# Quick Backup Current Limit Calculation

Quote of the Day

You know everybody is ignorant, only on different subjects.

— Will Rogers (1879 - 1935)

## Introduction

Figure 1: E95 D-Cell Energy Versus Load Current. (Source)

I was in a meeting this morning when I was told a battery pack had insufficient capacity to meet a 24 hour backup time requirement. While in the meeting, I grabbed a specification for the battery the test engineer was using, did a quick calculation of the backup time results that the test engineer should have expected, and what needed to change in order to pass the backup time requirement. While I have discussed different kinds of battery calculations in numerous blog posts, I thought this one was more typical than most and reflects the kind of work done daily by battery engineers.

For those who like to follow along, here is my Mathcad source and a PDF.

## Analysis

### Observation

You can see from Figure 1 that the amount of energy that you can extract from a D-cell alkaline battery is a strong function of the load current (aka drain current). The reason that the test failed is because the test engineer failed to use the correct load current, but I did not know that when I was informed that we failed the test – you never get the full story right away.

### Calculations

#### Capture Figure 1

Figure 2 shows how I captured the information in Figure 1 using Dagra, a program that allows you to digitize curves. I also created a function, E(x) where x is the load current, for interpolating Dagra's discrete data capture.

Figure 2: Digitize Figure 1 For Analysis.

#### Predict the Run Time Under the Test Conditions

The test engineer used a load current of 1.6 A, which is much higher than the backup current required for our products. I first wanted to verify that the backup time he measured was reasonable consider he used this load current. I can compute E(1.6 A), which is the available energy capacity of the battery in Amp-hours. You can estimate the run time by dividing the available energy capacity by the load current, which says we should be seeing ~1.5 hours. Since the test engineer is measuring 1.5 hours, everything is working as it should be – the test engineer's expectations were incorrect.

Figure 3: My Run-Time Prediction Versus Measured Result.

What happened here? The 1.6 A load current reflects normal product operation. When operating from battery, our products limit their power usage by turning off non-critical services, like wireless, that use much power.

#### Maximum Constant Current Load for 24 Hour Operation

The test engineer needed to know the correct load current to apply for meeting a 24 hour backup time requirement. Figure 4 shows I estimated the load current limit (422 mA) given a 24 hour backup time. Again, I used my digitized version of Figure 1. This load current level seems much more reasonable than what was tested initially.

Figure 5: Maximum Current Load for 24 Hour Operation.

I am confident that the unit will pass the 24 hour backup time requirement with a load current of ~400 mA.

## Conclusion

All this happened during a 30 minute call in which backup time and many other subject were covered. All you need is a portable computer, an internet connection, and the right tools to work many problems quickly.

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