cross-coupled waveguide

does anyone have any explanatios about cross-coupled waveguide?
i want to know the basic theory of it

thx before

masadi

I've no paper to suggest.
I try to write an intuitive explanation.
Do you know Yagi antennas and it's principle of operation? I thin so.
Cross coupled wg may be intuitively explained as particular case of Yagi.

How the coupler is made?

2 WG tubing are soldered together sharing a square area, the metal wall. The side is the WR size.

The coupling is made by two holes on the wall, placed along one (and one only) diagonal of the square, close to the corners.
But where exactly the hole are placed?
Projecting the hole's axial distance along the propagation axis, you'll obtain λg/4.

So, here the connection to the Yagi example; two discontinuity (the holes), λ/4 spaced, will radiate the coupled waveguide on the same direction of the main waveguide.

The principle of operation is the same for X-coupled WG and In-Line E coupled WG, but the 2nd usually is manufactured with much more holes so is more directive.

As big are the holes and as thin is the metal wall as the coupled power is high.

in microwave filter the cross coupling appear when there is coupling between non adjacent resonator, hence you will see a Transmission Zero form eather side (high or low) because it is depend on your structure of the filter.

I have some papers and documents

Please check them.