диафрагмированные волноводные фильтры / 810d1bc6-42fa-4896-a59e-0e9abdf5b9ca

Abstract—In this paper a low-loss pseudo-elliptical four-pole filter at 92.7GHz with two transmission zeros is presented in order to fulfill stringent specifications. Compared with traditional cross coupling filters, the proposed pseudo-elliptical filter can be manufactured more conveniently due to the introduced non-resonating nodes. What’s more, relatively simple structures to implement extracted poles have been proposed. Finally, the effect of fabrication process using high speed CNC milling machines is also discussed. The simulated result shows that the structure is insensitive to the fabrication tolerance and the insertion loss from 91.5GHz to 94GHz is less than 0.4dB, and the out of band rejection is more than 40dB at 89.2GHz and 96GHz.

Keywords—bandpass filter; waveguide; extracted pole; W- band

I.INTRODUCTION

The interest in imaging and radar applications at W-band (75–110 GHz) has increased recently, where high rejection and low insertion loss filters are undoubtedly required for improving system performance. Waveguide filters are a preferred option when losses, selectivity and process precision are mainly concerned. It is necessary to avoid using highdegree filters to fulfil stringent specifications in order to save mass and volume, which is good for system integration. Although cross coupling schemes [1] are popular to solve this problem, they tend to be too sensitive to manufacturing tolerances, especially for W-band filters. Inline extracted pole filters with non-resonating nodes (NRNs) was introduced in 2004 by S. Amari [2], which exhibits the excellent property of modularity since positions of transmission zeros can be controlled independently. This is a very important advantage from the engineering perspective to minimize the sensitivity of dimensions for mass production.

In this paper, the complete design and fabrication consideration of the filter with two transmission zeros based resonating nodes (NRNs) at W-band is carried out. The design presented in this paper is shown in Fig. 1. It is noteworthy that the filter is easy to fabrication without any complex structure.

Fig. 1. (a) The 3D image of the filter (b) The layout of the designed filter.

II.FILTER DESIGN

A. Filter Synthesis

The filter specifications are chosen for a 4 pole filter (with 2 NRNs) centered at 92.7 GHz and 2.5GHz bandwidth. Two transmission zeros are respectively located at 88.11 and 97.61 GHz. The return loss in the passband is 20 dB and the stopband attenuation is greater than 40 dB.

Fig. 2 shows the theoretical scattering parameter of the filter, which can be obtained by the method of generalized Chebyshev synthesis as explained in [1]. It should be noted that this response is a theoretical curve, and the dispersion effect of transmission line is ignored.

Fig. 2. Theoretical response of the fourth-order bandpass filter with 2 transmission zeros.

The low-pass prototype values obtained by extracting pole technique are summarized in Fig. 3. The synthesis is carried out as explained in [3]. The Circuit elements in Fig. 3 are:

Fig. 3. Low-pass prototype of the fourth-order filter with two extracted poles.

The coupling matrix (see Fig.4) for the direct-coupled extracted pole filter may be constructed using the theory in Cameron [3]. And the corresponding routing diagram is shown in Fig. 5 where the N1 and N2 are NRNs. The lines connecting the circles represent nonzero coupling matrix values.

Fig.4. Coupling matrix of the 4 pole filter. N1 and N2 are NRNs. S and L are source and load nodes.

Fig.5. Routing diagram of the 4 pole filter. Black circles are resonators, white numbered circles are NRNs. S and L stand for source and load.

Finally, a lowpass to bandpass transformation is used to obtain the circuit elements at the desired frequency band. And then, the resonant frequency of every waveguide cavity, coupling coefficients between waveguide cavities, and external quality factors can be calculated as explained in [4].

B. Structure Design and Optimization

The synthesized filter is implemented in standard WR-10 rectangular waveguide (width=2.54mm, height=1.27mm), as shown in Fig. 1. The main cavities 2 and 3 are halfwavelength resonantors based on the TE101 mode. Each coupling coefficient between waveguide cavities is achieved with an inductive iris i.e. H-plane topology, which leads to an ease machining [7]. The side cavities 1 and 4 are used to produce the transmission zeros (at 88.11 and 97.61 GHz). And the cavities N1 and N2 are the detuned resonators which connect side cavities with the main line. which can realize a modular design [5]. In our filter, the extracted poles are realized as shown in Fig. 6(b) and Fig. 6(c). Compared with the Fig. 6(a) presented in [6], there are some small improvements in order to make the fabrication process easier.

(a) (b) (c)

Fig. 6. Three structures that implement extracted poles. (a) The traditional structure. (b) The proposed structure used in the low frequency. (c) The proposed structure used in the high frequency.

Since the frequencies of detuned resonators are uncertain, much simulation optimization is required to determine specific dimensions in Fig.6 (b) and (c). The optimization goal in our design is making the attenuation pole and transmission pole of frequency response at the transmission zero and center frequency respectively. As for the rest parts of the filter, he literature [4] describes how to obtain corresponding dimensions according to the above filter synthesis results.Due to space limitations, more specific steps are omitted. Considering that mode matching technique (MMT) is more efficient applied to analysis of waveguide structures than full

wave numerical method, especially for H-plane topology, all optimization is carried out by the software using MMT.

The full wave simulation result of the optimized filter is shown in Fig. 7. The response differing from the ideal curve is caused by the dispersion of the rectangular waveguide. The transmission zeros (at 88.11 and 97.61 GHz) are produced by utilizing the physical effect of destructive interference between two signals in NRNs. To explain the mechanism of the NRN more clearly, the E-filed distribution of the filter at the center frequency and two transmission zeros is also presented in Fig.7.

Fig.7. Full-wave simulation result of the 4 pole filter including scattering parameters and the E-field distributions.

III.FABRICATION PROCESS CONSIDERATION

The 3D mode of the filter for fabrication is designed as shown in Fig.1(a). The waveguide is cut into two parts from the edge of the waveguide broadside which is called H-plane split block. Compared with the E-plane split block, all the structures including the rectangular resonant cavities and iris are milled in one part, while the another part of the filter is just act as a flat cover plate for waveguide, which will avoid the mismatch caused by the alignment deviation of the two symmetrical parts of the E-plane split block. In the side of the block, four screws are designed to ensure good contact of the two parts. The front and back side of the assembled fixture are patterned with a standard WR-10 waveguide flange.

To guarantee the quality of processing, two key problems should be taken into consideration; the first problem is that when milling the structure, the metal walls which parallel to the drill bit is difficult to form a right angle, but chamfers or rounded corners. So, when designing the filter, the chamfer should be taken into account. The second trouble is that these traditional milling processing techniques are hard to guarantee high-precision machining. Since the wave length at W-band is so small, the electrical properties are very sensitive to the physical dimension. Nevertheless, here are several special- discrete-radius chamfers that are relatively easy to process, such as the chamfers with radius of 0.2, 0.4 and 0.5 mm. Fig.8 shows that the center frequency shifts right when the chamfer radius increases from 0.2mm to 0.4mm. The influence of iris thickness is also investigated. Fig.9 show the effect of iris thickness to the bandwidth and center frequency. The

thickness of iris affects the bandwidth of the filter evidently. It also inspires us that by adjusting the thickness of the iris, designing a filter with different bandwidth at the same center frequency can be gotten easily.

Fig. 8. Effect of chamfer radius to frequency response.

Fig. 9. Effect of iris thickness to frequency response.

In order to ensure high precision machining, we are going to adopt a HSM400 series computer numerical control (CNC) machining solution developed by the Mikron Group in Switzerland. This machining solution is 10 times faster than conventional milling in term of cutting speed. The working spindle could be 42000 revolutions per minute (rpm).And a high machining accuracy up to ten microns and a better surface finish can also be achieved. A sensitivity analysis have been carried out to determinate the fabrication tolerance. All the dimensions of the filter were modified randomly by adding to each of the nominal values an independent uniform distribution between ±10 μm. The simulated results are shown in Fig. 10. As can be seen from Fig.10, the all return loss is less than -10dB in desired passband, and the frequency shift is less than 500MHz.

Fig. 10. Return loss of sensitivity analysis with 10um .

IV. CONCLUSION

A low-loss pseudo-elliptical four-pole filter based on non-resonating nodes at 92.7GHz with two transmission zeros is presented. The full filter synthesis and optimization procedure is given in this paper. And relatively easy structures to implement extracted poles have been proposed. The simulation result shows an excellent filtering performance. Finally, some important fabrication process consideration is also discussed.

REFERENCES

[1]R. J. Cameron, “Advanced coupling matrix synthesis techniques for microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 1–10, Jan. 2003.

[2]S. Amari and U. Rosenberg, “New Building Blocks for Modular Design of Elliptic and Self-Equalized Filters,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 2, pp. 721–736, Feb. 2004.

[3]R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communications Systems: Fundamentals, Design, Applications.

New York: Wiley, 2007.

[4]J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications. New York: Wiley, 2001.

[5]S. Cogollos, R. J. Cameron, R. R. Mansour, M. Yu, and V. E. Boria,

“Synthesis and Design Procedure for High Performance Waveguide Filters Based on Nonresonating Nodes,” in IEEE MTT-S Int. Microw. Symp., Honolulu, 2007, pp. 1297–1300.

[6]S. L. Romano and M. S. Palma, “Implementation of extracted pole filters in rectangular waveguide,” in Microwave Conference (EuMC),

2014, pp. 616–619.

[7]C. A. Leal-sevillano, J. R. Montejo-garai, and J. A. Ruiz-cruz,

“Experimental comparison of waveguide fi lters at W-band implemented by different machining processes and split-block,” vol. 27, no. 18, pp.