How to Calculate Temperature Transmitter 4-20mA Output Using Linear Equation and Percentage Method ?

The temperature transmitter functions as a vital instrument in industrial process control and automation technology. The temperature transmitter turns temperature measurements into an electrical signal expressed as 4-20 mA current output signals for controllers and monitoring devices. The transmission technology provides precise readings along with dependable process control features.

The following guide demonstrates current output calculations from a temperature transmitter at 26.1 degrees Celsius (converted from 79 Fahrenheit) with a combined analysis of linear equation method and percentage conversion method.

Understanding the Key Parameters

Transmitter Range (Span & LRV/URV)

This transmitter converts real-time temperature readings into a corresponding output current that functions within the specified 4-20 mA range.

Lower Range Value (LRV)

The lowest temperature measurement range of the transmitter corresponds to an output of 4 mA.

Upper Range Value (URV)

The transmitter will output 20 mA current when measuring temperatures at its operational maximum.

Span

The measurement span equals the difference between URV and LRV as they represent the complete measurement range.

In our case

LRV (Lower Range Value) = 10°C (50°F)  –  4 mA

URV (Upper Range Value) = 60°C (140°F) –  20 mA

Span measurement = URV – LRV which produces 60 – 10 = 50 °C

Measured Value

The process temperature which we measure represents the current real-time condition for determining the necessary output current.

Measured Temperature = 26.1°C (79°F)

Real-time process readings have to transform into equivalent 4-20 mA output signals for accurate process monitoring and control applications. The precise measurement of process temperature at any moment enables linear calculation of current output for temperature transmitters operated within their specified range.

Accurate temperature measurement in industrial settings maintains process stability alongside ensuring safety conditions and boosting operational efficiency.

The determination of the current signal at 26.1°C enables us to confirm that the transmitter functions properly while delivering dependable data to controllers and monitoring systems.

Lower Range Value: 10°C 

Upper Range Value:60°C

Measured Temperature:26.1°C.

Our transmitter currently functions under temperature conditions between 10°C and 60°C because we must ascertain its output current level at 26.1°C.

Refer the below link for the Transmitter Calibration Span, LRV and URV Value Calculator from Measured 4 to 20 mA

Step 1: Calculate the Slope (m)

A 4-20 mA signal behaves according to linear characteristics. 

y=mx+c

where:

y = output current in mA

x = temperature in °C

m = slope of the function (determined from range)

c = y-intercept

The slope value (m) depends on the output of the rise-over-run calculation.

The slope (m) determination for the linear function requires using Δy and Δx to represent value variations as they relate to finding m in temperature transmitter 4-20 mA output calculations.

Δy (Change in Output Current): 

The difference in current output between the upper and lower range values.
Δy=URV Current−LRV Current=20mA−4mA=16mA

Δx (Change in Temperature): 

The difference between the upper and lower temperature values.
Δx=URV Temperature−LRV Temperature=60°C−10°C=50°C

This slope represents the change in output current per degree Celsius. In practical terms, it means that for every 1°C increase in temperature, the output current increases by 0.32 mA.

Step 2: Find the y-Intercept (c)

We use the known point (LRV = 10°C, output = 4 mA) and place it into the equation.

To calculate ‘c’ we use the equation while substituting x=10 and y=4 into it.

4=(0.32×10)+c

4=(0.32×10)+c 

4=3.2+c

4 = 3.2 + c

c=4−3.2=0.8

The linear equation describing the temperature transmitter operates as following: 

y=0.32x+0.8

The presented equation enables the determination of current output across the entire measurement temperature range. The value of c at 0.8 guarantees the current output begins at 4 mA whenever the measured temperature reaches the lower end of 10°C.

Click here for Calibration Procedure for Temperature Transmitter – Thermocouple

Step 3: Calculate Current Output

Substituting 26.1°C into the equation:

y=(0.32×26.1)+0.8

y=8.35+0.8

y=9.15 mA

Thus, at 26.1°C, the temperature transmitter outputs 9.15 mA.

Refer the below link for the Collection of Temperature Measurement Calculators

Alternative Method: Percentage Conversion Method

The percentage conversion method replaces linear calculations through an approach that transforms temperature readings into scale values for the 4-20 mA system.

Since 4-20 mA represents 0-100%, we calculate the current output as:

y=(0.322×16)+4

y=5.15+4

y=9.15 mA

This method provides a more intuitive approach by expressing the measured temperature as a fraction of the total span and then mapping it proportionally to the 4-20 mA scale.

Click here for Calibration Procedure for RTD Temperature Transmitter

Key Takeaways from both Calculation Methods:

The output current stands at 9.15 mA when the temperature reaches 26.1°C through either calculation method.

• The linear equation serves as an exact mathematical expression to determine output current from any temperature reading which makes it suitable for automated calculations.
• The percentage conversion method serves as a fast evaluation method for understanding signal conversion factors.
• The preferred method between two options depends on the situation’s requirements since customized equations streamline continuous use but percentage conversion works best for single use situations.
• Engineers who apply this knowledge deliver precise temperature measurements and process management in their industrial operations which enhances operational safety and efficiency.

Temperature Transmitter FAQs

What is a temperature transmitter?

The temperature transmitter functions as an instrument that transforms thermocouple or RTD (Resistance Temperature Detector) signals into standardized 4-20mA current signals. The transmission of temperature data becomes more efficient for extended distances through this conversion method with reduced signal degradation.

Must read : How to Convert Thermocouple Millivolts to Temperature: A Step-by-Step Guide

What is the output of a temperature transmitter?

A standard output signal from a temperature transmitter takes the form of a 4-20mA current transmission that covers specified temperature levels. The temperature transmitter generates 4mA when it detects the LRV and outputs 20mA before URV.

You can determine a 4-20mA signal through a specific calculation.

How do you calculate the 4-20mA signal?

To convert temperature measurement to a 4-20mA signal you need to apply this mathematical formula:

Where:

• Measured Value = the actual temperature being read
• LRV (Lower Range Value) = the minimum temperature in the transmitter’s range
• URV (Upper Range Value) = the maximum temperature in the range
• Span = URV – LRV

Click here to access our Collection of Instrumentation Signal Conversion Calculators

Why is a 4-20mA signal used?

The 4-20mA current loop became an industry standard because of its wide adoption by various industrial sectors.

• This signal retention protocol protects information transmission from degradation during extended distance travels.
• The signal demonstrates better resistance to electrical noise compared to voltage signals.
• A configured 4mA lower range value allows for sensor failure detection through a dropped signal level below 4mA.
• The detector operates using a direct current power supply which runs from 8 to 32 volts DC being a standard input for control systems integration.

Must read to know about Burnout Function of a Temperature Transmitter with an example