Specifications and preliminary evaluation of the main filter parameters

In this section, we present the required specifications (Table 1). These concern an L-band duplexer, intended to equip the payload of a new-generation Global Navigation Satellite System (GNSS) satellite.

Table 1. Specifications of the L-band duplexer

As the Rx part of the duplexer is not concerned by the RF power handling, we focused only on the Tx part, for which it is reasonable to reserve at least ~70% of the whole available volume. The requested isolation between the Rx and the Tx parts, which is 90 dB, forced us to choose an eight-order Chebyshev electrical response. To minimize the number of resonators, which optimizes size economy, quality factor, and multipactor threshold, a sixth-order cross-coupled electrical response presenting transmission zeros was chosen. Under these conditions, the requested insertion losses and flatness in the passband gave a quality factor of around 4000. By considering a sixth-order filter in a volume of around 70% of that given by the specification, built on a footprint equal to 170 mm × 130 mm and a thickness of 40 mm, with metallic walls of 4 mm, the RF envelope of each elementary resonator will be around 51.2 mm × 51.2 mm × 32 mm.

At 1.5 GHz, the quarter wavelength in air is 50 mm, meaning that the length of a uniform coaxial resonator is too large to fit into the available volume. Therefore, to decrease these dimensions, we decided to design the filter based on SIR coaxial resonators.

SIR coaxial resonator and design methodology

An SIR coaxial resonator with two sections presented in Fig. 1 offers several degrees of freedom [Reference Aouidad, Favennec, Rius and Manchec14]. It consists of two cylindrical conductors C ₁ and C ₂, embedded in a rectangular metallic box C ₃. The structure is first composed of three transmission lines of respective characteristic impedances and lengths (Z ₁, l ₁), (Z ₂, l ₂), and (Z ₃, l ₃).

Fig. 1. SIR coaxial resonator: (a) 3D-exploded view, (b) front view, cross-section, and (c) top view, cross-section.

The characteristic impedances of each coaxial line supporting a TEM mode can be expressed as follows:

(1)$$Z_i = \displaystyle{{\eta _0} \over {2\pi \sqrt {\varepsilon _r} }}\;{\rm ln}\left({\displaystyle{{s\;R_{ext}} \over {R_{int}}}} \right)$$

where η ₀ and ɛ_r are the vacuum impedance and the relative dielectric constant of the material, respectively [Reference Vizmuller15, Reference Omar and Miller16]. R_ext and R_int are the outer and inner radii of the conductors, respectively. The parameter s is equal to 1 for an external circular section, and equal to 1.079 for a square section. The TEM signal propagation undergoes two SIR effects, characterized by the ratios M ₁₂ and M ₂₃ of the characteristic impedances, calculated as:

(2)$$M_{ij} = \displaystyle{{Z_j} \over {Z_i}}$$

To model the resonator correctly, several discontinuity effects also need to be considered at the open and shorted ends of each cylinder. Although the parasitic inductances at the shorted extremities of the cylinders can be ignored, it is vital to take one of the capacitive effects at the open extremities into account. This capacitance is located at the open end of cylinder C ₁ and is fully described in [Reference Atia and Williams5].

The geometric characteristics of this resonator were chosen according to a numerical procedure described in [Reference Hallet, Favennec, Rius, Bénédicto, Carpentier and Pacaud13]. This iterative procedure makes it possible to minimize the volume for a given quality factor, resonance frequency, and square footprint, which were fixed at 4000, 1.5 GHz, and 51.2 mm × 51.2 mm, respectively.

Due to the relation between the characteristic impedance ratios M on the resonant frequency, the transversal dimensions (r ₁, R ₁, r ₂, and R ₂), and the lengths (l ₁, l ₂, and l ₃) are linked together. If the radius r ₁ of the cylinder C ₁, the thickness of the cylinder C ₂ (e_{c 1} = r ₂ − R ₁) and length l ₂ are fixed, it is possible to obtain many pairwise combinations of (r ₂, l ₃, l _t, and d ₁) and (f ₀, Q, and V), characterized by different multipactor threshold values.

Simplified simulation model for multipactor threshold evaluation

To simplify the study of the impact of resonator geometry on multipactor threshold, the study was conducted on a second-order filter (Fig. 2) built based on the resonator defined in the previous section. Indeed, the evaluation of multipactor threshold, with Spark3d [17] requires the analysis of a correctly matched filtering response. To save time, working with a limited order is preferable.

Fig. 2. Example of a two-section second-order filter with SIR coaxial resonators: (a) 3D-exploded view, (b) front view 1, cross-section, and (c) front view 2, cross-section.

For this, once the electromagnetic simulation of the filter (S parameters; electrical field) with HFSS is done, the electromagnetic fields are exported to Spark3d which calculates the multipactor threshold.

Spark3d is partly based on a Monte Carlo statistical approach. The types of interactions (elastic backscattering, inelastic backscattering, and real secondary electrons) are distinguished according to the Vaughan model [Reference Gonzales-Iglesisas, Monerris, Gimeno, Díaz, Boria, Martin, Gomez Gomez, Fernandez, Vegas, Casas, Anza, Vicente, Gil, Mata, Montero and Raboso18, Reference Vicente, Mattes, Wolk, Hartnagel, Mosig and Raboso19].

In order to function, Spark3d needs to know the secondary emission yield (SEY) characteristic of the material. It is possible to use predefined material but also to define one's own model by setting the following characteristics: the maximum secondary emission coefficient (δ), electron energy at maximum SEY (E_m), and lower crossover electron energy (E ₁). Results on the variation of these parameters are highly sensitive. For instance, varying E ₁ and δ from 50 to 45 eV and from 2.2 to 2, respectively, increases the multipactor threshold by about 5 dB. It must be underlined that the variation of E ₁ particularly impacts parallel-plate like structures. The other settings are the power test interval and the number of primary electrons.

For this simplified filter, the center frequency, relative bandwidth, and matching level were set at 1.537 GHz, 2%, and 20 dB, respectively. The material considered was silver (ECSS [20]).

Design of the elementary resonator

The geometric parameters of an elementary SIR coaxial resonator, presented in Table 2, were obtained by the optimization procedure mentioned in the previous section, to which a constraint on the multipactor threshold was added. It should be remembered that the footprint of the resonator is fixed. The values of the resonant frequency and quality factor were validated electromagnetically with HFSS (Table 2).

Table 2. Geometric and electrical parameters of the SIR coaxial resonator

Design of the filter

Once the resonator was defined, the sixth-order filter could be designed (Fig. 6). A study based on Zabalawi synthesis [Reference Matthaei, Young and Jones22, Reference Zabalawi23] provided the coupling matrix (4). The electrical responses obtained from this matrix are represented in Figs 7(a) and 7(b) (red curves).

(4)$$M = \left[{\matrix{ 0 & {0.027} & 0 & 0 & 0 & 0 & 0 & 0 \cr {0.027} & 0 & {0.0282} & 0 & 0 & 0 & 0 & 0 \cr 0 & {0.0282} & 0 & {0.0194} & 0 & {-0.0006} & 0 & 0 \cr 0 & 0 & {0.0194} & 0 & {0.0188} & 0 & 0 & 0 \cr 0 & 0 & 0 & {0.0188} & 0 & {0.0194} & 0 & 0 \cr 0 & 0 & {-0.0006} & 0 & {0.0194} & 0 & {0.0282} & 0 \cr 0 & 0 & 0 & 0 & 0 & {0.0282} & 0 & {0.027} \cr 0 & 0 & 0 & 0 & 0 & 0 & {0.027} & 0 \cr } } \right]$$

Fig. 6. Sixth-order cross-coupled filter: (a) 3D view, (b) top view, cross-section, and (c) retro-coupling metal rod.

Fig. 7. Ideal (ADS) and electromagnetic (HFSS) simulated responses of the filter: (a) S ₂₁ frequency response and (b) S ₁₁ frequency response.

The layout of the final sixth-order cross-coupled filter is presented in Fig. 6. It consists of:

• • six quasi-identical two-sections SIR coaxial resonators whose dimensions are given in Table 2;

• • two coaxial connectors (TNC power connectors [24]);

• • five irises for the magnetic couplings;

• • a retro-coupling metal rod (rexolite support [ɛ_r = 2.53 − tan(δ) = 0.004] and copper [σ  = 58 MS/m]);

• • tuning screws to adjust the final response of the whole filter;

• • four holes of events of 1 mm radius, which allow air to escape from the filter as it passes from the terrestrial atmosphere to the vacuum of space and for multipactor measurement in the vacuum chamber; and

• • thinned walls to increase the irradiated energy required inside the filter for the initiation of secondary electronic emissions during the multipactor test. Thinning was done on the outside of the filter.

The optimization of the whole structure consists of adjusting different geometric parameters to satisfy the requested specifications. In the first-order, the width of the irises and geometric parameters of the isolated coupling metallic rod directly impact the bandwidth and transmission zero level, respectively. For the matching level, the height positioning of the connectors and a slight frequency adjustment of the pairs of resonators is required.

Once the resonator had been correctly defined, the step-by-step procedure required several simulations with HFSS software but converged quite well. Each characteristic of the electrical response, bandwidth (iris sizes), and central frequency (resonators dimensions, Table 2) mainly depends on one geometrical parameter, the influence of the others playing a secondary role. However, to save time or to be more efficient, it is also possible to use dedicated optimization algorithms in such circumstances [Reference Bila, Baillargeat, Aubourg, Verdeyme, Guillon, Seyfert, Grimm, Baratchart, Zanchi and Sombrin25].

Once the electrical response of the filter fulfilled the requested specifications, tuning screws were added. The role of these screws is to correct the eventual technical imperfections of the filter due for example to the tolerance of fabrication. These screws, shown in yellow in Fig. 6, were positioned near the shorted-ends of the C ₂ cylinders in order to reduce their impact on the multipactor threshold of the filter. Indeed, in this configuration, the screws are located in a region with a minimum of electric field. We tested several solutions, and the simulations show that the impact of the screws can be very detrimental if they are located, for example, on the opposite side of the filter where they would be close to the open ends of C ₂ cylinder.

The electrical responses are shown in Figs 7–10 (dotted lines). They respect the specifications, showing the ability of the topology to resolve this particular filtering problematic. The insertion losses, between 0.2 and 0.45 dB, are better than those imposed by the specifications (<0.5 dB).

Fig. 8. Measurement and electromagnetic simulation of the S ₁₁ frequency responses of the filter.

Fig. 9. Measurement and simulation of the S ₂₁ frequency responses of the filter: (a) insertion losses in the passband, (b) S ₂₁ parameter from 1.4 to 1.7 GHz, and (c) wideband.

Fig. 10. Measurement and electromagnetic simulation of the group delay.

Figure 11 presents the simulation of the multipactor threshold of the filter at the central frequency, f ₀ = 1.54 GHz, obtained with Spark3d software. The initial parameters used for this Spark3d simulation were 300 and 700 W for initial and final power, respectively, and the initial number of electrons was fixed at 10 000. The multipactor threshold of the designed filter was 410 W, in accordance with the requested specifications, thus validating the preliminary work presented in the Section “Multipactor threshold evaluation.” The multipactor effect appears between the C ₁ and C ₂ cylinders. Similar simulations were also performed for certain other frequencies located, for instance, at the maximum group delay, these values are shown in Table 3.

Fig. 11. Multipactor simulation of the L-band filter at 1.54 GHz: (a) SEY curve of silver (ECSS), (b) avalanche of electrons in the filter at 450 W, and (c) simulation results of multipactor threshold.

Table 3. Multipactor threshold for different frequencies in the passband

Fabrication

For the fabrication, classical mechanical manufacturing processes were used with a precision of ±50 μm.

The fabrication was carried out in three steps:

1. 1. Manufacturing of two aluminum blocks (body and cover) and a copper rod positioned within a rexolite block.

2. 2. A 5-μm thick layer of silver was deposited on the body and cover, to obtain the best electrical conductivity.

3. 3. Brazing of the connectors.

A photograph of the filter after the operation of silvering is shown in Fig. 12. A significant number of screws were added to hermetically close the RF volume.

Fig. 12. Manufactured L-band filter: (a) cover, (b) body, (c) copper rod within rexolite block, and (d) brazing of the connectors.

RF measurements

Figures 8–10 compare the measured and simulated S ₁₁ and S ₂₁ frequency responses, and group delay responses of the filter around the passband and in a wide band. The measured results show a relatively good agreement with the simulated ones, although some differences do appear. We can observe a slight frequency shift in the transmission zero position. We can also notice some differences for the insertion losses and for the matching level. The measured response was obtained by adjusting the tuning screws provided for this purpose, and pre-arranged on the filter body. During the measurements, the screws in the input/output resonators had to be screwed fully home. This is due to several problems that limit the tuning dynamics of these screws. We should point out a difference between the retro-coupling element that was designed and the one that was manufactured: in the latter, the fixation rod was made of copper instead of rexolite. The manufactured retro-coupling element does not match the designed and expected retro-coupling element (Fig. 6). This fabrication difference induced a slight modification of the position of the transmission zeros of the frequency response of the L-band filter. The brazing was also not exactly as requested. Moreover, the roughness of the metallic walls inside the filter impacted the insertion losses.

Test conditions

To measure multipactor effect, it was necessary to control the environment of the thermal vacuum chamber, particularly its cleanliness (atmospheric particles of class 8 according to ISO 14644-1), pressure (<1.5 mPa in the critical areas of the component) and temperature. Figure 13 shows the devices of the test bench, which are as follows. An ⁹⁰Sr radioactive source is positioned near the critical location of the electronic component. In the design, some parts of the filter walls were manufactured specifically to allow the introduction of primary electrons into the filter. This was practically achieved by making a local circular decrease in the thickness, on one of the walls of the filter, under the six rings between C ₂ and C ₃. To generate strong RF power, a synthesizer was used delivering a carrier in pulse mode, coupled with traveling-wave tube amplifiers. The multipactor phenomenon could be detected by two systems, based on a phase nulling and on third harmonic principles (Fig. 13) [20].

Fig. 13. Experimental multipactor test set-up overview.

Multipactor measurements

Multipactor measurements were performed for three different frequency points: the center frequency f ₀, and the frequencies at the group delay maxima f_TPG, for which energy storage was maximal within the filter (Fig. 10). The comparison between the measurements and the simulation performed with Spark3d software is shown in Table 4. The test bench used was limited to a maximum input power P_max = 450 W. At the center frequency of the filter, neither detection was observed. For the two other frequencies, a multipactor discharge was registered by the phase nulling detection method.

Table 4. Simulated and measured power results

As shown in Table 4, there is a difference of 5 dB between the measured and simulated values. Several hypotheses can explain this difference: a lack of precautions during the machining could have affected the roughness of the filter. A difference between the SEY parameters used during the Spark3d simulation and reality is also possible. We remind that in the Section “Multipactor threshold evaluation,” we pointed out the sensitivity of Spark3d to some SEY parameters. Considering the statistical method used by Spark3d, the final result should be considered as an estimation, particularly if the order (number of half periods) is high (unstable zone), as in the present case. In addition, the detection system (third harmonic principles) is not well suited to high orders [Reference Sorolla26].