диафрагмированные волноводные фильтры / e338df51-a78c-44eb-9b5a-28c7f78f4900

Abstract—This letter presents a design of a fifth-order linear phase filter with frequency-dependent couplings. The filter is composed of a triplet that is directly coupled to two resonators at the input and output. To provide group delay flattening a cross-cou- pling in the trisection has a strongly dispersive character with a negative slope parameter. To achieve this, an E-plane stub with a septum was used. To further improve the filter selectivity, the direct couplings connecting the triplet to the outer resonators are also frequency dependent. In this particular case, these were implemented in the form of two partial-height conducting posts to provide two imaginary transmission zeros, one on each side of the stopband. With three strongly dispersive couplings, four zeros were obtained in a fifth-order topology that generates only one imaginary transmission zero in a classical design. The filter was realized in the WR-90 waveguide and the measured characteristics match the simulated ones, confirming the validity of the concept.

Index Terms—Frequency-dependent couplings, generalized Chebyshev filters, linear phase filters, microwave bandpass filters (BPFs), mixed couplings, waveguide filters.

I. INTRODUCTION

M ICROWAVE filters are fundamental components of all wireless communication systems. Over the years, the most commonly used type of filtering functions have been based

on minimum phase characteristics, which ensure the highest attenuation rate in out-of-band frequencies (see Chapter 17 in [1]).

Nowadays, filters must exhibit selective amplitude performance while at the same time providing flat group delay characteristics to avoid signal blur. Generally, the filter amplitude response is improved via imaginary transmission zeros implemented in suitably cross-coupled resonator networks [2], [3], while the filter phase characteristics can be improved in two ways. These are, first, the use of external all-pass equalizers [4]–[6] and, second, using self-equalized filters, where flat group delay characteristics are obtained via complex transmission zeros (TZs). Using a classical filter synthesis method [2] that assumes only constant couplings, the smallest linear phase circuit (in terms of a filter order) is a quadruplet [7]. However, unless a diagonal coupling is used, which is often

Manuscript received September 07, 2013; revised November 21, 2013; accepted January 05, 2014. Date of publication February 13, 2014; date of current version November 04, 2014. This work was supported by the Polish National Science Centre under contract DEC-2011/01/B/ST7/06634.

The authors are with the Department of Electronics, Telecommunication and Informatics, WiComm Center of Excellence, The Gdańsk University of Technology, Gdańsk 80-233, Poland (e-mail: lukasz.szydlowski@ieee.org; m.mrozowski@ieee.org).

Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LMWC.2014.2303171

hard to implement, this solution suffers from the fact that the set of positions of TZs available is limited to a symmetrical pair of purely real or imaginary points in the s-domain.

On the other hand, an attractive alternative for conventional filters is circuits containing frequency-dependent (also called mixed [8] or resonant [9]) couplings. It has already been shown that engineering the dispersive character of couplings vastly expands the capabilities of topologies operating with frequency invariant couplings [8]–[14]. In most cases, additional zeros can be generated when the couplings are frequency dependent. For instance, making the coupling between source and load resonant and using dispersive coupling inside the network results in filters with more finite transmission zeros than reflection zeros [15].

In this letter, we propose a novel concept of a fifth-order filter with frequency-dependent couplings. The filter consists of a triplet (with one strongly dispersive cross-coupling) that is further directly connected (also via dispersive couplings) to two resonators placed at the input and output. Due to the dispersive couplings, the circuit provides four transmission zeros (a complex pair and two imaginary ones) compared to just a single imaginary zero for frequency-invariant connections. In the proposed circuit, the trisection part is responsible for group delay equalization. This effect can only be obtained, however, if the slope of the coupling is negative. To achieve this, a series E-plane stub with a septum was developed. The use of a septum makes the dimensional synthesis more flexible as far as engineering the dispersive coupling is concerned. Note that the proposed triplet may be designed as a standalone self-equal- ized filter and, to the best of our knowledge, this is the minimal filtering network (in terms of order) providing group delay equalization. To improve the amplitude response, two imaginary transmission zeros were introduced by means of two direct dispersive couplings that were implemented in the form of partial-height conducting posts. Since each post is directly responsible for one imaginary transmission zero this approach offers easy tuning capabilities (by a simple height adjustment). All constant couplings were implemented in the form of H-plane irises. The proposed filter was centered at with a fractional bandwidth of 0.0321. The positions of the imaginary transmission zeros were and , while the complex transmission zeros were chosen to provide group delay equalization across almost 40% of the passband.

II. FILTER DESIGN

The prototype filter response with the corresponding topology is shown in Fig. 1. Resonators denoted as black circles (in the inset in Fig. 1) form a triplet that is directly coupled to two resonators placed at the input and output (dispersive couplings being indicated by lines crossed by an

Fig. 1. Prototype filter response (topology shown in the inset).

Fig. 3. Top view of the filter layout with imposed dimensions; perspective view shown in the inset (units: mm).

arrow). For the filter under study, the normalized positions of imaginary transmission zeros were chosen arbitrarily to be , while the positions of complex TZs, found to be , were obtained numerically via optimization to provide group delay equalization across almost 40% of the passband. Having defined the filter specification and topology, the next step is circuit synthesis. Since the assumed topology involves dispersive coupling, we used the synthesis technique presented in [3] and obtained the impedance matrix (1), as shown at the bottom of the page, where the impedances of external couplings from source/load to the first/last resonator

denotes the prototype angular frequency.

The next step in the filter design is the dimensional synthesis of a certain microwave component which emulates its equivalent lumped model. Half-wavelength resonant cavities (made in WR-90 waveguide) operating with the mode were used as resonators. To implement constant internal and external couplings, simple H-plane irises were used. The most challenging

Fig. 5. Comparison between measured and simulated group delay.

part of the project was engineering the dispersive couplings. One should note that matrix contains dispersive couplings with both positive and negative slope parameters. To implement the first type, a partial-height conducting post similar to the one presented in [12], [16] was used. This approach ensures relatively easy fabrication and allows tuning. To realize

Fig. 6. Out-of-band filter performance (photograph of the fabricated circuit shown in the inset).

frequency-dependent coupling with negative slope, an E-plane stub with an additional septum is proposed. The normalized transfer impedance characteristics of the discontinuity are presented in Fig. 2. In particular, the strongly dispersive character as well as negative slope are clearly observable. To be able to control the values of the slope parameter and position of zero transmission one has to adjust four parameters as indicated in the inset in Fig. 2. As can be seen, changing the length of the stub moves the position of a zero on the frequency axis while preserving the value of the slope parameter. A similar behavior is observable when the height of the septum is adjusted. Combining the two allows one to control the slope and position of the zero. However, for particular values of slope parameters and position of transmission zero one has to adjust the width of the septum and the stub. The dimensions of the partial-height post yielding the couplings with positive slope were found using the technique presented in [12].

The filter was designed with our in-house 3-D FEM solver and results obtained were validated in the full-wave electromagnetic simulator Ansoft HFSS. To reach the final solution, a zero-pole optimization algorithm similar to the one presented in [17] was used. The filter layout with imposed dimensions is presented in Fig. 3.

III. EXPERIMENTAL VERIFICATION

The filter was made from two pieces of aluminum (body and cover) held together with screws. Resonant cavities, the series stub as well as irises and the conducting posts were made using a CNC milling machine. Note that the series stub was hollowed out in the filter cover. Fig. 4 compares measured and simulated scattering parameters. As can be seen, the filter bandwidth, position of transmission zeros and assumed return loss level are close to the desired values. The minimum insertion loss in the passband equals 1.02 dB. A comparison between measured and simulated group delay performance is shown in Fig. 5. As can be seen, within the assumed bandwidth, the measured characteristic is almost coincident with the simulated one. The sight discrepancy around the center frequency is attributable to the effect of the nonzero imaginary part of the resulting complex transmission zeros. Nevertheless, the overall group delay performance is satisfactory and group delay flattening is clearly observable when the measured characteristics are compared to those obtained from an equivalent minimum phase network. As can be seen, the peak-to-peak aspect ratio is almost 40% higher

in the minimum phase network and group delay is only constant for a narrow range of frequencies in the vicinity of the filter center frequency. The out-of-band filter performance is shown in Fig. 6. As can be seen the first spurious resonance occurs at 8.2 GHz and is mainly controlled through the series stub length. The second spurious band occurs around 12.5 GHz, and is the result of higher order modes.

IV. CONCLUSION

In this letter, a novel concept of a generalized Chebyshev filter with frequency-dependent couplings containing positive and negative slope parameters within same network is proposed. Notably, the circuit has flattened group delay and selective amplitude response. The measured characteristics agreed with the numerical experiment.

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