How to do with Linear Calibration?

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**~ Table of Contents:**

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= 1. Instroduction =

This chapter shows how to perform linear calibration.

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= 2. Linear calibration =

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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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== 2.1 Solve the linear relationship manually ==

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(% 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.

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We can make a coordinate axis as below:

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1. (% style="color:#4f81bd" %)**Y**(%%) axis is the real value, from 0~~10 meters

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1. (% style="color:#4f81bd" %)**X**(%%) axis is the probe output , from 4~~20mA

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We use two points to make the linear line: Point1(x1,y1) = (4,0), Point2(x2,y2)= (20,10).

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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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* **Step1:** Get (% style="color:#4f81bd" %)**realk(Slope)**(%%) for the line:

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k=(y2-y1)/(x2-x1) = (10-0)/(20-4) =10/16= 0.625

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* **Step2:** Get (% style="color:#4f81bd" %)**real value( y )**(%%):

k =(y-y1)/(x-x1)

~-~-> y = k*(x-x1)+y1 = 0.625 * (x-4) + 0.

~= 0.625 * (x-4)

Thus, we can introduce x-values to the already obtained equations to derive the corresponding y-values：

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When x=12 mA , y=5 meters

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When x=8 mA, y=2.5 meters

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A more general formular:

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(% style="color:#4f81bd" %)**Y=(y2-y1)/(x2-x1)* (x-x1) + y1**

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Calibration Curve Schematic：

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[[image:image-20240902114541-1.png||height="479" width="851"]]

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== 2.2 Performing linear calibration curves in Excel ==

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In addition, we can also perform calibration curves in Excel and directly obtain linear equations by statistics of X and Y values.

= 3. Case examples =

Some case for example which we can use Linear Calibration:

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(% style="color:blue" %)**Case 1: Calibrate Microwave Radar Readling.**

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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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(% style="color:blue" %)**Case 2: Calibrate the Soil EC base on SE01 soil sensor raw EC reading.**

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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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(% style="color:blue" %)**Case 3: use water level probe to calibrate for oil.**

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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

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(% style="color:red" %)**Notice for Linear Calibrate:**

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1. k(Slope) is very important, We can measure more points to calculate the most accuracy k.

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1. Make sure the mapping is linear, and choose two calibrate points as "far" as possible.

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Wiki source code of How to do with Linear Calibration?

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author	version	line-number	content
		1	~ Table of Contents:
		2
		3	{{toc/}}
		4
		5
		6
		7	= 1. Instroduction =
		8
		9
		10	This chapter shows how to perform linear calibration.
		11
		12
		13	= 2. Linear calibration =
		14
		15
		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.
		17
		18
		19	== 2.1 Solve the linear relationship manually ==
		20
		21
		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.
		23
		24	We can make a coordinate axis as below:
		25
		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
		28
		29	We use two points to make the linear line: Point1(x1,y1) = (4,0), Point2(x2,y2)= (20,10).
		30
		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:
		32
		33	* Step1: Get (% style="color:#4f81bd" %)realk(Slope)(%%) for the line:
		34
		35	k=(y2-y1)/(x2-x1) = (10-0)/(20-4) =10/16= 0.625
		36
		37	* Step2: Get (% style="color:#4f81bd" %)real value( y )(%%):
		38
		39	k =(y-y1)/(x-x1)
		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
		52	A more general formular:
		53
		54	(% style="color:#4f81bd" %)*Y=(y2-y1)/(x2-x1) (x-x1) + y1**
		55
		56
		57	Calibration Curve Schematic：
		58
		59	[[image:image-20240902114541-1.png\|\|height="479" width="851"]]
		60
		61
		62	== 2.2 Performing linear calibration curves in Excel ==
		63
		64
		65	In addition, we can also perform calibration curves in Excel and directly obtain linear equations by statistics of X and Y values.
		66
		67
		68
		69
		70
		71
		72
		73
		74	= 3. Case examples =
		75
		76
		77	Some case for example which we can use Linear Calibration:
		78
		79
		80	(% style="color:blue" %)Case 1: Calibrate Microwave Radar Readling.
		81
		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.
		83
		84
		85	(% style="color:blue" %)Case 2: Calibrate the Soil EC base on SE01 soil sensor raw EC reading.
		86
		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
		88
		89
		90	(% style="color:blue" %)Case 3: use water level probe to calibrate for oil.
		91
		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
		93
		94
		95	(% style="color:red" %)Notice for Linear Calibrate:
		96
		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.
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