How to calculate s11 of microstrip ring with one feeding port?

[Terminator3]

i want to know impedance of microstrip ring, that have only one port. Ring is one wavelength microstrip. Can it be represented by two parallel 180 deg lines? open-circuited termination? i am not sure how to calculate it. I read some papers, but it is too advanced for me at this time.

 

[WimRFP]

Hello, you are right, when you feed it via a capacitive gap or directly from another microstrip, you have two same length lines. The resonant impedance will be high when each half is a half wavelength long. Though they are connected at the end, they appear as an open circuit. The waves from the two halves appear at the opposit side same time and same amplitude, but travel in opposite direction. Because of the opposite direction of travel, net current is zero. This equals +1 reflection coefficient, so an open circuit.

there is no E-field fringing at the opposite side as you normally have in a real open terminated line.

If you feed them from a line that runs along the resonator, you get a directional coupling and than this simple approach doesn't hold as the waves in both sides have different amplitude.

 

[Terminator3]

I tried to make some formula for Zin of microstrip ring. Here is result and my new question:

It looks like ring resonator impedance for the same frequency would be twice smaller. Or there is an error in my calculation.
Hope for explanation.

 

[WimRFP]

You have two electrically open transmission lines in parallel, so the impedance halves. You would get the same result when using one transmission line with half the characteristic impedance of the reference situation.