# 3D Plot Example Using PCB Trace Current vs Trace Area and Temperature Rise

Quote of the Day

Reproducibility, automation,  it's just text, and easy to communicate.

— Hadley Wickham, virtuoso in data visualization, on why we should use a programming language for data analysis.

## Introduction

I was asked this morning about how to create a 3D plot in Mathcad that shows a surface, two lines on the surface, and marks the point of intersection of the two lines (Figure 1). It just so happens that I have been looking at the amount of current that a PCB trace of a given area can carry for a given temperature rise above ambient – I will use this function for my 3D plot example. While the curve itself is a bit boring and viewing it in 3D does not add any value, this example does illustrate the procedure for generating this type of plot.

For those who are interested, my Mathcad source is here.

## Background

The equation that I am plotting comes from this document on outer layer trace current (IOuter) versus versus trace area (A) and allowed temperature rise (ΔT).

## Analysis

### Setup the Formula

The commonly used formulas for the current carried by a PCB trace with a given cross-sectional area and temperature rise are given by the following documents:

• Document used for these calculations (I have used this for years)
• An update to the document above that I have not gone through yet
• The original mil-spec (1970s) on which much PCB thermal work is still based

Figure 2 shows the formula that I usually use and a traditional 2D representation of a 3D data.

### Setup the 3D Plot

Figure 3 shows how I setup the 3D plot. In this case, I decided to plot the surface using parametric equations – the only reason I did this was to demonstrate the parametric concept.

The actual plot is shown in Figure 4, which is the same as Figure 1 but with the graphic arguments shown.

## Conclusion

I hope this helps folks who are struggling with 3D plots in Mathcad. They can be frustrating.

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