The basic 3D model of the dielectric loaded combline resonators designed using Ansys HFSS software is shown in Fig. 1. The metal cavity is loaded by the dielectric cylinder with high permittivity values in order to increase the volume and mass saving (more than 50%) compared to standard TE113 resonators. The dielectric element is only joined to one side of the cavity, as shown in Fig. 1b. Two sixth-order filter models were designed considering the different permittivity values of commercially available dielectric elements. The proposed resonator model for the filters is presented in Fig. 2; the high permittivity dielectric element is mixed with “barrel-shaped” metal cavity. Fig. 2a shows the combline resonator, which is based on ceramic material characterized by a permittivity of 12.6 and low loss-tangent (8e-5). This solution allows for a very compact structure while maintaining high unloaded Q-factor values (>4500) when considering a standard square cavity.
According to [7] and [8], along with the cavity height, the shape of the cavity can also be optimized to improve the Q-factor. It is well-known that a spherical shaped cavity is the best solution to maximize the Q-factor, however this approach could become critical to achieve the required coupling values for our filter since it increases the distance between two adjacent resonators.

Fig. 2 - Proposed dielectric loaded combline resonator designed in Ansys HFSS: a) side view of resonator with εr=12.6, b) side view of resonator with εr=24, c) 3D view of resonator with background conditions of metallic cavity.

Fig. 3 - 3D view of sixth-order Ku-band filters: a) Model 1 (ε_r=12.6), b) Model 2 (ε_r=24).

Fig. 4 - Top views of sixth-order Ku-band filters: a) Model 1 (ε_r=12.6), b) Model 2 (ε_r=24).

Based on preliminary eigenmode analyses [7] performed in HFSS, the best cavity shape to further improve the Q-factor is the “Barrel” which allows the simulated unloaded Q-factor of the resonator in Fig. 2a to be increased up to 6000. In [7], [8] multiple parametric analyses were performed in HFSS with respect to the variation of the main parameters such as the radius of dielectric cylinder, cavity height, and curvature of the barrel cavity. As a result, (see Fig. 2a), the required aspect ratio of the ceramic cylinder to maximize the unloaded Q-factor is very high but a potentially vibration-sensitive structure is obtained. Therefore, support mechanisms (Teflon cups) were used to lock the ceramic cylinder in place on the top of the cavity. Along with the properties of the dielectric elements, the nonideal characteristics of metallic material are also considered. The finite conductivity background conditions used in the models shown in Fig. 2a and Fig. 2b are set in order to consider the loss contribution due to the metal casing, as shown in Fig. 2c. Aluminum’s similar bulk conductivity (σ=3e7 S/m) was also considered despite a silvering process having been performed on the cavity surfaces, which allows for a margin over than the desired true Q-factor.
In Fig. 2, the first prototype resonator (Fig. 2a) is compared with a smaller barrel-shaped resonator (Fig. 2b) in which a ceramic material with higher permittivity is used. Due to εr=24, additional shrinkage of the structure is achieved while maintaining a sufficiently high unloaded Q-factor value (about 4000-5000). The barrel shape of the cavity is less pronounced in the second resonator solution. To increase the “barrel-shape” to be similar to the first prototype, the diameter of the ceramic cylinder must be decreased. However, in this case, a minimum diameter of 2 mm was chosen to avoid possible criticality due to the robustness of the ceramic parts; for this reason a less pronounced barrel was obtained.
Two sixth-order elliptical filter models were designed using the dielectric loaded combline resonators in Fig. 2. The 3D models of proposed Ku-band filters are compared in Fig. 3 where the difference in size is highlighted.
Both filters are based on the same folded configuration in which all positive couplings between adjacent resonators are used while a negative cross-coupling has been designed between the non-adjacent resonators 2-5 to achieve two transmission zeros (TZs) in the lower and upper stop bands. The difference in footprint is shown in Fig. 4 where top views of the filters are presented.

Fig. 5 - Ku-band filter duplet for coupling design: a) Input coupling design model, b) Intra-positive coupling design model, c) Negative cross-coupling design Model 1, d) Negative cross-coupling design Model 2.

The intra-couplings were designed by simulating odd and even resonant modes (eigenmode analysis) between each resonator duplet; whereas the Group Delay (GD) method was used to design the input couplings [9] where the WR75 waveguide interface was used. In this scenario, the GD of the reflection characteristic was simulated by performing a Driven Modal analysis of the S-parameters in HFSS. The models used to design the input and intra-couplings are shown in Figs. 5a and 5b, respectively, while Figs. 5c and 5d are the models used to design the negative cross-couplings.
In the first filter model in Fig. 3a, the negative cross-coupling was achieved by using a capacitive iris loaded with high-permittivity (εr=24) material [7]. This cross-coupling solution is impractical in the second filter model because the smaller size of the structure does not allow the desired negative coupling value to be achieved. However, in this case the cross-coupling was achieved by designing a shaped metal probe supported by a Teflon interface (Fig. 5d).
In the first filter model (Fig. 3a), tuning screws were added to the cavity and coupling irises to compensate for the variation in filter response due to manufacturing tolerances. Similar tuning mechanisms can be used in the second filter model, however the structure shown in Fig. 3b is only a preliminary model, and the tuning screws are not present.

Driven Modal simulations were performed in HFSS to simulate and optimize the S-parameters of both sixth-order Ku-band filters. In each case, the wave-ports were defined as signal excitations of the 3D model while the adaptive meshing solutions were used for the simulation setup. The central frequency of the filter (11 GHz) was chosen as the single solution frequency. Concerning the mesh, curvilinear elements were applied since the models show numerous curved surfaces. The full-wave response of the first sixth-order filter model (Fig. 3a) is shown in Fig. 6, while the simulated S-parameters of the second prototype (Fig. 3b) are depicted in Fig. 7. Both simulations converged with a maximum Delta-S magnitude of less than 0.01.
All in-band and out-of-band requirements (Fig. 6) are satisfied in the case of the first filter model. Return loss (RL) greater than 19 dB and insertion loss (IL) less than 0.8 dB are over the entire passband (240 MHz), while all near-band rejection requirements are met due to the TZs. Regarding the second filter model, similar results were obtained but a wider bandwidth was achieved despite using the higher permittivity values of the ceramic elements have been used. This shows that “strong” coupling values can be achieved with the proposed design even though the E-field is more confined within the dielectric elements.

Fig. 6 - Simulated response of Ku-band filter Model 1 (blue line is transmission characteristic, red line is reflection characteristic).

Fig. 7 - Simulated response of Ku-band filter Model 2 (blue line is transmission characteristic, red line is reflection characteristic).

Fig. 8 - Ansys vibration analysis of the sixth-order filter Model 1.

Fig. 9 - Ansys and HFSS high-power thermal simulations of the sixth-order filter Model 1 at the central frequency.

The first model was chosen for manufacturing because it is less critical in terms of manufacturing tolerances, and therefore additional analyses were performed during the design procedure. Vibration analyses were performed in Ansys Mechanical to identify the first mechanical resonance mode of the sixth-order filter in Fig. 3a. As shown in Figs. 8a and 8b, the first modes are at 4059.9 Hz for the aluminum casing and at 2245.9 Hz for the ceramic cylinders, respectively; these are above the range of the specification for the vibration level (2000 Hz). Simulated results of the high-power thermal analyses performed at the central frequency are shown in Fig. 9.
A combination of HFSS and Mechanical simulations in Ansys Workbench was used to calculate the thermal drift with 150 W input power and to calculate the thermal drift of the S-parameter response.
The simulations were performed including all physical properties of the metallic and dielectric parts. The estimated change in relative permittivity over the predicted temperature for the dielectric parts was also considered. A similar high-power thermal analysis was also performed at the passband edge frequency. The maximum temperature is reached on the ceramic elements, in particular the maximum temperature is 130 °C for the central frequency and 200 °C for the passband edge.
Concerning the thermal drift of the frequency, the maximum shift estimated by simulation is in the range 8÷16 MHz corresponding to 5÷8 ppm/°C (higher for the edge frequency, and lower for the central frequency). Fig. 10 shows the high-power thermal results of the analysis at the passband edge frequency.
High-power thermal simulations were also performed on the second filter model. However, the estimated temperature rise is greater due to the smaller volume and the smaller heat transfer surfaces. The maximum temperature reached on the ceramics is over 200°C.

Fig. 10 - Ansys and HFSS high-power thermal simulation of the sixth-order Model 1 filter at the edge of the passband.

The first sixth-order Ku-band filter model was manufactured by achieving a volume reduction of about 50% compared to a standard filter based on the TE113 resonators, while keeping the Q-factor values compliant with the requirements. Fig. 11 shows the prototype of the manufactured filter and its 3D mechanical model, the structure is made of silver-plated aluminum. The final size (LxWxH) is 92mm x 45mm x 41mm with a mass of less than 200g in accordance with expectations.
The comparison between the measured (solid lines) and simulated (dashed lines) responses is shown in Fig. 12. According to [7], the measured response has shifted upward in frequency by about 100 MHz compared to the simulated response in Fig. 6. This is attributed to the actual value of the dielectric constant of the ceramic resonators that have a tolerance that is difficult to compensate for using only tuning screws. The actual value of the permittivity of the dielectric elements (εr=12.4) was used in the simulation for a proper comparison with the measurement as shown in Fig. 12.
The measured unloaded Q-factor is above 4500 as expected, and the out-of-band attenuation is very good taking into account the frequency shift. In addition, the insertion loss of less than 1 dB (objective) over the entire passband is compliant.
According to [8], the final environmental and high-power tests were also performed in this filter model and promising results were obtained. Fig. 13 shows the RF breakdown test setup in which the filter is placed inside the Thermal Vacuum Chamber (TVAC).