# microwave resonator optimizations

A W-band (90GHz) resonator used for EPR in physical chemistry research had quite a number of parameters that were arbitrarily choosen. Tests revealed that it didn't perform as expected. Microwave studio from CST was used for the simulation to find the influence of the various parameters. The structure in question is a round resonator with a quartz tube sample, fed by a rectangular waveguide. As can be seen from a cut view :

there are some parameters apparent.
• the position and length of the coupling wire into the rectangular waveguide
• the position, diameter and angle of the loop into the round resonator
• diameter and length of the resonator
• cuts and grooves to suppress unwanted modes in the resonator
Of interest is the dependence of the Q from the parameters as well as the modes in the resonator, the shift induced by the quartz tube sample.

## The coupling between rectangular and round waveguide

As first approach, the coupling was calculated between the extended round waveguide and the rectangular waveguide. While the round waveguide was fed with a circulare TE mode, the output on the rectangular waveguide was measured as TE mode. Then some of the parameteres were swept. It was found the coupling is dependent on
• the wire into the rectangular should be half the waveguide height in length
• the wire should be lambda half from the ending wall
• the position of the hole between 0.7 and 1.4mm has the best broadband performance at 0.7mm
• the angle of the wire between 0 and 40 degrees gives strange alternating results.
• the hole diameter between 0.4 and 0.8mm does not matter much
• the loop diameter between 0.8 and 1.6mm does not matter much
• the wire diameter between 0.1 and 0.6mm does not matter much
The coupling was in the order of -20 to -10dB broadband from 86GHz up, where the round part started to conduct.

A sample parameter sweep shows the coupling in dependence of the loop diameter :

## The modes in the resonator

While the coupling between the waveguides is disturbingly independent of most of the parameters, the propagating modes are not. Especially when the round waveguide becomes a resonator. So as next step, the round waveguide was changed to a resonator. It was immediately visible that there were multiple modes competing with the circular TE mode. The circular TE mode is unique by not having current through the top and bottom plates. Therefore circular groves at the top and the bottom plate as well as the hole for the quartz sample tube prefer the circular TE mode. A sample video (420k). Another one (9.7M)

The field homogenity was found to be acceptable. The E-field at resonance looks like

While the H-field looks like

Yes, building this resonator was a different story. The parts were rather tiny.

simulations page