What Actually Creates The 90 Degree Coupler Phase Shift?

In a coupler made up of parallel coupled lines there is a phase relationship between the through port and the coupled port. The electrical phase of the coupled port is 90 degrees when the through port is referenced as 0 degrees. This 90 degree phase occurs at all frequencies for which the coupler has a good match. Parallel line couplers which have this characteristic are designed symmetrically with an odd number of sections.

It is true that these couplers have 90 degree electrical length lines at the center frequency of operation, but this has nothing to do with the 90 degree phase relationship between coupled and through ports. It does have everything to do with getting maximum coupling amplitude at the center frequency. Whatever creates this phase shift must then be independent of frequency.

The explanation for this can summed up in one sentence but would take pages of derivation to prove it. The explanation is the following sentence. "At a coupled port equal forward and reverse propagating waves combine 0 degree and 180 degree phase components generated by mode reflection coefficients to produce a 90 degree phase shift independent of frequency." This statement now needs to be put into the correct context with transmission line theory along with even and odd mode analysis. It should now be clear that variation of line length will not "tune" the relative phase shift of the coupled port. It is only the even and odd mode impedances that can do this. This frequency independent 90 degree phase shift is a very useful property, especially for passive broadband designs.