# The Area Ratio for Odd-Shaped Stencil Apertures

Joey writes:

Dear Dr. Ron,

I have a stencil aperture with an unusual shape. See Figure 1. How do I calculate the area ratio? The stencil thickness is 5 mils. The dimensions of the aperture are also in mils.

Joey,

The area ratio is simply the area of the stencil aperture opening divided by the area of the sidewalls. For common aperture geometries such as circles, squares, etc. it is easy to derive formulas. See Figure 2.

For an unusual shape like yours, it is easiest to simply calculate and divide the areas. From Figure 1, we get that area of the aperture opening as: 40*24+ the area of the two triangles. A little geometry (can you do it?) shows each triangle to have an area of 89 sq mils. So, the total area is 960 + 2*89 = 1138 sq mils. The perimeter is 40+24+16+16+28+12+16+16 = 168 mils, hence the area of the sidewalls is 168*5 = 840 sq mils. Therefore, the area ratio is 1138/840 = 1.355. Experience has shown that an area ratio of > 0.66 is needed for good solder paste transfer efficiency, so this stencil aperture will do well for transfer efficiency.

Careful thought would suggest that the triangular protrusions alone do not have a good area ratio. Calculations show their area ratios to be 0.37. So, the transfer efficiency in this part of the aperture might not be good. However, the area of the rectangle is so great, more than five times that of the triangles, as to alleviate this concern.

Dr. Ron

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## About Dr. Ron

Materials expert Dr. Ron Lasky is a professor of engineering and senior lecturer at Dartmouth, and senior technologist at Indium Corp. He has a Ph.D. in materials science from Cornell University, and is a prolific author and lecturer, having published more than 40 papers. He received the SMTA Founders Award in 2003.