диафрагмированные волноводные фильтры / 02b4f031-22e5-4f12-a6bb-36b7e9da314c

Abstract — In this paper, the realization of X-band waveguide filters based on extracted pole design realized with additive manufacturing (AM) techniques is discussed. All filters proposed here benefit from a symmetrical layout and can hence been cut in the E-plane. Design strategies for the proposed filter set-up are presented. Measurement results for a four cavity filter with up to two real frequency axis transmission zeros (TZs) are discussed. An extension to a higher number of TZs is possible. To reduce the production costs the commonly known fused deposition modelling (FDM) technique is used for the realization of the waveguide filters. Subsequent electroplating necessary for implementation of conductive surfaces will be discussed. The insertion loss of the proposed filters can drastically be reduced by the use of the E-plane cut.

Keywords — Additive Manufacturing, E-plane waveguide filter, Fused Deposition Modeling (FDM), X-band.

I. INTRODUCTION

3-D printing has arrived in the manufacturing of prototypes for high frequency applications since around 15 years. In the beginning, this technique was limited to prototypes without technical function. Nevertheless, today the realization of functional parts like waveguide blends or twists and filters is possible and has long time ago been introduced [1]. In [2] a third order E-plane cut filter is realized with low insertion loss based on T E101 mode resonators. In [3] a waveguide filter with spherical resonators is proposed. Due to the structure of this filter, it must be printed and silver plated in three parts, which requires a high quality of the printing and metal plating process. Therefore, in both references the more expensive SLA (stereo lithography) printing technique is used. Nevertheless, in both cases no transmission zeros are reported.

Generally, TZs are useful in the filter design process as stringent requirements in the stopband may be achieved more easily. In conventional design, they are realized by cross-coupling the corresponding cavities as given by the coupling matrix topology [4]. Depending on the sign of the cross-coupling and the position in the coupling matrix, the realization of the cross-coupling aperture may be associated with some difficulties, especially in additive manufacturing. Extracted pole filters benefit from the realization of TZs in the near passband region of a bandpass filter without the need for a physical cross-coupling path. The extracted pole technique allows the designer to extract the finite position TZs in terms of extracted resonators, avoiding the need for

a physical cross-coupling. In this paper the realization of filters based on extracted pole design with different numbers of finite real frequency axis TZs is discussed. The filters are symmetrical and can hence be cut in the E-plane, which allows them to be manufactured in two identical halves where no additional loss is introduced as no surface current is disturbed [5]. Therefore, the filter can be realized in low-cost FDM techniques.

II. EXTRACTED POLE FILTER THEORY

In comparison to conventional realizations of TZs, where cavities are physically cross-coupled, the extracted pole technique benefits from the extraction of the TZs without the need for a cross-coupling aperture. The synthesis of the equivalent circuit, from which a coupling matrix may be derived, is described in [4]. Generally speaking, the extracted pole cavity is coupled to the main part of the filter by means of nonresonating nodes (NRN), which are usually realized by strong de-tuned cavities or pieces of transmission lines [4], [6]. The position of the transmission zero is determined by the resonance frequency of the extracted pole resonator coupled to the NRN. A typical realization of an extracted pole cavity in waveguide techniques with inductive main-line couplings is shown in Fig. 1 (a), where in (b) the corresponding low-pass discrete equivalent circuit is shown. The NRN of Fig. 1 (a)

k

... k-1 k+1 k+2...

JNRN,k

Fig. 1. (a) Realization of an extracted pole cavity in waveguide techniques, (b) Discrete low-pass equivalent circuit. Ck denotes the k-th low-pass resonator and Bk the k-th frequency invariant reactance. Jij denotes inverters.

is realized by a frequency invariant reactance (FIR) BNRN in

(b). Couplings between resonators or NRNs are termed Jij. However, if the bandwidth of the filter is increased, all

coupling factors have to be enlarged as well. This leads in general to wider blend widths. For wide-band applications the appearance of the extracted pole cavity can be changed to a symmetrical one, which was first proposed in [7] and is repeated in Fig. 2 for the sake of clarity. In this paper several

Fig. 2. (a) Conventional realization of an extracted pole, (b) extracted pole for wide-band applications and (c) symmetrical extracted pole realization for wide-band applications as proposed in [7].

of the symmetrical oversized extracted-pole cavities are used to realize advanced filter responses. A similar idea was proposed in [8] but leads to asymmetrical filter set-ups, which is a large disadvantage in low-cost 3-D printing applications. The filters realized within this paper are all symmetrical regarding the E-plane.

III. FILTER SET-UP

For all filters proposed here the specifications are set to a minimal in-band return loss of RL = 20 dB. The band edges are f1 = 10:5 GHz and f2 = 11:5 GHz (F BW 9:1%). The number and position of TZs varies within the different set-ups.

The main building block for the realization of TZs is shown in Fig. 3. Depending on the dimensions lep, lnrn, wep as well as wnrn, the building block supports one TZ above or below the passband and at least one reflection zero contributing to the transmission characteristic of the filter. The S-Parameter response of the building block of Fig. 3 with a TZ below the passband is shown in Fig. 4. The dimensions are indicated in the caption. In Fig. 4 the TZ arises at around 10.3 GHz. Please note that the building block supports two modes in the near passband region. The desired mode in this case is the mode near the TZ at 10.6 GHz. Nevertheless, by using strong input- / output couplings, as in the case of wide-band filters, the second mode at 12.1 GHz can be shifted in the direction of the

passband while the lower mode is minor affected by changing the input- / output coupling strength. Therefore, the building block can contribute up to two resonant modes in dependency of the dimensions for improving the filtering characteristic. The H-fields at 10.6 as well as 12.1 GHz are shown in Fig. 5.

Fig. 5. H-fields of the building block with dimensions as indicated in the caption of Fig. 4. (a) at 10.6 GHz and (b) at 12.1 GHz.

It becomes clear that wider input- / output couplings decrease the resonance frequency of the upper mode, as a large amount of the H-fields exist in the coupling aperture.

Filters can be constructed with the building block introduced above in combination with standard single mode T E101-cavities. In the first step of the layout process the filter only consists of T E101-cavities, which can be dimensioned

lep lnrn

wep wnrn wOC

wIC

Fig. 3. Building block with dimensions indicated in Fig. 4.

wnrn = 39:6 mm,

Fig. 7. Simulated S-Parameters with one ”building block” realizing one TZ below the passband. In total five resonance arise in the passband. Dimensions are in the caption of Fig. 6.

as described in the literature, e.g. [4]. In the second step as many single-mode cavities are replaced by the building block of Fig. 3 as the number of TZs to be introduced. Proper dimensioning regarding the position of the TZ and the matching in the passband can take place by optimization or coupling matrix extraction techniques. The dimensions of a filter with a TZ below the passband are shown in Fig. 6, while Fig. 7 shows the corresponding simulated S-Parameters. Two filters are implemented within this paper, one of which has one TZ above the passband while the second one has a symmetrical pair of TZs realized by two building blocks.

IV. MEASUREMENT RESULTS AND DISCUSSION

The filters are printed with the low-cost FDM technique (Printer: Flashforge Dreamer) with PLA as filament. Afterwards, they are spray coated with a copper spray to get a conductive surface for the subsequent galvanization of further copper. The filter with two symmetrically placed TZs is shown in Fig. 8 before galvanization but after spray coating. The

Fig. 8. Photograph of one half of the spray coated waveguide filter with two ”building blocks” at cavity one and four.

corresponding measurement results are shown in Fig. 9 for the filter with one TZ above the passband and in Fig. 10 for the filter with two symmetrically TZs. The insertion loss in the passband is between 0.6 and 1 dB. Due to tolerances in the printing / painting and galvanization process, the TZ above the passband in case of Fig. 9 does not occur.

V. CONCLUSION

Symmetrical X-band waveguide filters based on extracted pole design are discussed within this paper. Due to the symmetry the filters are 3-D printed with low-cost FDM printing techniques in two halves with an E-plane cut. A

Fig. 9. Comparison of S-Parameters of simulation and measurement from the four cavity filter with theoretically one TZ. The inset shows the cutting plane.

Fig. 10. Comparison of S-Parameters of simulation and measurement from the four cavity filter with two TZs. The inset shows the cutting plane.

building block which realizes one TZ above or below the passband and at least one resonance is used for the design. The insertion loss in the passband is limited to around 1 dB.

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