Maximum Reach Estimates for Low-Voltage DC Power Delivery

Quote of the Day

Before you act, listen. Before you react, think. Before you spend, earn. Before you criticize, wait. Before you pray, forgive. Before you quit, try.

— Ernest Hemingway

Introduction

Figure 1: Wiring is Getting Out of Control and People are Trying to Use Existing Cables to Run Power. (Source)

It is no secret that I prefer Mathcad for the vast bulk of my computational work, but I live in a world in which Excel is universally available. As such, I must prepare Excel workbooks for others to use. Today, I was asked to prepare an Excel worksheet that our salesman could use for estimating the maximum range over which different combinations of wire and voltage could deliver useful power. I include my Excel workbook here for those who wish to follow along.

I am facing quite a bit of DC analysis lately because customers are doing everything they can to reuse existing cabling. Many customers are facing wiring nightmares (Figure 1) and are trying to find ways of minimizing the clutter.

This analysis is just an exercise in applying Ohm's law, but it does illustrate a type of calculation that electrical engineers regularly encounter.

I actually performed the calculation in two different ways:

• filled down formulas
• data table

As you can see in my workbook, both methods give the same answer – as they should.

Background

Schematic

Figure 2 shows my schematic model of this DC powering configuration.  The key features of this schematic are:

• The cable consists of pairs of wires.
• The resistance of the each wire in the pair is identical.
• The wire pairs will be connected in parallel, so the total cable resistance will be , where N is the number of wire pairs in parallel.
• Each wire end is inserted into a connector, which will add a contact resistance (R_C).

Figure 2: Electrical Schematic.

Basic Formulas

Figure 3 shows the formulas used to determine the maximum cable reaches. While it looks complex, it is just Ohm's law being applied to the configuration of Figure 3.

Figure 3: Reach Formula Summary.

Analysis

Parametric Assumptions

Figure 4 shows my parametric assumptions.

Figure 4: Key Analysis Parameters.

Final Result

Figure 5 shows my final result. While this specific result is important for some staff members, my interest here is sharing how the calculations are performed using Excel (workbook).

Figure 5: Max Reach Table.

Conclusion

This post was focused on how to present a simple electrical analysis in Excel. While Excel is not an ideal tool for mathematical work, I was able to prepare a workbook that others found useful and were able to modify to suite their needs.

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