{"id":3153,"date":"2024-08-26T22:05:21","date_gmt":"2024-08-26T22:05:21","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=3153"},"modified":"2024-08-26T22:05:22","modified_gmt":"2024-08-26T22:05:22","slug":"signal-processing","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/26\/signal-processing\/","title":{"rendered":"\u00a0Signal Processing"},"content":{"rendered":"\n

The output signal from the sensor of a measurement system or the signal from the control unit might have to be processed in some way to make it suitable to operate the next element in the control system. For example, the signal may be too small and have to be amplified, be analog and have to be made digital, be digital and have to be made analog, be a resistance change and have to be made into a current change, be a voltage change and have to be made into a suitable size current change, be a pressure change and have to be made into a current change, etc. All these changes can be referred to as signal processing.<\/em> For example, the output from a thermocouple is a very small voltage, a few millivolts. A signal processing module might then be used to convert this into a larger voltage and provide cold junction compensation (i.e., allow for the cold junction not being at 0\u00b0C).<\/p>\n\n\n\n

The following are some examples of signal processing commonly encountered in control systems.<\/p>\n\n\n\n

18.5.1 Resistance to Voltage Converter<\/h3>\n\n\n\n

Consider how the resistance change produced by a thermistor when subject to a temperature change can be converted into a voltage change.\u00a0Figure 18.34\u00a0shows how a\u00a0potential divider circuit<\/em>\u00a0can be used. A constant voltage, of perhaps 6\u00a0V, is applied across\u00a0the thermistor and another resistor in series. With a thermistor with a resistance of 4.7\u00a0k\u03a9, the series resistor might be 10\u00a0k\u03a9. The output signal is the voltage across the 10\u00a0k\u03a9 resistor. When the resistance of the thermistor changes, the fraction of the 6\u00a0V across the 10\u00a0k\u03a9 resistor changes.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.34<\/strong> Resistance to voltage conversion for a thermistor<\/p>\n\n\n\n

The output voltage is proportional to the fraction of the total resistance, which is between the output terminals. Thus:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

where\u00a0V<\/em>\u00a0is the total voltage applied, in\u00a0Figure 18.34\u00a0this is shown as 6\u00a0V,\u00a0R<\/em>\u00a0the value of the resistance between the output terminals (10\u00a0k\u03a9) and\u00a0R<\/em>t<\/sub>\u00a0the resistance of the thermistor at the temperature concerned. The potential divider circuit is thus an example of a simple resistance to voltage converter. Another example of such a converter is the Wheatstone bridge.<\/p>\n\n\n\n

18.5.2 Protection<\/h3>\n\n\n\n

An important element that is often required with signal processing is protection against high currents or high voltages. A high current can be protected against by the incorporation in the input line of a series resistor to limit the current to an acceptable level and a fuse to break if the current does exceed a safe level (Figure 18.35).<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.35<\/strong> Protection against high currents<\/p>\n\n\n\n

It is often so vital that high currents or high voltages are not transmitted from the sensor to a microprocessor that it may be necessary to completely isolate circuits so there are\u00a0no electrical connections between them. This can be done using an\u00a0optoisolator<\/em>\u00a0(Figure 18.36). Such a device converts an electrical signal into an optical signal, transmits it to a detector which then converts it back into an electrical signal. The input signal passes through an infrared light-emitting diode (LED) and so produces a beam of infrared radiation which is detected by a phototransistor.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.36<\/strong> Optoisolator: infrared radiation is used to transmit signal from input to output circuit<\/p>\n\n\n\n

18.5.3 Analog-to-Digital Conversion<\/h3>\n\n\n\n

The electrical output from sensors such as thermocouples, resistance elements used for temperature measurement, strain gauges, diaphragm pressure gauges, LVDTs, etc. is in analog form. An analog signal (Figure 18.37(a)) is one that is continuously variable, changing smoothly over a range of values. The signal is an analog, i.e., a scaled version, of the quantity it represents. A digital signal increases in jumps, being a sequence of pulses, often just on-off signals (Figure 18.37(b)). The value of the quantity instead\u00a0of being represented by the height of the signal, as with analog, is represented by the sequence of on-off signals.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.37<\/strong> Signals: (a) analog; (b) digital<\/p>\n\n\n\n

Microprocessors require digital inputs. Thus, where a microprocessor is used as part of a control system, the analog output from a sensor has to be converted into a digital form before it can be used as an input to the microprocessor. Thus there is a need for an\u00a0analog-to-digital converter<\/em>\u00a0(ADC). Analog-to-digital conversion involves a number of stages. The first stage is to take samples of the analog signal (Figure 18.38(a)). A clock supplies regular time signal pulses (Figure 18.38(b)) to the analog-to-digital converter and every time it receives a pulse it samples the analog signal. The result is a series of narrow pulses with heights which vary in accord with the variation of the analog signal (Figure 18.38(c)). This sequence of pulses is changed into the signal form shown in\u00a0Figure 18.38(d)\u00a0by each sampled value being held until the next pulse occurs. This holding is necessary to allow time for the conversion to take place at an analog-to-digital converter. This converts each sample into a sequence of pulses representing the value. For example, the first sampled value might be represented by 101, the next sample by 011, etc. The 1 represents an \u201con\u201d or \u201chigh\u201d signal, the 0 an \u201coff\u201d or \u201clow\u201d signal. Analog-to-digital conversion thus involves a sample and hold unit followed by an analog-to-digital converter (Figure 18.39).<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.38<\/strong> (a) Analog signal; (b) time signal; (c) sampled signal; (d) sampled and held signal<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.39<\/strong> Analog-to-digital conversion<\/p>\n\n\n\n

To illustrate the action of the analog-to-digital converter, consider one that gives an output restricted to three bits. The binary digits of 0 and 1, i.e., the \u201clow\u201d and \u201chigh\u201d signals, are referred to as bits.<\/em> A group of bits is called a word.<\/em> Thus the three bits give the word length<\/em><\/a> for this particular analog-to-digital converter. The word is what represents the digital version of the analog voltage. With three bits in a word we have the possible words of:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

There are eight possible words which can be used to represent the analog input; the number of possible words with a word length of\u00a0n<\/em>\u00a0bits is 2n<\/sup><\/em>. Thus we divide the maximum analog voltage into eight parts and one of the digital words corresponds to each. Each rise in the analog voltage of (1\/8) of the maximum analog input then results in a further bit being generated. Thus for word 000 we have 0\u00a0V input. To generate the next digital word of 001 the input has to rise to 1\/8 of the maximum voltage. To generate the next word of 010 the input has to rise to 2\/8 of the maximum voltage.\u00a0Figure 18.40\u00a0illustrates this conversion of the sampled and held input voltage to a digital output.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.40<\/strong> Digital output from an ADC<\/p>\n\n\n\n

Thus if we had a sampled analog input of 8 V, the digital output would be 000 for a 0 V input and would remain at that output until the analog voltage had risen to 1 V, i.e., 1\/8 of the maximum analog input. It would then remain at 001 until the analog input had risen to<\/a> 2 V. This value of 001 would continue until the analog input had risen to 3 V. The smallest change in the analog voltage that would result in a change in the digital output is thus 1 V. This is termed the resolution<\/em> of the converter.<\/p>\n\n\n\n

The word length possible with an analog-to-digital converter determines its resolution.<\/em> With a word length of n<\/em> bits the maximum, or full scale, analog input V<\/em>FS<\/sub> is divided into 2n<\/sup><\/em> pieces. The minimum change in input that can be detected, i.e., the resolution,<\/em> is thus V<\/em>FS<\/sub> \/2n<\/sup><\/em>. With an analog-to-digital converter having a word length of 10 bits and the maximum analog signal input range 10 V, then the maximum analog voltage is divided into 210<\/sup>=1024 pieces and the resolution is 10\/1024=9.8 mV.<\/p>\n\n\n\n

There are a number of forms of analog-to-digital converter; the most commonly used being successive approximations, dual-slope and flash. Successive approximations converters are probably the most widely used; dual slope converters have the advantage of excellent noise rejection and flash converters give the highest conversion rates.<\/p>\n\n\n\n

18.5.4 Digital-to-Analog Conversion<\/h3>\n\n\n\n

The output from a microprocessor is digital. Most control elements require an analog input and so the digital output from a microprocessor has to be converted into an analog form before it can be used by them. The input to a digital-to-analog converter is a binary word and the output its equivalent analog value. For example, if we have a full scale output of 7\u00a0V then a digital input of 000 will give 0\u00a0V, 001 give 1\u00a0V \u2026 and 111 the full scale value of 7\u00a0V.\u00a0Figure 18.41\u00a0illustrates this.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.41<\/strong> Digital-to-analog conversion<\/p>\n\n\n\n

18.5.5 Amplifiers<\/h3>\n\n\n\n

The\u00a0operational amplifier<\/em>\u00a0is the basis of many signal processing elements, the basic amplifier being supplied as an integrated circuit on a silicon chip. It has two inputs, termed the inverting input (-) and the noninverting input (+) and is a high gain DC amplifier, the gain typically being of the order of 100,000 or more.\u00a0Figure 1<\/a>8.42<\/a>\u00a0shows the pin connections for a 741 operational amplifier with the symbol for the operational amplifier. Pins 4 and 7 are for the connections to the supply voltage for the amplifier, pin 2 for the inverting input, pin 3 for the noninverting input. The output is taken from pin 6. Pins 1 and 5 are for the offset null. These are to enable circuits to be connected to enable corrections to be made for the nonideal behavior of the amplifier.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.42<\/strong> Amplifier<\/p>\n\n\n\n

Consider the amplifier when used as an\u00a0inverting amplifier<\/em>\u00a0(Figure 18.43), i.e., an amplifier which gives an output, which is out-of-phase with respect to the input. For the circuit shown in\u00a0Figure 18.43, the connections for the power supply and the offset null have been omitted. The input is connected to the inverting input, the noninverting\u00a0input being connected to earth. A feedback loop is connected, via the resistor\u00a0R<\/em>2<\/sub>, to the inverting input. The output voltage of such an amplifier is limited to about \u00b110\u00a0V and thus, since the gain is about 100,000, the input voltage to the inverting input at\u00a0X<\/em>,\u00a0V<\/em>x<\/sub>, must be between about +0.0001V and -0.0001V. This is virtually zero and so point\u00a0X<\/em>\u00a0is at virtually earth potential. For this reason it is called a\u00a0virtual earth.<\/em>\u00a0The potential difference across the input resistance\u00a0R<\/em>1<\/sub>\u00a0is (V<\/em>in<\/sub>–V<\/em>x<\/sub>) and thus (V<\/em>in<\/sub>–V<\/em>x<\/sub>)=I<\/em>1<\/sub>R<\/em>1<\/sub>. But\u00a0V<\/em>x<\/sub>\u00a0is virtually zero and so we can write:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.43<\/strong> Inverting amplifier<\/p>\n\n\n\n

Operational amplifiers have very high resistance between their input terminals; for example, the resistance with the 741 operational amplifier is about 2 M\u03a9. Thus virtually no current flows from point X through the inverting input and so to earth. Thus the current I<\/em>1<\/sub> that flows through R<\/em>1<\/sub> must be essentially the current flowing through R<\/em>2<\/sub>. The potential difference across R<\/em>2<\/sub> is (V<\/em>x<\/sub>–V<\/em>out<\/sub>). Thus we can write (V<\/em>x<\/sub>–V<\/em>out<\/sub>).=I<\/em>1<\/sub>R<\/em>2<\/sub>. But as V<\/em>x<\/sub> is effectively zero, we can write:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Eliminating 11 from these two simultaneous equations gives:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The negative sign indicates that the output is 180\u00b0 out-of-phase with the input. The gain is determined solely by the values of the two resistors. A noninverting amplifier can likewise be produced by taking the input to the noninverting input instead of the inverting input.<\/p>\n\n\n\n

As an illustration of the use of an operational amplifier, consider\u00a0Figure 18.44\u00a0which shows how it can be used as a differential amplifier to amplify the difference between two input voltages. Since there is virtually no current through the high resistance in the operational amplifier between the two input terminals, both the inputs X will be at the same potential. The voltage\u00a0V<\/em>2<\/sub>\u00a0is across resistors\u00a0R<\/em>1<\/sub>\u00a0and\u00a0R<\/em>2<\/sub>\u00a0in series. Thus, the potential\u00a0V<\/em>x<\/sub>\u00a0at X is:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.44<\/strong> Differential amplifier<\/p>\n\n\n\n

Since the operational amplifier has a very high input resistance, the current through the feedback resistance will be equal to that from V<\/em>1<\/sub> through R<\/em>1<\/sub>. Hence, we have:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

and so:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Hence, substituting for V<\/em>x<\/sub> using the earlier equation, gives:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The output is a measure of the difference between the two input voltages.<\/p>\n\n\n\n

More information on op-amps can be found in\u00a0<\/p>\n\n\n\n

The output signal from the sensor of a measurement system or the signal from the control unit might have to be processed in some way to make it suitable to operate the next element in the control system. For example, the signal may be too small and have to be amplified, be analog and have to be made digital, be digital and have to be made analog, be a resistance change and have to be made into a current change, be a voltage change and have to be made into a suitable size current change, be a pressure change and have to be made into a current change, etc. All these changes can be referred to as signal processing.<\/em> For example, the output from a thermocouple is a very small voltage, a few millivolts. A signal processing module might then be used to convert this into a larger voltage and provide cold junction compensation (i.e., allow for the cold junction not being at 0\u00b0C).<\/p>\n\n\n\n

The following are some examples of signal processing commonly encountered in control systems.<\/p>\n\n\n\n

18.5.1 Resistance to Voltage Converter<\/h3>\n\n\n\n

Consider how the resistance change produced by a thermistor when subject to a temperature change can be converted into a voltage change.\u00a0Figure 18.34\u00a0shows how a\u00a0potential divider circuit<\/em>\u00a0can be used. A constant voltage, of perhaps 6\u00a0V, is applied across\u00a0the thermistor and another resistor in series. With a thermistor with a resistance of 4.7\u00a0k\u03a9, the series resistor might be 10\u00a0k\u03a9. The output signal is the voltage across the 10\u00a0k\u03a9 resistor. When the resistance of the thermistor changes, the fraction of the 6\u00a0V across the 10\u00a0k\u03a9 resistor changes.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.34<\/strong> Resistance to voltage conversion for a thermistor<\/p>\n\n\n\n

The output voltage is proportional to the fraction of the total resistance, which is between the output terminals. Thus:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

where\u00a0V<\/em>\u00a0is the total voltage applied, in\u00a0Figure 18.34\u00a0this is shown as 6\u00a0V,\u00a0R<\/em>\u00a0the value of the resistance between the output terminals (10\u00a0k\u03a9) and\u00a0R<\/em>t<\/sub>\u00a0the resistance of the thermistor at the temperature concerned. The potential divider circuit is thus an example of a simple resistance to voltage converter. Another example of such a converter is the Wheatstone bridge.<\/p>\n\n\n\n

18.5.2 Protection<\/h3>\n\n\n\n

An important element that is often required with signal processing is protection against high currents or high voltages. A high current can be protected against by the incorporation in the input line of a series resistor to limit the current to an acceptable level and a fuse to break if the current does exceed a safe level (Figure 18.35<\/a>).<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.35<\/strong> Protection against high currents<\/p>\n\n\n\n

It is often so vital that high currents or high voltages are not transmitted from the sensor to a microprocessor that it may be necessary to completely isolate circuits so there are\u00a0no electrical connections between them. This can be done using an\u00a0optoisolator<\/em>\u00a0(Figure 18.36). Such a device converts an electrical signal into an optical signal, transmits it to a detector which then converts it back into an electrical signal. The input signal passes through an infrared light-emitting diode (LED) and so produces a beam of infrared radiation which is detected by a phototransistor.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.36<\/strong> Optoisolator: infrared radiation is used to transmit signal from input to output circuit<\/p>\n\n\n\n

18.5.3 Analog-to-Digital Conversion<\/h3>\n\n\n\n

The electrical output from sensors such as thermocouples, resistance elements used for temperature measurement, strain gauges, diaphragm pressure gauges, LVDTs, etc. is in analog form. An analog signal (Figure 18.37(a)) is one that is continuously variable, changing smoothly over a range of values. The signal is an analog, i.e., a scaled version, of the quantity it represents. A digital signal increases in jumps, being a sequence of pulses, often just on-off signals (Figure 18.37(b)). The value of the quantity instead\u00a0of being represented by the height of the signal, as with analog, is represented by the sequence of on-off signals.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.37<\/strong> Signals: (a) analog; (b) digital<\/p>\n\n\n\n

Microprocessors require digital inputs. Thus, where a microprocessor is used as part of a control system, the analog output from a sensor has to be converted into a digital form before it can be used as an input to the microprocessor. Thus there is a need for an\u00a0analog-to-digital converter<\/em>\u00a0(ADC). Analog-to-digital conversion involves a number of stages. The first stage is to take samples of the analog signal (Figure 18.38(a)). A clock supplies regular time signal pulses (Figure 18.38(b)) to the analog-to-digital converter and every time it receives a pulse it samples the analog signal. The result is a series of narrow pulses with heights which vary in accord with the variation of the analog signal (Figure 18.38(c)). This sequence of pulses is changed into the signal form shown in\u00a0Figure 18.38(d)\u00a0by each sampled value being held until the next pulse occurs. This holding is necessary to allow time for the conversion to take place at an analog-to-digital converter. This converts each sample into a sequence of pulses representing the value. For example, the first sampled value might be represented by 101, the next sample by 011, etc. The 1 represents an \u201con\u201d or \u201chigh\u201d signal, the 0 an \u201coff\u201d or \u201clow\u201d signal. Analog-to-digital conversion thus involves a sample and hold unit followed by an analog-to-digital converter (Figure 18.39).<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.38<\/strong> (a) Analog signal; (b) time signal; (c) sampled signal; (d) sampled and held signal<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.39<\/strong> Analog-to-digital conversion<\/p>\n\n\n\n

To illustrate the action of the analog-to-digital converter, consider one that gives an output restricted to three bits. The binary digits of 0 and 1, i.e., the \u201clow\u201d and \u201chigh\u201d signals, are referred to as bits.<\/em> A group of bits is called a word.<\/em> Thus the three bits give the word length<\/em><\/a> for this particular analog-to-digital converter. The word is what represents the digital version of the analog voltage. With three bits in a word we have the possible words of:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

There are eight possible words which can be used to represent the analog input; the number of possible words with a word length of\u00a0n<\/em>\u00a0bits is 2n<\/sup><\/em>. Thus we divide the maximum analog voltage into eight parts and one of the digital words corresponds to each. Each rise in the analog voltage of (1\/8) of the maximum analog input then results in a further bit being generated. Thus for word 000 we have 0\u00a0V input. To generate the next digital word of 001 the input has to rise to 1\/8 of the maximum voltage. To generate the next word of 010 the input has to rise to 2\/8 of the maximum voltage.\u00a0Figure 18.40\u00a0illustrates this conversion of the sampled and held input voltage to a digital output.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.40<\/strong> Digital output from an ADC<\/p>\n\n\n\n

Thus if we had a sampled analog input of 8 V, the digital output would be 000 for a 0 V input and would remain at that output until the analog voltage had risen to 1 V, i.e., 1\/8 of the maximum analog input. It would then remain at 001 until the analog input had risen to<\/a> 2 V. This value of 001 would continue until the analog input had risen to 3 V. The smallest change in the analog voltage that would result in a change in the digital output is thus 1 V. This is termed the resolution<\/em> of the converter.<\/p>\n\n\n\n

The word length possible with an analog-to-digital converter determines its resolution.<\/em> With a word length of n<\/em> bits the maximum, or full scale, analog input V<\/em>FS<\/sub> is divided into 2n<\/sup><\/em> pieces. The minimum change in input that can be detected, i.e., the resolution,<\/em> is thus V<\/em>FS<\/sub> \/2n<\/sup><\/em>. With an analog-to-digital converter having a word length of 10 bits and the maximum analog signal input range 10 V, then the maximum analog voltage is divided into 210<\/sup>=1024 pieces and the resolution is 10\/1024=9.8 mV.<\/p>\n\n\n\n

There are a number of forms of analog-to-digital converter; the most commonly used being successive approximations, dual-slope and flash. Successive approximations converters are probably the most widely used; dual slope converters have the advantage of excellent noise rejection and flash converters give the highest conversion rates.<\/p>\n\n\n\n

18.5.4 Digital-to-Analog Conversion<\/h3>\n\n\n\n

The output from a microprocessor is digital. Most control elements require an analog input and so the digital output from a microprocessor has to be converted into an analog form before it can be used by them. The input to a digital-to-analog converter is a binary word and the output its equivalent analog value. For example, if we have a full scale output of 7\u00a0V then a digital input of 000 will give 0\u00a0V, 001 give 1\u00a0V \u2026 and 111 the full scale value of 7\u00a0V.\u00a0Figure 18.41\u00a0illustrates this.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.41<\/strong> Digital-to-analog conversion<\/p>\n\n\n\n

18.5.5 Amplifiers<\/h3>\n\n\n\n

The\u00a0operational amplifier<\/em>\u00a0is the basis of many signal processing elements, the basic amplifier being supplied as an integrated circuit on a silicon chip. It has two inputs, termed the inverting input (-) and the noninverting input (+) and is a high gain DC amplifier, the gain typically being of the order of 100,000 or more.\u00a0Figure 18.42\u00a0shows the pin connections for a 741 operational amplifier with the symbol for the operational amplifier. Pins 4 and 7 are for the connections to the supply voltage for the amplifier, pin 2 for the inverting input, pin 3 for the noninverting input. The output is taken from pin 6. Pins 1 and 5 are for the offset null. These are to enable circuits to be connected to enable corrections to be made for the nonideal behavior of the amplifier.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 18.42<\/strong> Amplifier<\/p>\n\n\n\n

Consider the amplifier when used as an\u00a0inverting amplifier<\/em>\u00a0(Figure 18.43), i.e., an amplifier which gives an output, which is out-of-phase with respect to the input. For the circuit shown in\u00a0Figure 18.43, the connections for the power supply and the offset null have been omitted. The input is connected to the inverting input, the noninverting\u00a0input being connected to earth. A feedback loop is connected, via the resistor\u00a0R<\/em>2<\/sub>, to the inverting input. The output voltage of such an amplifier is limited to about \u00b110\u00a0V and thus, since the gain is about 100,000, the input voltage to the inverting input at\u00a0X<\/em>,\u00a0V<\/em>x<\/sub>, must be between about +0.0001V and -0.0001V. This is virtually zero and so point\u00a0X<\/em>\u00a0is at virtually earth potential. For this reason it is called a\u00a0virtual earth.<\/em>\u00a0The potential difference across the input resistance\u00a0R<\/em>1<\/sub>\u00a0is (V<\/em>in<\/sub>–V<\/em>x<\/sub>) and thus (V<\/em>in<\/sub>–V<\/em>x<\/sub>)=I<\/em>1<\/sub>R<\/em>1<\/sub>. But\u00a0V<\/em>x<\/sub>\u00a0is virtually zero and so we can write:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.43<\/strong> Inverting amplifier<\/p>\n\n\n\n

Operational amplifiers have very high resistance between their input terminals; for example, the resistance with the 741 operational amplifier is about 2 M\u03a9. Thus virtually no current flows from point X through the inverting input and so to earth. Thus the current I<\/em>1<\/sub> that flows through R<\/em>1<\/sub> must be essentially the current flowing through R<\/em>2<\/sub>. The potential difference across R<\/em>2<\/sub> is (V<\/em>x<\/sub>–V<\/em>out<\/sub>). Thus we can write (V<\/em>x<\/sub>–V<\/em>out<\/sub>).=I<\/em>1<\/sub>R<\/em>2<\/sub>. But as V<\/em>x<\/sub> is effectively zero, we can write:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Eliminating 11 from these two simultaneous equations gives:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The negative sign indicates that the output is 180\u00b0 out-of-phase with the input. The gain is determined solely by the values of the two resistors. A noninverting amplifier can likewise be produced by taking the input to the noninverting input instead of the inverting input.<\/p>\n\n\n\n

As an illustration of the use of an operational amplifier, consider\u00a0Figure 18.44\u00a0which shows how it can be used as a differential amplifier to amplify the difference between two input voltages. Since there is virtually no current through the high resistance in the operational amplifier between the two input terminals, both the inputs X will be at the same potential. The voltage\u00a0V<\/em>2<\/sub>\u00a0is across resistors\u00a0R<\/em>1<\/sub>\u00a0and\u00a0R<\/em>2<\/sub>\u00a0in series. Thus, the potential\u00a0V<\/em>x<\/sub>\u00a0at X is:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Figure 18.44<\/strong> Differential amplifier<\/p>\n\n\n\n

Since the operational amplifier has a very high input resistance, the current through the feedback resistance will be equal to that from V<\/em>1<\/sub> through R<\/em>1<\/sub>. Hence, we have:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

and so:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Hence, substituting for V<\/em>x<\/sub> using the earlier equation, gives:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The output is a measure of the difference between the two input voltages.<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

The output signal from the sensor of a measurement system or the signal from the control unit might have to be processed in some way to make it suitable to operate the next element in the control system. For example, the signal may be too small and have to be amplified, be analog and have […]<\/p>\n","protected":false},"author":1,"featured_media":3149,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[423],"tags":[],"class_list":["post-3153","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-control-and-instrumentation-systems"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/system.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3153","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=3153"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3153\/revisions"}],"predecessor-version":[{"id":3154,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3153\/revisions\/3154"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/3149"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=3153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=3153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=3153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}