 ## Current Measurement with a Shunt Resistor – 1

In my first article I explained what a shunt resistor and a kelvin connection are. If you haven’t read it yet, I suggest you first read this article 👇

In this article, I will mention how to do hardware design calculations for the shunt resistor. These calculations will also enable us to select the shunt resistor according to their specs.

## History and Motivation

Let me briefly explain how I gathered all the information and what the application is for.

I have started this project as an MSc project. It is a Current Measurement Companion device for battery powered systems, especially electric vehicles (EVs). It is designed to be used along with a Battery Management System (BMS). BMS typically needs an accurate measurement of the current and the voltage of the cells, and the drawn energy from/to a battery. Having higher accuracy of the measurement will lead to better State of Charge (SoC) and State of Health (SoH) estimations. So, this device is developed to do accurate measurements.

I talked about the Kelvin connection and the shunt resistors in the first article. In this article, I will focus on the hardware design side for this project. Hence, I will explain all the important calculations when designing a current measurement device with a shunt resistor.

## Design Criteria

In applications where higher accuracy is needed. A low tolerance, low ppm and high-power shunt resistor is necessary. There is a resistor WSBS8518L5000JK35 from Vishay Dale selected as an example (also used in the previous article) with the following specification which matches the selection criteria and trade-offs.

The maximum estimated current for this example is ±45A which can pass through the resistor.

The specs from the datasheet are as follows:

The shunt resistor is 500 µOhms. So, the total sense voltage across the resistor can be;

V_{SENSE} = ± 45A \times 500μΩ = \pm0.225V

Maximum Dissipated Power on Shunt resistor is:

P_{SHUNT} = I^2 \times R = 45^2 \times 500 μΩ = 1,0125W

Maximum Dissipated power is lower than the shunt resistor’s power rating.

## Errors

The accuracy of a current sensor system depends mainly on the tolerance and temperature dependency of the shunt. A larger error contribution to the shunt is a result of shunt tolerances. The shunt tolerances can be eliminated by using compensation techniques. To perform compensation, LMT87 temperature sensor is used to detect the temperature of the shunt. This temperature information is obtained from the MCU and then a compensation algorithm can be performed. Below figure shows a plot of the shunt at different temperature coefficient resistance (TCR) values, the resistance versus temperature change.

In Figure below, there is a plot of power dissipation vs shunt resistance for a fixed load current. Power dissipation in the shunt resistor is the product of voltage across it and current flowing through it, or equivalently, the product of the shunt resistance and square of the current flowing through it. Increasing the value of the current-shunt resistor increases the differential voltage developed across the resistor, reducing errors caused by VOS. However, the power that is dissipated across the shunt resistor also increases, which can cause heat, size, and cost problems in a real application.

Power Dissipation (W) = R_{SHUNT} \times {I_{LOADMAX}}^2\\
I_{LOADMAX} = 45A

I will continue with the Current Sense Op-Amp in the next article.

Stay Tuned! :)

Resource: TI, Vishay, Wikipedia.