Linear to Square Root Extraction Signal Converter: 4-20mA, 3-15 Psi, 1-5 Volt Signals
- In certain applications, pressure measurements are utilized to indirectly determine other variables, such as the rate of flow of a gas or liquid.
- In a closed pipe, the flow rate is directly linked to the square root of the pressure drop, also known as the differential pressure, between two points.
- This relationship is non-linear, meaning that there’s a more significant change in flow at lower pressures compared to higher ones.
- To enhance the resolution of flow measurement, some differential pressure transmitters can be adjusted so that their output is directly proportional to the flow rate rather than the differential pressure.
Formula for Conversion
For the conversion of a linear 4-20mA current loop signal to a square root extraction type, the following formula can be applied:
Output SqRt = 4mA + (4 x √(OutputLinear – 4mA))
Example Calculation
Let’s say we have a linear 4-20mA current loop signal reading of 12mA and we want to convert it to a square root extraction type using the provided formula:
OutputSqRt = 4mA + (4 x √(OutputLinear – 4mA))
Substituting the given value:
OutputSqRt = 4mA + (4 x √(12mA – 4mA))
OutputSqRt = 4mA + (4 x √8mA)
Now, √8mA ≈ 2.83 (approximately)
OutputSqRt = 4mA + (4 x 2.83)
OutputSqRt = 4mA + 11.32mA
OutputSqRt ≈ 15.32mA
So, the square root extraction type output for a linear input of 12mA is approximately 15.32mA.
Linear Signal to Square Root Extraction Signals Conversion Table
The conversion table below illustrates the values for linear to square root extraction conversion from 4 to 20 milliamp current loop signals:
| Linear (mA) | Square Root (mA) | Square Root (%) | Square Root (psi) | Square Root (V) |
| 4 | 4.00 | 0.00 | 3.00 | 1.00 |
| 5 | 8.00 | 25.00 | 6.00 | 2,00 |
| 6 | 9.66 | 35.36 | 7.24 | 2.41 |
| 7 | 10.93 | 43.30 | 8.20 | 2.73 |
| 8 | 12.00 | 50.00 | 9.00 | 3.00 |
| 9 | 12.94 | 55.90 | 9.71 | 3.24 |
| 10 | 13.80 | 61.24 | 10.35 | 3.45 |
| 11 | 14.58 | 66.14 | 10.93 | 3.65 |
| 12 | 15.31 | 70.71 | 11.49 | 3.83 |
| 13 | 16.00 | 75.00 | 12.00 | 4.00 |
| 14 | 16.65 | 79.06 | 12.49 | 4.16 |
| 15 | 17.27 | 82.91 | 12.95 | 4.31 |
| 16 | 17.86 | 86.60 | 13.39 | 4.46 |
| 17 | 18.42 | 90.14 | 13.82 | 4.60 |
| 18 | 18.97 | 93.54 | 14.23 | 4.74 |
| 19 | 19.49 | 96.83 | 14.62 | 4.88 |
| 20 | 20.00 | 100.00 | 15.00 | 5.00 |
Instrumentation Standard 4 to 20mA Linear Signal to Square Root Extraction Signals
This below calculator is used for converting instrumentation standard signals from 4 to 20mA Linear Signal to Square Root Extraction 4 to 20 mA, Pneumatic 3 to 15 Psi and voltage 1 to 5 volt Signals
Click here for Square Root Extraction Signal to Linear Signal Converter: 4-20mA, 3-15 Psi, 1-5 Volt Signals
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