диафрагмированные волноводные фильтры / 0f80ff34-e24e-414f-87ec-d99c0b24af38

-PLANE filters have been extensively reported in nu- E merous publications [1]–[7]. They are popular due to their unique features such as low cost, low loss and suitability for mass production. However, despite their favorable characteristics, E-plane filters suffer from the relative narrow bandwidth due to the minimum realizable width of the metallic strip and the narrow second stop-band.

To alleviate the latter problem, several solutions have been proposed in the 1980s [8]–[10]. Although most of these solutions have achieved a good stop-band performance, it is at the expense of manufacturing complexity or high pass-band insertion loss. Solutions proposed in [11]–[13] obtained a higher attenuation and a wider stop-band in the second stop-band without introducing any complexity in the fabrication process, but the maximum realizable band-width is still too narrow for wideband applications.

When designing a broad-band fin-line filter, one usually meets the problem that the coupling strength between two outermost coupling structures is not large enough due to the manufacturing tolerance. To effectively address this issue, a fin-line post structure, as shown in Fig. 1, has been proposed to design broad-band fin-line filter in [14], which focused on the coupling characteristic of the fin-line-post structure.

In this letter, we present a broad-band E-plane filter with a wide stop-band. In the proposed filter, transmission zeros are introduced in the stop-band by using fin-line post structures

Manuscript received February 07, 2011; revised April 03, 2011; accepted May 02, 2011. Date of publication June 09, 2011; date of current version July 07, 2011.

The authors are with the State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China (e-mail: zhengbin_xu@hotmail.com; mnigj@hotmail.com; cqian@seu.edu.cn; wbdou@seu.edu.cn).

Digital Object Identifier 10.1109/LMWC.2011.2156775

as coupling elements. By choosing those transmission zeros properly, the stop-band is widened. Both simulated and experimental results achieve good stop-band performance and wide bandwidth simultaneously. Meanwhile, it maintains the low cost and mass producible characteristics of the conventional E-plane filters.

II. ANALYSIS AND DESIGN

The layout of the proposed E-plane filter is illustrated in Fig. 2. Different from conventional E-plane band-pass filter, the fin-line post structures are employed as coupling elements in the proposed filter. Fig. 3(a) depicts the equivalent T-network of the fin-line post structure. Considering the capacitance introduced by the gap, a series resonator (LC) is loaded in the branch arm of the T-network, as shown in Fig. 3(a). When the frequency of interest is far away from the resonant frequency of the series resonator, the reactance of the resonator is capacitive or inductive. By adding an appropriate length of transmission line at both sides of the T-network, a K-inverter is achieved, as shown in Fig. 3(b). On the other hand, the reactance of the resonator becomes zero at the resonant frequency , resulting in a stop band with transmission zero at . Therefore, at resonant frequency , it is appropriate to consider the fin-line post structure as a short circuit instead of a K-inverter.

In order to investigate into the properties of the transmission zero and the coupling strength of the fin-line post structure, 3-D EM simulator (CST Design Environment) is used. Fig. 4 shows variation of the resonant frequency and coupling strength for different values of and . It is clearly shown that the transmission zero moves towards higher frequencies as increases. When the , the resonant frequency is beyond the TE20 mode cutoff frequency of the waveguide, in

XU et al.: BROAD-BAND E-PLANE FILTERS

Fig. 3. (a) Equivalent circuit of the proposed coupling structure. (b) Impedance inverter.

Fig. 4. Normalized characteristic impedance of K-inverter (at 30 GHz) and resonant frequency for different dimensions of the fin-line post structure. (waveguide dimensions: , , substrate thickness

, , metallization thickness ).

351

TABLE I

DIMENSIONS (IN MILS) OF THE COUPLING STRUCTURES AND THE RESONATORS

band E-plane filter with an improved stop band performance is obtained.

The design procedure developed by Konishi and Uenakada [2] for conventional E-plane filters is applied to our proposed filter design. The initial K impedance of K-inverter is obtained by using the method proposed by Bui et al. [6]. The resonant frequency of the coupling structure is set in the spurious pass-band of standard E-plane filter according to the available coupling structure. As Fig. 4 shows that coupling strength depends on both strip width and width of the gap , while the resonant frequency mainly depends on the width of the gap and weakly depends on the strip width . Thus, in the filter design, we can determine the gap width first according to the given resonant frequency, and then determine the strip width according to the required coupling strength and gap width . After the initial dimensions of the filter are determined, a fine tuning process can be carried out with CST Design Environment.

Fig. 5. Equivalent circuit of the proposed filter in the second stop-band.

which the power is increasingly transported by the propagating wave along the coupling section of the conventional E-plane filter, resulting in a poor second stop-band performance [8]. By choosing properly, a notch band can be achieved in the second stop-band or spurious pass-band of the conventional E-plane filter. Thus, at the stop-band, the proposed filter is equivalent to a series of series resonators separated by transmission lines, as shown in Fig. 5. By setting the resonant frequency of each series resonator properly, band-stop performance can be achieved in the second stop-band or spurious pass-band of the conventional E-plane filter, and broad stop-band performance is obtained. On the other hand, when the frequency is much less than , the fin-line post structure can be considered as coupling element and the filter behaves as the direct coupled half-wave- length filter. Since the fin-line post structure based K-inverter can achieve higher coupling strength than its counterpart with the same metallic strip width [14], a broad-band E-plane filter can be obtained without any extra increase in the fabrication difficulty.

As discussed above, by designing the fin-line post structure to achieve certain coupling strength at the pass-band and proper resonant frequency at the stop-band simultaneously, a broad

III. SIMULATED AND MEASURED RESULTS

In order to demonstrate the improvement in both band width and stop-band performance, a five-order filter has been designed using WR-28 waveguide (, ) and 10-mil-thick RT/duroid 5880 substrate . As required by a particular application, 30 GHz center frequency, 0.1 dB pass-band ripple and 10% fractional bandwidth are chosen for the filter design. The filter is simulated and optimized by CST Design Environment. In order to obtain a clear comparison, a conventional filter with the same parameters discussed above is also designed and simulated by CST Design Environment. Table I shows the dimension of the coupling structures and the resonators of both conventional and our proposed filters. As shown in Table I, the dimension of the outermost coupling structure is: , for the proposed filter and for the conventional E-plane filter. Obviously, conventional fin-line filter cannot achieve such wide band width using the regular processing technique. The transmission zeros corresponding to the fin-line post structures are , , , respectively.

Fig. 6 gives the simulated results of two designed filters. It is clearly shown that the proposed filter achieved better second stop-band performance. Transmission zeros introduced by the fin-line post structures are observed in the stop-band of the proposed filter. Due to the coupling between the adjacent series resonators, the observed transmission zeros have little deviation from the transmission zeros corresponding to uncoupled fin-line

Fig. 7. Measured and simulated filter responses.

Fig. 8. Photo of the fin-line filter with the proposed coupling structure.

post structures. As shown in Fig. 6, the stop-band of the conventional E-plane filter extended up to about 44 GHz, while the proposed filter extended to about 52 GHz. Moreover, the proposed filter has better selectivity than its conventional E-plane counterpart in the second stop-band. As the resonator of the proposed filter is coupled by shunt capacitive elements, the attenuation on the lower side of the pass-band is lower than that of conventional E-plane filter. However, a higher attenuation on the lower side of the pass-band can be obtained by increasing the filter order. In order to demonstrate the improvement of the lower side rejection, a seven-order proposed E-plane filter is designed and simulated. The simulated results are shown in Fig. 6, in which an improvement on the lower side rejection can be clearly observed.

The proposed filter designed above (five-order) has been fabricated and measured. Measured results are given only up to 50 GHz due to a shortage of a VNA operating above 50 GHz. Measurements show that the minimum insertion loss in the passband is 0.5 dB and the return loss is more than 19 dB from 28.55 to 31.5 GHz. Its fractional bandwidth is about 10%. Fig. 7 compares simulated and measured results and good agreement is observed. The observed stop-band performance degradation

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