Enter the distance between two vias rows, the vias diameter, and the distance between two successive vias in the same row to determine the effective width of a SIW (substrate integrated waveguide).

## SIW Formula

The following formula is used to calculate the effective width of a substrate integrated waveguide (SIW).

aeff = a – (d^2/0.95*s)

• Where aeff is the effective width
• a is the distance between two vias rows
• d is the vias diameter
• s is the distance between two successive vias in the same row

## SIW Definition

A SIW, short for substrate integrated waveguide, is a synthetic electromagnetic waveguide, often in a rectangular shape, formed in a dielectric substrate by densely arrayed metal posts.

## Example Problem

How to calculate the effective width of a SIW?

1. First, determine the distance between two vias rows.

For this example, simple numbers will be used to show the process of calculation. The distance between two vias rows in this example is 5.

2. Next, determine the diameter of the vias.

The diameter of the vias is measured to be 1.

3. Next, determine the distance between two successive vias in the same row.

In this case, the distance is 3.

4. Finally, calculate the effective width.

Using the formula above, the effective width is calculated to be:
aeff = a – (d^2/0.95*s)
aeff = 5 – (1^2/(0.95*))
aeff = 4.649