December 5, 2016

# Bi-Objective optimization of the waveguide

Industry: Electronics | Product: pSeven

## Objective

Waveguides are used to confine the electromagnetic and other waves to propagation in one dimension, so that (under ideal conditions) the wave loses no power while propagating. They are largely applied in transmitting power between the components of a system such as radio, radar, optical devices, all sorts of electrical appliances. There are different types of waveguides for each type of wave. In this case, an optimization of T-junction waveguide characteristics is considered.

## Challenges

The waveguide has a septum inside which serves to divide power. Waveguide designers have to set the septum position in such a way that the power would be divided between the ports in a given proportion with the minimal power caused by the signal reflection. In this case, the challenge is to divide power from Port 1 between Ports 2 and 3 in 1:2 proportion, by changing the septum position (h), with the minimal reflection of the signal. Frequency set is 8GHz. Calculation of power was made with help of ANSYS HFSS.

## Solution

Out of experiments, it was obvious that to correctly solve the challenge we had to take into account both the reflection of the signal and efficiency of the power split. Two different solution approaches were applied. First one was the single-objective optimization of the septum position, with the power split deviation set to zero (0) as a constraint and the minimal reflection as an objective.

Three different methods of optimization were considered – GT Opt direct (or gradient) optimization, GT Opt SBO (global) optimization and internal optimizer in ANSYS HFSS.

The correct solution was found just after 11 iterations compared to 40 iterations of HFSS internal optimizer!

 Method № of function calls Solution h (cm) Constr. violation S11 (dB) Optimizer in HFSS 40 0.1431 8e-4 -18.263 Direct optimization in pSeven 18 0.1451 9e-5 -18.522 Surrogate-based optimization in pSeven 11 0.147 4e-4 -19.328

The second way was to solve the challenge as an unconstrained bi-objective optimization, where the signal reflection and the power split deviation were considered as objectives which were to be minimized.

## Benefit

As a result, the Pareto frontier of the results was obtained. It demonstrates the trade-off between maintaining the required power split and minimal signal loss caused by reflection. As we can see from the chart below, further decrease of the reflected signal (S11) does not allow to split the power in the required ratio. Thus, it is up to the designers to decide what criterion is more important in their case and set the septum accordingly, based on the optimization results.

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