Figure 1: two successive -3dB-couplers
Filter in a waveguide-system consist of two successive -3db couplers. Let's survey Figure 1. The green circles label the -3db couplers. The waveguide- sections between these couplers still have got the same length. Both parts of energy suffer the same phaseshift therefore. (This system is relatively frequency-independent.)
In figure 2 the coupler divides the energy too. The upper one arm is the same as in figure 1. The bottom one arm is longer, and the parts of energy suffers a different phaseshift now. If the length of the detour line is a integer value of the wavelength, then the phases are relevant like the case in figure 1.
If the length of the detour line is not a integer value of the wavelength,
then the phases are different and both parts of energy are weakened.
This system is frequency-dependent now: This is a filter!
In this case the energy with reversed-phase is invigorated in the direction of the Dummy.
If the length of the detour line causes a phase-difference of 180 degrees, then the branch connexion can be used as a diplexer and the crotched energy (and this is the part with another frequency!) can be connected with e.g. a second receiverchannel (instead of the dummy).
Figure 2: the detour line in the lower arm causes different conditions for the phases