Optimization and Full Wave Simulation Using CST

W g a b

2.4 0.3 11 13

Table 7. 1 Ring dimensions with initial calculation (unit:mm)

Using the method stated above, the tunable resonator using ring resonator is designed to work at 2.4GHz, and the dimensions for the ring resonator is shown in Table 7.1. Since it is difficult to find an effective equivalent lumped element model for ring resonator, and the equations 7-1 to 7-11 can give the resonant frequency directly, so there is no need to carry out the lumped element modeling using ADS. The dimensions in Table 7.1 are directly used to build 3D model in CST. Figure 7.4(a) shows the layout of the proposed ring resonator and Figure 7.4(b) presents the cross-section view of the ring resonator. It uses the same materials as the tunable devices in previous chapters.

(a)

(b)

Figure 7. 4 (a) Schematic view of ring resonator (b) Cross section view of ring resonator (Not drawn to scale)

The full wave simulation is conducted using the dimensions in Table 7.5. The resonant frequencies are generated with using LCs switching from unswitched state to switched state. The simulated results of resonant frequency at unswitched and switched states are shown in Figure 7.5. As can be seen from Figure 7.5, the resonant frequency shifts from 2.35GHz to 2.11GHz from unswitched state to switched state. The tuning range is 0.24GHz and it corresponds to a tunability of 11.4%. Since the tunable bandpass ring resonator is designed to work at 2.4GHz, the optimization is carried out to adjust the working frequency and maximize the tuning range.

Figure 7. 5 Resonant frequency for ring resonator using CST

Before the optimization, the influences of the each dimensions to the resonant frequency needs to be investigated. There are two dimension which are important for designing the ring resonator, and they are the mean radius of the ring r and the gap g between the ring and the feed lines, respectively. The gap

g between the ring and the feed line slightly affect the resonant frequency and

mainly affects the magnitude of the resonant frequency [Bashore, 2000]. Therefore, the radius r of the ring and the gap g between ring and feed lines are investigated using CST to find out how the changes in these parameters affect the resonant frequency.

(a)

(b)

Figure 7. 6 Resonant frequency with (a) changing mean radius r of the ring resonator (b) changing gap g of the ring resonator

The mean radius r of the ring resonator is changed from 10mm to 14mm to find out the influences and the simulation results of the resonant frequency are shown in Figure 7.6(a). As can be seen from Figure 7.6(a), with changing the mean radius r, there is a clear shift in the resonant frequency. The resonant frequency changes from 2.82GHz to 2.02GHz with changing the mean radius from 10mm to 14mm with a step of 1mm. With changing every 1mm in the mean radius, the minimum resonant frequency changes is 0.18GHz and the

largest change is 0.22GHz, which means the resonant frequency is very sensitive to the mean radius r. Therefore, in the fabrication process, a high resolution mask is needed to fabricate this resonator so that the fabrication errors can be minimized. The gap g is then varied from 0.2mm to 0.7mm to find out the influences to the resonant frequency. As can be seen from the Figure 7.6(b), changing the gap g slightly affects the resonant frequency, which decreases from 2.37GHz to 2.30GHz with increasing the gap g from 0.2mm to 0.7mm. The magnitude decreases from -29.8dB to -19.7dB with increasing the gap from 0.2mm to 0.7mm, which means an average of 2dB change with changing gap of 0.1mm. In order to have a good return loss, large gap should not be chosen.

With the understanding of how each dimensions affects the resonant frequency, the optimization is carried out to adjust the working frequency and optimize the maximum tuning range. The dimensions for the ring resonator after the optimization is shown in Table 7.2, and these dimensions can be used to achieve the adjusted working frequency of 2.4GHz and the maximum tuning range.

W g a b

2.4 0.2 12 13

Table 7. 2 Dimensions for the ring resonator after optimization

The 3D model is updated with the dimensions after optimization and the full wave simulation results using CST is shown in Figure 7.7. As can be seen from Figure 7.7, the resonant frequency shifts from 2.4GHz to 2.12GHz from unswitched state to switched state. The tuning range is 0.28GHz and it is a tunability of 13.2%. The 3dB bandwidth is 170MHz and remains constant at both states. The return loss is around -28dB at both states and insertion loss is nearly 0dB. The tunable bandpass ring resonator shows very good frequency selectivity and return loss, but the area for the ring is 𝜋 × 132_𝑚𝑚2_,

which is large. Therefore, this ring structure can be alternated so that a size reduction can be achieved.

7.1.3 Conclusion

The tunable LC resonator using sing ring resonator is designed and simulated. It has a tuning range of 0.28GHz and the advantages of good return loss and very low insertion loss. However, the size for the single ring resonator is relatively big. In order to reduce the size, more possible structures, such as dual mode ring resonators and split ring resonators, can be studied in the future work.

For the ring resonator, there are gaps between the feed lines and the ring structure. In order to apply bias voltage to the feed lines and the ring resonator to switch the LCs in the region, a novel approach needs to be found out. Since the bias voltage is applied separately to each elements of the tunable resonators to switch the LC, the non-uniformity of switching LCs needs to be considered and minimized to achieve the best performance.