Changes for page How to do with Linear Calibration?

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16	16	In some case, the measurement and real value are in different range, but they are both linear, we have to calculate the real value with the measurement we can use a simple Linear Calibration.
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18	18
19		-Example: we have a water level probe, the measurement range is 0 ~~ 10 meters, and the output is 4~~20mA, this means the when the water level is 0 meter, the output is 4mA, when the water level is 10 meters, the output is 20mA. We can make a coordinate axis as below:
	19	+== 2.1 Solve the linear relationship manually ==
20	20
21		-1. Y axis is the real value, from 0 ~~ 10 meters
22		-1. X axis is the probe output , from 4~~20mA
23	23
24		-We use two points to make the linear line: point1(x1,y1) = (4,0), point2(x2,y2)= (20,10). Since the reading is linear, all probe output and real value is on this line, so we can calculate the real value by probe output in two steps:
	22	+(% style="color:blue" %)**Example:**(%%) we have a water level probe, the measurement range is 0 ~~ 10 meters, and the output is 4~~20mA, this means the when the water level is 0 meter, the output is 4mA, when the water level is 10 meters, the output is 20mA.
25	25
26		-Step1: Get k(Slope) for the line: k=(y2-y1)/(x2-x1) = (10-0)/(20-4) =10/16= 0.625
	24	+We can make a coordinate axis as below:
27	27
28		-Step2: Get real value ( y ):
	26	+1. (% style="color:#4f81bd" %)**Y**(%%) axis is the real value, from 0~~10 meters
	27	+1. (% style="color:#4f81bd" %)**X**(%%) axis is the probe output , from 4~~20mA
29	29
30		-k=(y-y1)/(x-x1)
	29	+We use two points to make the linear line: Point1(x1,y1) = (4,0), Point2(x2,y2)= (20,10).
31	31
32		-~-~-> y = k*(x-x1)+y1 = 0.625 * (x-4) + 0.
	31	+Since the reading is linear, all (% style="color:#4f81bd" %)**probe output**(%%) and (% style="color:#4f81bd" %)**real value**(%%) is on this line, so we can calculate the real value by probe output in two steps:
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34		- ~= 0.625 * (x-4)
	33	+* **Step1:** Get (% style="color:#4f81bd" %)**realk(Slope)**(%%) for the line:
35	35
36		-When x=12mA , y=5 meters
	35	+ k=(y2-y1)/(x2-x1) = (10-0)/(20-4) =10/16= 0.625
37	37
38		-When x=8mA, y= 2.5 meters
	37	+* **Step2:** Get (% style="color:#4f81bd" %)**real value( y )**(%%):
39	39
	39	+ k =(y-y1)/(x-x1)
40	40
	41	+ ~-~-> y = k*(x-x1)+y1 = 0.625 * (x-4) + 0.
	42	+
	43	+ ~= 0.625 * (x-4)
	44	+
	45	+Thus, we can introduce x-values to the already obtained equations to derive the corresponding y-values：
	46	+
	47	+When x=12 mA , y=5 meters
	48	+
	49	+When x=8 mA, y=2.5 meters
	50	+
	51	+
41	41	A more general formular:
42	42
43		-Y=(y2-y1)/(x2-x1)* (x-x1) + y1
	54	+(% style="color:#4f81bd" %)**Y=(y2-y1)/(x2-x1)* (x-x1) + y1**
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45	45
46		-[[image:image-20240902114541-1.png||height="492" width="874"]]
	57	+Calibration Curve Schematic：
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	59	+[[image:image-20240902114541-1.png||height="479" width="851"]]
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49	49
50		-= 3. Case examples =
	62	+== 2.2 Performing linear calibration curves in Excel ==
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52	52
53		-Some case for example which we can use Linear Calibration:
	65	+In addition, we can also perform calibration curves in Excel and directly obtain linear equations by statistics of X and Y values.
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55	55
56		-Case 1: Calibrate Microwave Radar Readling.
57	57
58		-The microwave radar reading might effect by the OUM(Object Under Measured), but the reading still linear. In this case, we can measure the closest(x1,y1) and the farthest point(x2,y2). Where the x is reading in platform, y is the real value. And use above method to calibrate.
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60	60
61		-Case 2: Calibrate the Soil EC base on SE01 soil sensor raw EC reading.
62	62
63		-The SE01 probe is calibrated via mineral soil. The reading for other soil will be different by still in linear, In this case, we can measure two points (x1,y1) and (x2,y2). Where the x is reading of Raw EC, y is the real EC for the soil. And use above method to calibrate
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65	65
66		-Case 3: use water level probe to calibrate for oil.
	74	+= 3. Case examples =
67	67
68		-Oil has different density vs water, but we can still use the immersion type water level pressure sensor to get the oil level. In this case, we can measure two points (x1,y1) and (x2,y2). Where the x is reading of water level, y is the oil level. And use above method to calibrate
69	69
	77	+Some case for example which we can use Linear Calibration:
70	70
71		-Notice for Linear Calibrate:
72	72
73		-1. k(Slope) is very important, We can measure more points to calculate the most accuracy k.
74		-1. Make sure the mapping is linear, and choose two calibrate points as “far” as possible.
	80	+(% style="color:blue" %)**Case 1: Calibrate Microwave Radar Readling.**
75	75
	82	+The microwave radar reading might effect by the OUM(Object Under Measured), but the reading still linear. In this case, we can measure the closest(x1,y1) and the farthest point(x2,y2). Where the x is reading in platform, y is the real value. And use above method to calibrate.
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77	77
	85	+(% style="color:blue" %)**Case 2: Calibrate the Soil EC base on SE01 soil sensor raw EC reading.**
78	78
	87	+The SE01 probe is calibrated via mineral soil. The reading for other soil will be different by still in linear, In this case, we can measure two points (x1,y1) and (x2,y2). Where the x is reading of Raw EC, y is the real EC for the soil. And use above method to calibrate
79	79
80	80
	90	+(% style="color:blue" %)**Case 3: use water level probe to calibrate for oil.**
81	81
	92	+Oil has different density vs water, but we can still use the immersion type water level pressure sensor to get the oil level. In this case, we can measure two points (x1,y1) and (x2,y2). Where the x is reading of water level, y is the oil level. And use above method to calibrate
82	82
83	83
	95	+(% style="color:red" %)**Notice for Linear Calibrate:**
84	84
	97	+1. k(Slope) is very important, We can measure more points to calculate the most accuracy k.
	98	+1. Make sure the mapping is linear, and choose two calibrate points as "far" as possible.
	99	+
	100	+
85	85