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?

**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.

**Next, determine the diameter of the vias.**The diameter of the vias is measured to be 1.

**Next, determine the distance between two successive vias in the same row.**In this case, the distance is 3.

**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