Bi-objective optimization of a waveguide


Waveguides are structures that guide electromagnetic waves, sound waves or other kinds of wave. Their function is to propagate a signal while minimizing energy loss by restricting its expansion to one dimension or two. A common application is signal transmission between components of a system such as a radio, radar, or other electronic or electro-optical device. This case involved bi-objective optimization of a waveguide for correct power split with minimal reflection loss.

There are different types of waveguides for each type of wave. This case involved a T-junction waveguide. The waveguide had a septum inside which served to divide power. The task for the waveguide’s designers was to set the septum position so that power would be divided between the ports in a given proportion, while minimizing signal reflection. The challenge was to divide power from Port 1 between Ports 2 and 3 at a 1:2 ratio, by changing the septum position (h), with minimal signal reflection. The frequency was set to 8GHz. Power calculation was done with Ansoft HFSS (now owned by ANSYS).

power calculation waveguide_2

From experiments, it was obvious that to correctly solve the problem, the designers had to take into account both the reflection of the signal and the efficiency of the power split. Two different solution approaches were applied. The first was a single-objective optimization of the septum position, with the power split deviation set to zero as a constraint, and minimal reflection as an objective.

For this approach, three different optimization methods were compared: (1) the GTOpt direct (or gradient) optimization algorithm of DATADVANCE’s MACROS, (2) the GTOpt SBO (global) optimization algorithm of MACROS, and (3) the internal optimizer in HFSS. The correct solution was found by the SBO global optimizer after just 11 iterations—compared with 40 iterations by the HFSS internal optimizer.

2-optimization results waveguide_3

The second approach was to solve the challenge as an unconstrained bi-objective optimization, where the signal reflection and the power split deviation were considered as objectives to be minimized. This approach yielded a Pareto frontier of the results, which graphed the tradeoff between maintaining the required power split and minimizing signal loss caused by reflection.

Pareto frontier waveguide_4

As the tradeoff results showed, further decrease of the reflected signal (S11) would make it impossible for power to be split in the required ratio. Thus, it was up to the designers to decide what criterion was more important in their case and set the septum accordingly, based on the optimization results.