Analogue Inputs Resolution Assignment a) Describe the relationship between the number of bits used in an analogue signal and the resolution available. b) A system has a level sensor which measures the level of water in a tank. It provides -1V signal which is read by a 12 bit A-D converter. Given the system has a stroke of 25mm, calculate the minimum increment in the height of the water that the system can discern. LO2.2
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. If we read a 1v signal and we only have 1 bit signal V PLC A-D
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. If we read a 1v signal and we only have 1 bit signal 1V PLC A-D 1 States 2, steps 1 Resolution 1V
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. If we read a 1v signal and we only have 2 bit A to D converter V PLC A-D Bit 1 Bit 1 1 1 1
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. If we read a 1v signal and we only have 2 bit A to D converter 3.33V PLC A-D Bit 1 Bit 1 1 1 1
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. If we read a 1v signal and we only have 2 bit A to D converter 6.66V PLC A-D Bit 1 Bit 1 1 1 1
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. If we read a 1v signal and we only have 2 bit A to D converter 1V PLC A-D Bit 1 Bit 1 1 1 1 States 4 steps 3 Resolution 3.33V
Analogue I/O Resolution 4 bit binary enables us to count to 15 Bit 3 Bit 2 Bit 1 Bit Analogue Voltage 2 3 2 2 2 1 2 8 4 2 1 V max = 1V 1.66 1 1.33 1 1 2 1 2.67 1 1 3.34 1 1 4.1 1 1 1 4.68 1 5.35 1 1 6.2 1 1 6.69 1 1 1 7.36 1 1 8.3 1 1 1 8.7 1 1 1 9.37 1 1 1 1 1.4 States 16, steps 15 resolution 1V/15 steps =.66v
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. If we read a 15v signal and we now have 12 bit A to D converter 15v PLC A-D 1 1 1 1 1 1
Analogue I/O Resolution Step size is 3.66mV 12 bit binary enables us to count to.495 Bit 11 Bit 1 Bit 9 Bit 8 Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Bit Analogue Voltage 2 11 2 1 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 248 124 512 256 128 64 32 16 8 4 2 1 V max = 15V 1 3.66mV 1 7.32mV 1 1 1.98mV 1 etc 1 1 1 1................................................................................................ 1 1 1 1 1 1 1 1 1 1 1 1 15v
Analogue I/O Resolution 12 bit binary enables us to count to 495 Step size = V max 2 12-1 There are 496 different states But only 495 steps between them. V max = 15V then step size (resolution) is 15/495 = 3.66mV
Analogue I/O Resolution 16 bit binary enables us to count to? Step size = V max 2 16-1 There are...different states But only... steps between them. V max = 1V then step size (resolution) is 1/ =
Analogue I/O Resolution 16 bit binary enables us to count to 65536? Step size = V max 2 16-1 There are 65536 different states But only 65535 steps between them. V max = 1V then step size (resolution) is 1/65535 =.152mV
Example Question a) Describe the relationship between the number of bits used in an analogue signal and the resolution available. b) A system has a level sensor which provides 1 bit -1V signal and measures the level of water in a tank. Given the system has a stroke of 5mm, calculate the voltage change per step and the minimum increment in the height of the water that the system can discern.
Example Question b) A system has a level sensor which provides a 1 bit -1V signal and measures the level of water in a tank. Given the system has a stroke of 5mm, calculate the minimum increment in the height of the water that the system can discern. Vmax/2 1-1 = 1/123 =.97v per step 5/123 =.488mm End
Analogue Inputs - Resolution The resolution, the smallest change that an Analogue input can detect, is determined by how many binary bits the A-D converter has. 6.2v PLC 12 bit A-D (-1V output) 1 1 1 1 1 1 2 11 2 1 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 248 124 512 256 128 64 32 16 8 4 2 1 1 1 1 1 1 1
Analogue I/O Resolution 4 bit binary enables us to count to 15 Bit 3 Bit 2 Bit 1 Bit Analogue Voltage 2 3 2 2 2 1 2 8 4 2 1 V max = 15V 1 1 1 2 1 1 3 1 4 1 1 5 1 1 6 1 1 1 7 1 8 1 1 9 1 1 1 1 1 1 11 1 1 12 1 1 1 13 1 1 1 14 1 1 1 1 15 Step size = There are 16 different states V max 2 4-1 But only 15 steps between them.
Analogue I/O Resolution Digital to Analogue Conversion Four bit binary number Analogue -15V v Digital 4 bit
Analogue I/O Resolution Digital to Analogue Conversion Four bit binary number Analogue -15V 1v 1 Digital 4 bit
Analogue I/O Resolution Digital to Analogue Conversion Four bit binary number Analogue -15V 1 2v Digital 4 bit
Analogue I/O Resolution Digital to Analogue Conversion Four bit binary number Analogue -15V 1 3v 1 Digital 4 bit