Table 4. Variations of F_{0} and Q_{0} for the topology No. 1.

W = 285 µm and spaced out of 20 µm with regard to the cross.

The obtained results are presented in the Table 5.

With this topology we were able to have a gap of 7.4 × 10^{–}^{4} MHz for a variation of 2 µm (between 495 and 497 µm). In the case of the topology in initial cross, we had a gap of 2.4 × 10^{–}^{3} MHz. We thus obtain a 69% decrease.

For this topology we obtain the module of presented S21 represent Figure 7.

3.4. Experiment—4

After vertical bar optimization to have the minimum of possible frequency gap, we added a horizontal bar as showed on Figure 8.

The bar is optimized for a length L = on 2405 µm and a width W = 290 µm and spaced out by 40 µm with regard to both quoted by the cross.

For this topology we obtain the module of presented S21 represent Figure 9.

The obtained results are presented in Table 6.

We notice that with this topology we were able to have a gap of 6.5 × 10^{–}^{4} MHz for a variation of 2 µm (between 495 and 497 µm). This represents a 73% decrease with regard to the initial topology.

The introduction of coplanar structures allows decreasing the variation of the frequency of echo according to the height of the substratum but degrades the quality

Figure 6. Topology No. 2.

Figure 7. Module of S21 according to the frequency for the topology No. 2.

Figure 8. Topology No. 3.

Notice: the bar dimensions are obtained after several simulations of S21 relative to lengths and heights variations of ±1 µm. One always looks for the dimensions which present not enough frequency gap with regard to the echo frequency 4 GHz.

Figure 9. S21 module visualization of according to the frequency of the resonator No. 3.

Table 5. Variations of F_{0} and Q_{0} for the topology No. 2.

factor [11].

This various topologies also has the advantage to decrease the dimensions of the resonator because to obtain a frequency of echo of 4 GHz, it would be necessary to decrease the structure dimensions.

Table 7 shows that the final topology (full cross) has allowed to decrease the frequency gap of 73% with regard to the initial structure (empty cross) this topology then present the advantage to be insensible in the sub-

Table 6. Variations of F_{0} and Q_{0} for the topology No. 3.

Table 7. Comparison of the topology.

stratum height variations.

4. Conclusions

The topology in cross presents the advantage to be little sensitive to the variations of substratum height.

It thus allows freeing himself from regulations systems which increase the dimensions and the weight of filters. The purpose of this article was the improvement of the superconductive planar resonator performances in cross dedicated to the realization of microwaves filters used in the payload of communications satellites, to look for possibility of obtaining a minimum of the echo frequency gap without degrading the quality factor.

The study carried out on this topology consisted in making simulations with the aim of seeing the effect of the addition of a vertical bar, then a horizontal bar inside the initial structure. These modifications allow concentrating the electromagnetic field meadows of the surface of the circuit between the superconductor and the substratum. Our final structure (full cross) has allowed to decrease the effect of the substratum thickness on the echo frequency everything one keeping a high value of quality.

The addition of vertical bar and\or a horizontal bar allows adjusting the frequency gap caused by the manufacturing errors by moving the echo frequency to the left or to the right. This technique allows freeing itself from cumbersome regulation systems.

5. Acknowledgements

This work was realized in the electronics and communications laboratory of the Mohammadia School of engineers in cooperation with Meknes Graduate School of Technology.

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