likely to be a large number of smart sensors, each providing information which has to be fed back to a control panel. To avoid using separate cables for each sensor to transmit their data, a bus system can be used. A bus is a common highway for signals which is used to link components. Thus each sensor would put its information onto the common highway for transmission to the control panel. The Hart communication protocol is widely used for such transmissions. This involves the digital signal from a smart sensor being superimposed on an analogue 4-20 mA current loop signal. With this protocol, a 0 is represented by a 2200 Hz frequency and a 1 by a 1200 Hz frequency and these are superimposed on the d.c. signal to give simultaneous digital and analogue transmission. The digital data transfer rate is 1200 bits/s. The arrangement is that a master, such as a display terminal, sends a message with a request for data to a device, the device interprets the request and replies with the data.
12. Data presentation elements
The elements that can be used for the presentation of data can be classified into three groups: indicators, illuminative displays and recorders. Indicators and illuminative displays give an instant visual indication of the sensed variable while recorders record the output signal over a period of time and give automatically a permanent record. A recorder will be the most appropriate choice if the event is high speed or transient and cannot be followed by an observer, or there are large amounts of data, or it is essential to have a record of the data. The following are some brief notes about some of the characteristics of commonly used data presentation methods.
12.1 Indicator
The moving coil meter is an analogue data presentation element involving a pointer moving across a fixed scale. The basic instrument movement is a d.c. microammeter with shunts, multipliers and rectifiers being used to convert it to other ranges of direct current and alternating current, direct voltage and alternating voltage. With alternating current and voltages, the instrument is restricted to frequencies between about 50 Hz and 10 kHz. The overall accuracy is generally of the order of ±0.1 to ±5%. The time taken for a moving coil meter to reach a steady deflection is typically in the region of a few seconds. The low resistance of the meter can present loading problems.
FIG. 88 (a) 7-segment format with examples of the numbers 2 and 5, (b)
7 by 5 dot matrix format with examples of the numbers 2 and 5.
FIG. 89 Bar type of display.
12.2 Illuminative displays
Commonly used illuminative display systems generally use light-emitting diodes (LEDs) or liquid crystal displays. Light-emitting diodes require low voltages and low currents in order to emit light and are cheap. The most commonly used LEDs can give red, yellow or green colors. The term alphanumeric display is used for one that can display the letters of the alphabet and numbers. Two basic types of array are used to generate alphanumeric displays, segmented and dot matrix. The 7-segment display (FIG. 88(a)) is a common form. By illuminating different segments of the display the full range of numbers and a small range of alphabetical characters can be formed. For example, to form a 2 the segments a, b, d, e and g are illuminated. The 5x 7 dot-matrix (FIG. 88(b)) display enables a full range of numbers and alphabetical characters to be produced by illuminating different segments in a rectangular array.
LEDs can also be arranged in other formats. For example, they can be arranged in the form of bars, the length of the illuminated bar then being a measure of some quantity (FIG. 89). A speedometer might use this form of display.
Liquid crystal displays do not produce any light of their own but use reflected light and can be arranged in segments like the LEDs shown above. The crystal segments are on a reflecting plate (FIG. 90). When an electric field is applied to a crystal, light is no longer passed through it and so there is no reflected light. That segment then appears dark.
FIG. 90 Electric field: (a) applied, (b) not applied
FIG. 91 Principle of the digital voltmeter.
Application---An example of an instrument using LED or crystal forms of display is the digital voltmeter. This gives its reading in the form of a sequence of digits and is essentially just a sample and hold unit feeding an analogue-to-digital converter with its digital output counted and the count displayed (FIG. 91). It has a high resistance, of the order of 10 M-ohm, and so loading effects are less likely than with the moving coil meter with its lower resistance. The sample and hold unit takes samples and thus the specification of the sample rate with such an instrument gives the time taken for the instrument to process the signal and give a reading. Thus, if the input voltage is changing at a rate which results in significant changes during the sampling time the voltmeter reading can be in error.
Large screen displays, termed visual display units (VDUs), are basically just a form of cathode ray tube which is used to display alphanumeric, graphic and pictorial data. The cathode ray tube (FIG. 92) consists of an electron gun which produces a focused beam of electrons and a deflection system. The beam of electrons in the cathode ray tube is deflected in the Y direction by a potential difference applied between the Y-deflection plates and in the X direction by a potential difference between the X-deflection plates.
FIG. 92 The basic form of the cathode ray tube
FIG. 93 Raster form of display
With the raster form of VDU, saw-tooth signals are applied to both the X- and the Y-deflection plates. FIG. 93 illustrates the principle.
The Y signal causes the beam to move at a constant rate from top to bottom of the screen before flying back to the top again. The X signal causes the beam to move at a constant rate from left to right of the screen before flying back to the left again. The consequence of both these signals is that the beam pursues a zigzag path down the screen before flying back to the top left comer and then resuming its zigzag path down the screen. During its travel down the screen, the electron beam is switched on or off, with the result that a picture or character can be 'painted' on the screen. The standard monochrome VDU has a 312-line raster display.
The raster form of display illustrated in FIG. 93 is said to be non-interlaced, the electron beam just following a single zigzag path down the screen. An interlaced display has two beams following a zigzag pattern down the screen (FIG. 94). The screen of the visual display unit is coated with a large number of phosphor dots, these dots forming the pixels. The term pixel is used for the smallest addressable dot on a display device. Character generation is by the selective illuminations of these pixels. Thus for a 7 by 5 matrix, FIG. 95 shows how characters are built up by the electron beam moving in its zigzag path down the screen.
The input data to the VDU is usually in digital ASCII (American Standard Code for Information Interchange) format so that as the electron beam sweeps across the screen it is subject to on-off signals which end up 'painting' the characters on the screen. The ASCII code is a 7-bit code and so can be used to represent 2^7 = 128 characters. This enables all the standard keyboard characters to be covered, as well as some control functions such as RETURN which is used to indicate the return from the end of a line to the start of the next line (see Table 2.2 for an abridged list of the code). The cathode-ray oscilloscope is a voltage-measuring instrument using a cathode ray tube. The deflection of the electron beam is a measure of the input voltage. A general-purpose instrument can respond to signals up to about 10 MHz while more specialist instruments can respond up to about 1 GHz. Double-beam oscilloscopes enable two separate traces to be observed simultaneously on the screen while storage oscilloscopes enable the trace to remain on the screen after the input signal has ceased, only being removed by a deliberate action of erasure.
FIG. 94 An interlaced display
FIG. 95 Character build-up by pixels
FIG. 96 The principle of the galvanometric chart recorder
12.3 Recorders
The galvanometric type of chart recorder (FIG. 96) works on the same principle as the moving coil meter movement. A coil is suspended between two fixed points by a suspension wire and in the magnetic field produced by a permanent magnet. When a current passes through the coil a torque acts on it, causing it to rotate and twist the suspension. The coil rotates to an angle at which the torque is balanced by the opposing torque resulting from the twisting of the suspension. The rotation of the coil results in a pen being moved across a chart.
The ultraviolet galvanometric chart recorder works on the same principle but instead of using a pointer moving a pen across the chart, a small mirror is attached to the suspension and reflects a beam of ultraviolet light onto sensitive paper. When the coil rotates, the suspension twists and the mirror rotates and so moves the beam across the chart.
While analogue chart recorders give records in the form of a continuous trace, digital printers give records in the form of numbers, letters or special characters. Such printers are known as alphanumeric printers. These can be dot-matrix, ink-jet or laser printers.
The dot-matrix printer has a print head of either 9 or 24 pins in a vertical line (FIG. 97). Each pin is controlled by an electromagnet which when turned on presses the pin onto the inking ribbon and so gives a small blob of ink on the paper behind the ribbon. The alphanumeric characters are formed by moving the print head across the paper and firing the appropriate pins.
The ink jet printer uses conductive ink being forced through a small nozzle to produce a jet of drops of ink. Very small, constant diameter, drops of ink are produced at a constant frequency and so regularly spaced in the jet. With one form a constant stream of ink passes along a tube and is pulsed to form fine drops by a piezoelectric crystal which vibrates at a frequency of about 100 kHz (FIG. 98). Another form uses a small heater in the print head with vaporized ink in a capillary tube, so producing gas bubbles which push out drops of ink (FIG. 99). In one form each drop of ink is given a charge as a result of passing through a charging electrode. The charged drops then pass between deflection plates which can deflect the stream of drops in a vertical direction, the amount of deflection depending on the charge on the drops. In another form, a vertical stack of nozzles is used and the jets of each just switched on or off on demand.
The laser printer has a photosensitive drum which is coated with a selenium-based material that is light sensitive (FIG. 100). In the dark the selenium has a high resistance and becomes charged as it passes close to the charging wire. This is a wire which is held at a high voltage and charge leaks off it. A light beam is made to scan along the length of the drum by a small eight-sided mirror which rotates and so reflects the light that it scans across the drum. When light strikes the selenium its resistance drops and it can no longer remain charged. By controlling the brightness of the beam of light, so points on the drum can be discharged or left charged. As the drum passes the toner reservoir, the charged areas attract particles of toner which then stick to its surface to give a pattern of toner on the drum with toner on the areas that have not been exposed to light and no toner on the areas exposed to light. The paper is given a charge as it passes another charging wire, the so-called corona wire, with the result that as the paper passes close to the drum it attracts the toner off the drum. A hot fusing roller is then used to melt the toner particles so that, after passing between rollers, they firmly adhere to the paper.
FIG. 98 Continuous flow printing
FIG. 99 Principle of the on-demand system
FIG. 100 Basic elements of a laser printer
Magnetic recording involves data being stored in a thin layer of magnetic material as a sequence of regions of different magnetism. The material may be in the form of magnetic tape or disks, the disks being referred to as hard disks or floppy disks. FIG. 101 shows the basic principle of magnetic recording. The recording current is passed through a coil wrapped round a ferromagnetic core. This core has a small non magnetic gap. The proximity of the magnetic tape or disk to the gap means that the magnetic flux in the core is readily diverted through it.
The magnetic tape of disk consists of a plastic base coated with a ferro magnetic powder. When magnetic flux passes through this material it becomes permanently magnetized. Thus a magnetic record can be produced of the current through the coil. The patterns of magnetism on a tape or disk can be read by passing it under a similar head to the recording head. The movement of the magnetized material under the head results in magnetic flux passing through the core of the head and electromagnetic induction producing a current through the coil wrapped round the head.
FIG. 101 A magnetic recording write/read head.
Problems
Questions 1 to 19 have four answer options: A, B, C and D. Choose the correct answer from the answer options.
Questions 1 to 6 relate to the following information. The outputs from sensors can take a variety of forms. These include changes in:
A. Displacement
B. Resistance
C. Voltage
D. Capacitance
Select the form of output from above which is concerned with the following sensors:
1. A thermocouple which has an input of a temperature change.
2. A thermistor which has an input of a temperature change.
3. A diaphragm pressure cell which has an input of a change in the pressure difference between its two sides.
4. A L VDT which has an input of a change in displacement.
5. A strain gauge which has an input of a change in length.
6. A Bourdon gauge which has an input of a pressure change.
7. Decide whether each of these statements is True (T) or False (F). In selecting a temperature sensor for monitoring a rapidly changing temperature, it is vital that the sensor has: (i) A small thermal capacity, (ii) High linearity.
Which option BEST describes the two statements?
A. (i)T (ii)T
B. (i)T (ii)F
C. (i)F (ii)T
D. (i)F (ii)F
8. A copper-constantan thermocouple is to be used to measure temperatures between 0 and 200C. The e.m.f. at 0°C is 0 mV, at 100C it is 4.277 mV and at 200T it is 9.286 mV. If a linear relationship is assumed between e.m.f. and temperature over the full range, the non-linearity error at 100°C is:
A. -3.9C
B. -7.9C
C. +3.9C
D. +7.9C
9. The change in resistance of an electrical resistance strain gauge with a gauge factor of 2.0 and resistance 50 ohm when subject to a strain of 0.001 is:
A. 0.0001 ohm
B. 0.001 ohm
c. 0.01 ohm
D. 0.1 ohm
10. An incremental shaft encoder gives an output which is a direct measure of
A. The absolute angular position of a shaft.
B. The change in angular rotation of a shaft.
C. The diameter of the shaft.
D. The change in diameter of the shaft.
11. A pressure sensor consisting of a diaphragm with strain gauges bonded to its surface has the following information in its specification:
Range: 0 to 1000 kPa
Non-linearity error: ± 0.15% of full range
Hysteresis error: ±0.05% of full range
The total error due to non-linearity and hysteresis for a reading of 200 kPa is:
A. ±0.2 kPa
B. ±0.4 kPa
C. ±2kPa
D. ±4kPa
12. The water level in an open vessel is to be monitored by a diaphragm pressure cell responding to the difference in pressure between that at the base of the vessel and the atmosphere. The range of pressure differences across the diaphragm that the cell will have to respond to if the water level can vary between zero height above the cell measurement point and 1 m above it is (take the acceleration due to gravity to be 9.8 m/s^ and the density of the water as 1000 kg/m^3):
A. 102 Pa
B. 102 kPa
C. 9800 Pa
D. 9800 kPa
13. Decide whether each of these statements is True (T) or False (F). A float sensor for the determination of the level of water in a container is cylindrical with a mass 1.0 kg, cross-sectional area 20 cm^2 and a length of 0.5 m. It floats vertically in the water and presses upwards against a beam attached to its upward end.
(i) The maximum force that can act on the beam is 9.8 N. (ii)
The minimum force that can act on the beam is 8.8 N.
Which option BEST describes the two statements?
A (i)T (ii)T
B (i)T (ii)F
C (i)F (ii)T
D (i)F (ii)F
14. A Wheatstone bridge when used as a signal processing element can have an input of a change in resistance and an output of:
A. A bigger resistance change.
B. A digital signal.
C. A voltage.
D. A current.
15 The resolution of an analogue-to-digital converter with a word length of 8 bits and an analogue signal input range of 10 V is:
A. 39 mV
B. 625 mV
C. 1.25 V
D. 5 V
16. A sensor gives a maximum analogue output of 5 V. The word length is required for an analogue-to-digital converter if there is to be a resolution of 10 mV is:
A 500 bits
B 250 bits
C 9 bits
D 6 bits 17.
Decide whether each of these statements is True (T) or False (F).
A cold junction compensator circuit is used with a thermocouple if it has: (i) No conjunction.
(ii) A cold junction at the ambient temperature.
Which option BEST describes the two statements?
A (i)T (ii)T B (i)T (ii)F C (i)F (ii)T D (i)F (ii)F
18. Decide whether each of these statements is True (T) or False (F). A data presentation element which has an input which results in a pointer moving across a scale is an example of: (i) An analogue form of display, (ii) An indicator form of display.
Which option BEST describes the two statements?
A (i)T (ii)T B (i)T(ii)F C (i)F (ii)T D (i)F (ii)F
19. Suggest sensors which could be used in the following situations:
(a) To monitor the rate at which water flows along a pipe and given an electrical signal related to the flow rate.
(b) To monitor the pressure in a pressurized air pipe, giving a visual display of the pressure.
(c) To monitor the displacement of a rod and give a voltage output.
(d) To monitor a rapidly changing temperature.
20. Suggest the type of signal processing element that might be used to:
(a) Transform an input of a resistance change into a voltage.
(b) Transform an input of an analogue voltage into a digital signal.
21. A potentiometer with a uniform resistance per unit length of track is to have a track length of 100 mm and used with the output being measured with an instrument of resistance 10 k-ohm. Determine the resistance required of the potentiometer if the maximum error is not to exceed 1% of the full-scale reading.
22. A platinum resistance coil has a resistance at 0 C of 100 ohm. Determine the change in resistance that will occur when the temperature rises to 30°C if the temperature coefficient of resistance is 0.0039 K^-1.
23. A platinum resistance thermometer has a resistance of 100.00 ohm at 0 C, 138.50 ohm at 100 C and 175.83 ohm at 200C. What will be the non-linearity error at 100°C if a linear relationship is assumed between 0°C and 200 C?
24. An electrical resistance strain gauge has a resistance of 120 ohm and a gauge factor of 2.1. What will be the change in resistance of the gauge when it experiences a uniaxial strain of 0.0005 along its length?
25. A capacitive sensor consists of two parallel plates in air, the plates each having an area of 1000 mm^2 and separated by a distance of 0.3 mm in air. Determine the displacement sensitivity of the arrangement if the dielectric constant for air is 1.0006.
26. A capacitive sensor consists of two parallel plates in air, the plates being 50 mm square and separated by a distance of 1 mm. A sheet of dielectric material of thickness 1 mm and 50 mm square can slide between the plates. The dielectric constant of the material is 4 and that for air may be assumed to be 1. Determine the capacitance of the sensor when the sheet has been displaced so that only half of it is between the capacitor plates.
27. A chromel-constantan thermocouple has a cold junction at 20 C. What will be the thermoelectric e.m.f when the hot junction is at 200 C? Tables give for this thermocouple: 0 C, e.m.f 0.000 mV; 20 C, e.m.f 1.192 mV; 200 C, e.m.f 13.419 mV.
28. An iron-constantan thermocouple has a cold junction at 0 C and is to be used for the measurement of temperatures between 0° C and 400°C. What will be the non-linearity error at 100 C, as a percentage of the full-scale reading, if a linear relationship is assumed over the full range? Tables give for this thermocouple: 0° C, e.m.f 0.000 mV; 100°C, e.m.f 5.268 mV; 400 C, e.m.f 21.846 mV.
29. Show that the output voltage for a Wheatstone bridge with a single strain gauge in one arm of the bridge and the other arms all having the same resistance as that of the unstrained strain gauge is VAVSGS, where Vs is the supply voltage to the bridge, G the gauge factor of the strain gauge and 8 the strain acting on the gauge.
30. A Wheatstone bridge has a platinum resistance temperature sensor with a resistance of 120 ohm at 0 C in one arm of the bridge. At this temperature the bridge is balanced with each of the other arms being 120 ohm. What will be the output voltage from the bridge for a change in temperature of 20 C? The supply voltage to the bridge is 6.0 V and the temperature coefficient of resistance of the platinum is 0.0039 K^-1 .
31. A diaphragm pressure gauge employs four strain gauges to monitor the displacement of the diaphragm. A differential pressure applied to the diaphragm results in two of the gauges on one side of the diaphragm being subject to a tensile strain of 1.0 x 10^-5 and the two on the other side a compressive strain of 1.0 x 10^-5 The gauges have a gauge factor of 2.1 and resistance 120 ohm and are connected in the bridge with the gauges giving subject to the tensile strains in arms 1 and 3 and those subject to compressive strain in arms 2 and 4 (FIG. 61). If The supply voltage for the bridge is 10 V, what will be the voltage output from the bridge?
32. A thermocouple gives an e.m.f of 820 uV when the hot junction is at 20°C and the cold junction at 0 C. Explain how a Wheatstone bridge incorporating a metal resistance element can be used to compensate for when the cold junction is at the ambient temperature rather than 0 C and determine the parameters for the bridge if a nickel resistance element is used with a resistance of 10 C at 0°C and a temperature coefficient of resistance of 0.0067 K^-1 and the bridge voltage supply is 2 V.
33. An operational amplifier circuit is required to produce an output that ranges from 0 to -5 V when the input goes from 0 to 100 mV. By what factor is the resistance in the feedback arm greater than that in the input?
34. What will be the feedback resistance required for an inverting amplifier which is to have a voltage gain of 50 and an input resistance of 10 k-Ohm?
35. What will be the feedback resistance required for a non-inverting amplifier which is to have a voltage gain of 50 and an input resistance of 10 k-Ohm?
36. A differential amplifier is to have a voltage gain of 100 and input resistances of 1 k-Ohm. What will be the feedback resistance required?
37. A differential amplifier is to be used to amplify the voltage produced between the two junctions of a thermocouple. The input resistances are to be 1 k-Ohm. What value of feedback resistance is required if there is to be an output of 10 mV for a temperature difference between the thermocouple junctions of 100 C with a copper-constantan thermo couple. The Thermocouple can be assumed to give an output of 43 uV/C
38. What is the resolution of an analogue-to-digital converter with a word length of 12 bits?
39. A sensor gives a maximum analogue output of 5 V. What word length is required for an analogue-to-digital converter if there is to be a resolution of 10 mV?
40. What is the voltage resolution of an 8-bit DAC when it has a full scale input of 5 V?
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