# 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

# Area Ratios for Elongated “D” Apertures

Folks,

Ismail writes: Dr. Ron, I know that the area ratio for circular and square stencil apertures is 4d/t.  What is it for an elongated “D” aperture?

The area ratio of a stencil aperture is the area of the aperture opening divided by the area of the side walls.  It is interesting, as Ismail points out, that the area ratio of a circular aperture is the same as that of a square aperture.  A little 10th-grade geometry will point this fact out.  It ends up that the area ratio of an elongated “D” is a little more complex.  All of these aperture shapes and that for a rectangle aperture are shown in Figure 1.   The area ratio formulas are at the bottom of the figure. Figure 1. The area ratio for several shaped apertures. The elongated “D” aperture is third from the left.

A rule of thumb that still seems to hold is that the area ratio should be 0.66 or greater for the best printing result.  It is possible to do somewhat better (i.e with an area ratio less than 0.66) with a superior solder paste and/or some of the new stencil nano-coatings.

The derivation of the area ratio for the elongated “D” is in Figure 2. Figure 2.  The derivation of the area ratio for an elongated D shaped aperture.

Cheers,

Dr. Ron