Introduction •  Download •  Usage •  Calculating Span •  Credits

Introduction

Span Calculator is an interactive tool for calculating and visually representing the linear relationship between an input and output signal. The graph and table are updated accordingly when adjustments are made to the input or output upper or lower range values. The application also allows for calculating a specific value's proportional response, by inputting the desired value into either the input or output boxes.

Usage

This section covers 2 example problems.

1. A 4-20mA pressure sensor is returning 8.5mA. If the pressure sensor's range is 0-50psi, what pressure is it reading?
   • Start by clicking the signal type drop-down to select the desired signal type.
   • Next, set up the input and output parameters by adjusting the range sliders or input boxes accordingly.
   • Finally, select the radio static button for the milliamp signal and input the given value (8.5ma). After you add the value to the input box a new point is created on the graph. The answer is the y coordinate: 14.06psi.

Note

In this example I have the input representing the range and feedback from the sensing device, and the output representing the range and measurement of the sensing device. Flipping these will cause no problems though.

Note

If the Signal Type drop-down doesn't include the desired signal, you can select Custom which will give you a range from [-100, 100]

Solving by hand

Starting with the Input equation:

$$ \begin{gather*} 8.5 = (20-4) \cdot x + 4\\ 4.5 = 16 \cdot x\\ x = 0.28125\\ \end{gather*} $$

Now that we have the per-unit percentage of the milliamp signal we can now calculate the pressure.

$$ \begin{gather*} \text{Output} = (50-0) \cdot (0.28125) + 0\\ \text{Output} = 50 \cdot (0.28125)\\ \text{Output} = 14.1\text{psi} \end{gather*} $$

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2. The sensor is now reading 32psi. What should the milliamp reading be?
   • Sticking with the same parameters from the previous example, just select the output radio-static button and enter 32psi in the numeric input box. The final answer should be 14.24mA

Solving by hand

Starting with the Output equation:

$$ \begin{gather*} 32 = (50-0) \cdot x + (0)\\ 32 = 50 \cdot x\\ x=0.64=64% \end{gather*} $$

Now calculate the current:

$$ \begin{gather*} \text{Input} = (20-4) \cdot (0.64)+ 4\\ \text{Input} = 14.24\text{mA} \end{gather*} $$

Download

You can download the latest version of Span Calculator for Windows.

Calculating Span

Uses the slope intercept formula:

$$y=mx + b$$

$$ \begin{gather*} \frac{\text{Input}-LRV_{in}}{URV_{in}-LRV_{in}}=\frac{\text{Output}-LRV_{out}}{URV_{out}-LRV_{out}} = \text{per-unit ratio (x)} \end{gather*} $$

Solving for $\text{Input}$ and $\text{Output}$, we get two equations:

$$ \begin{gather*} \text{Input}=(URV_{in}-LRV_{in})\cdot\text{x}+LRV_{in} \end{gather*} $$

$$ \text{or}\\ $$

$$ \begin{gather*} \text{Output}=(URV_{out}-LRV_{out})\cdot\text{x}+LRV_{out} \end{gather*} $$

• $URV_{in}$
  • The output range high feedback/response of the sensing device
• $LRV_{in}$
  • The output range low feedback/response of the sensing device
• $URV_{out}$
  • The unit output range high of the sensing device
• $LRV_{out}$
  • The unit output range low of the sensing device

Credits

This software uses the following open-source packages:

• Electron
• Angular
• node.js
• Chart.js
• Angular Material