диафрагмированные волноводные фильтры / e19ce755-8eae-4426-b489-efd7336e2735

Propagation and EMC Technologies for Wireless Communications (MAPE 2009), Beijing, China, 27–29 October 2009, pp. 140–143.

4.M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqus, and Y. Kivshar, Structural tunability in metamaterials, Appl Phys Lett 95 (2009), 084105.

5.S. Zhang, D.B. Ge, and B. Wei, Numerical study of a new type of tunable SRR metamaterial structure, J Electromagn Waves Appl 22 (2008), 1819–1828.

6.M.F. Khan and M.J. Mughal, Effective permeability of inner ring shorted split ring resonator, Microwave Opt Technol Lett 50 (2008), 624–627.

7.Z. Sheng and V.V. Varadan, Tuning the effective properties of metamaterials by changing the substrate properties, J Appl Phys 101 (2007), 041909.

8.I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, Tunable metamaterial transmission lines based on varactor-loaded split-ring resonators, IEEE Trans Microwave Theory Tech 54 (2006), 2665–2674.

9.I.V. Shadrivov, S.K. Morrison and Y.S. Kivshar, Tunable split ring resonators for nonlinear negative index metamaterials, Opt Express 14 (2006), 9344–9349.

10.M.F. Khan, M.J. Mughal and M. Bilal, Effect of rotation of bottom metallic strips shorted S-shaped resonator on its working frequencies, 8th International Bhurban Conference on Applied Sciences & Technology (IBCAST), Islamabad, Pakistan, 10–13 January 2011.

11.H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T.M. Grzegorczyk, and J.A. Kong, Left handed materials composed of only S-shaped resonators, Phys Rev E 70 (2004), 057605.

12.M.F. Khan and M.J. Mughal, Tuned S-shaped resonators, Proceeding of IEEE 2007 International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications (MAPE 2007), Hangzhou, China, 16–17 August 2007, pp. 1017–1019.

13.X. Cheng, H. Chen, L. Ran, B.I. Wu, T.M. Grzegorczyk, and J.A. Kong, A bianisotropic left-handed metamaterials compose of S-ring resonator, PIERS online 3 (2007), 593–598.

VC 2011 Wiley Periodicals, Inc.

FOLDED SUBSTRATE INTEGRATED WAVEGUIDE CROSS-COUPLED FILTERS WITH NEGATIVE COUPLING STRUCTURE FOR WIRELESS SYSTEMS

O. Glubokov, S. Nagandiram, A. Tarczynski, and D. Budimir

Wireless Communications Research Group, School of Electronics and Computer Science University of Westminster, London W1W 6UW, United Kingdom; Corresponding author: d.budimir@westminster.ac.uk

Received 22 January 2011

ABSTRACT: In this article, a compact multilayer substrate integrated filter with pseudoelliptic power transfer function is presented. The fourth-order bandpass filter designed by optimization has a central frequency of 10 GHz with a bandwidth of 800 MHz. It possesses two transmission zeros and exhibits return loss of 30 dB. Miniaturization is achieved using folded waveguide technology. Novel negative coupling structure based on upside–down-folded iris-coupled resonators is introduced and investigated. Design procedure is briefly explained, coupling matrix is derived, and investigation of coupling elements is carried out to match calculated coupling coefficients. Results of fullwave simulation of the filter are in good agreement with the prototype.

VC 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:2521– 2526, 2011; Published online in View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26341

Key words: folded waveguide; substrate integrated waveguide; crosscoupled filter; negative coupling; multilayer design

1. INTRODUCTION

Rapid growth of telecommunications has created enormous demand for cheap and high-performance bandpass filters with sharp selectivity, compact size, and low insertion loss. New planar substrate integrated waveguides (SIWG), capable of meeting the aforementioned requirements, were proposed as a replacement of massive and expensive in fabrication conventional rectangular waveguides [1]. Hollow SIWG resonators became very popular for the design of direct-coupled [2], and cross-coupled microwave filters [3] that are based on the principle of the multiple paths through which the signal passes from the input to the output either in phase, transmitting the power, or out of phase, canceling itself at predicted frequencies and providing finite transmission zeros at the stopband.

Miniaturization techniques for SIWG resonators have been extensively studied lately. Among the approaches to achieve size reduction of SIWG resonators and filters, there are ridged SIWG [4], EBG-substrate [5], and folded SIWG (SIFW) [6] concepts. SIFWs exhibit similar cutoff frequency and propagation characteristics while occupy only half the area of its SIWG equivalent structure. Compact SIFW resonant cavities of two different types have been proposed and compared in [7], quarter-wavelength SIFW cavity has been used for a filter design in [8], and another miniaturization technique for SIFW resonators has been developed in [9] and investigated in [10].

This article is dedicated to design of a pseudoelliptic crosscoupled filter based on quarter-wavelength folded substrate integrated resonators using multilayer printed circuit board (PCB) substrate. A new simple idea for obtaining negative coupling coefficient using positive coupling structure for folded waveguides is introduced, investigated, and applied in bandpass filter structure.

2. FOLDED WAVEGUIDE RESONATORS

Conventional hollow rectangular waveguide resonator in planar form is a k/2 long section of the waveguide limited with viaholes connecting top and bottom ground planes. Consider a halfwavelength section of the SIWG folded along its longitudinal axis while maintaining its standing waves. Obtained structure is called half-wavelength folded-waveguide resonator. It consists of two layers and occupies only half the area comparing to the conventional waveguide resonator. Folding the resonator by 90 in the plane of substrate a new structure of quarter-wavelength folded-resonator can be achieved. Complete quarter-wave resonator contains a guiding part with a C-shaped slot (I-shaped longitudinal slot for half-wave resonator), made by the side walls which comprise of several metallic posts. Input/output striplines are used for feeding of the resonator through the input and output apertures in side walls. Views of the half-wave and quarterwave SIFW resonators are presented in Figure 1. Both structures will be further used in Sections 3 and 4 for the design of crosscoupled filter.

The structures were analyzed using commercial Ansoft HFSSTM software with finite element method. Obtained distribution of electric and magnetic fields in the half-wavelength resonator at the resonant frequency is presented in Figure 2. It is seen that electric field is concentrated at the region of slot in the metallization between top and bottom layers. Magnetic field has its maximum near the metallic vias where E-field has minimum, forming a magnetic line which passes a region near the side walls at top layer clockwise, then the slot near the input, then bottom side walls region anticlockwise returning to the top layer through the slot near the output. Field distribution in quarter-

wavelength resonator is similar to the described one with respect to the waveguide bend by 90 and is not listed here.

3. COUPLING STRUCTURES

Some types of cross-coupled filters require pairs of resonators which have positive and negative coupling coefficients. Several techniques are usually used for the realization of specified coupling coefficients. The simplest of them bases on coupling through irises in walls between integrated cavities.

3.1. Positive Coupling Structure

To realize a positive coupling coefficient between two folded resonators by means of coupling iris, it is sufficient to design a conventional pair of single-layer resonators [3] and fold them around their longitudinal axes afterward.

In case of direct coupling, the gap in the middle metallization layer runs from one resonator to another, while two halves of coupling iris formed by plated vias, are located one upon another in different layers. This principle is used to couple a pair of quarter-wave folded resonators, shown in Figure 3. Direct coupling can be also realized by the principle used for design of conventional E-plane filters in rectangular waveguide [11], where a septum placed in the E-plane acts as an inductive

discontinuity. Taking into account, that the E-plane of a folded waveguide coincides with the gap in the middle layer, the coupling septum can be easily applied. However, to provide low coupling coefficients, the width of the septum has to be significant. Nevertheless, narrow septa can be used in combination with coupling irises to regulate values of coupling coefficients. In case of side coupling, folding does not affect a coupling iris and coupling is provided by an inductive iris in regular way.

3.2. Negative Coupling Structure

Electric coupling provides negative coupling coefficient, and it can be realized with a slot or gap at the region of the resonator where maximum of E-field and minimum of H-field occur. However, for the case of considered SIFW resonator, maximum of electric field occurs in the slot and direct realization of negative coupling coefficient is possible only if slots of two adjacent resonators are located by the common wall. Such a configuration becomes inapplicable when the layout must be built so that the slots are located by the opposite side walls. To overcome the issue occurred in this case, we propose to use magnetic coupling through the slot between top and bottom layers of resonators instead of electric coupling.

It can be concluded from analysis made by Thomas in [12] that in two positively coupled resonators fields oscillate in phase

Figure 3 Coupled pair of quarter-wavelength FSIW resonators (top view)

at low mode and reveal a shift of 180 in high mode. In contrary, in pair of negatively coupled resonators, fields are out of phase at low mode and not shifted at high mode. Thus, assuming that fields in the first resonator are same for both positively and negatively coupled pairs, in the remaining driven resonator a phase shift of 180 between positively and negatively coupled cases will be observed at both low and high modes. In other words, it means that to create negative coupling from the positive one, a series signal inverter is required at all the outputs of the second resonator. One of the advantages of using folded resonators is an opportunity to integrate such an inverter inside the resonator. It can be noticed from field distribution in folded resonator at resonant frequency that electric and magnetic fields in top and bottom layers swap over one another each half a period. Thus, to invert signal in a folded resonator, it is sufficient to swap top and bottom layers of the structure.

Let us consider a pair of single-layer substrate integrated resonators positively coupled by an iris in common side wall [Fig. 4(a)]. To create a positively coupled pair of double-layer folded resonators it is necessary to fold up both resonators around their axes of symmetry clockwise and anticlockwise as it is shown in Figure 4(b). Swapping of layers of the second driven resonator can be performed by folding it clockwise [or upside–down; Fig. 4(c)]. Resulting structure consists of three layers and their number can be reduced by shifting one of resonators up or down by the thickness of substrate. Such procedure will cause deformation of the area where coupling iris is located so that the iris becomes a slot in the middle metallization layer [Fig. 4(d)]. The

Figure 5 Comparison of phase responses of positively and negatively coupled resonators

structure reveals the properties of a pair of negatively coupled resonators. It can be proven by comparison of phase responses of positive and negative coupled pairs in Figure 5. Indeed, at the neighborhood of the resonant modes, phases of S21 are shifted by 180 , while phases of S11 remain equal. Feasibility of the upside–down negative coupling structure in cross-coupled filter will be proven in Section 4.

4. CROSS-COUPLED FILTERS

Cross-coupled filters have an important advantage over directcoupled filters as they exhibit very sharp slopes and specified adjacent channel suppression because of transmission zeros placed in stopband, whereas direct-coupled show the sharper slope the more resonators they include. Transmission zeros appear because in cross-coupled filters more than one signal path between input and output exists and waves coming to the load out of phase annihilate one another.

4.1. Coupling Matrix

Synthesis of cross-coupled filter with synchronously tuned resonators lies in derivation of coupling matrix for a low-pass prototype from known initial specifications such as central frequency, bandwidth, ripple constant, adjacent channel selectivity, and so forth. For a pseudoelliptic filter response the matrix can be derived by optimization and the corresponding procedure is presented in [13]. Table 1 gives the initial specifications of the filter designed. Coupling scheme chosen to realize a low-pass prototype of the corresponding filter (Fig. 6) with four poles and two

TABLE 1 Specifications of the Bandpass Filter

transmission zeros at 6j1.5 leads to the following generalized coupling matrix M:

(1)

A program for the calculation of coupling matrix has been developed in MATLABTM by authors. Matrix M is then denormalized with respect to the required center frequency f0 and bandwidth Df so that such design parameters as coupling coefficients kij and external quality factor Qext can be obtained using the following formulae:

Therefore, the following design parameters can be obtained for the filter: k12 ¼ k34 ¼ 0.044; k23 ¼ 0.036; k14 ¼ 0.009; Qext ¼ 17.3.

4.2. Filter Design

When the coupling matrix is obtained, a correspondence between theoretical coupling coefficients and dimensions of coupling slots and gaps is to be established. It can be done using the graphs of the dependence of coupling coefficients on the slot/gap dimensions, for various types of couplings between a pair of resonators, built during the preliminary analysis. Alternative method for the designer is calculation of corresponding slot/ gap dimensions theoretically. However, this approach usually leads to bulky calculations.

Figure 6 Coupling scheme of the bandpass filter

Figure 7 Coupling coefficients k12 and k34 versus iris width W12

To determine how coupling coefficients depend on the dimensions of irises and slots, pairs of coupled resonators have been simulated in electromagnetic full-wave simulator Ansoft HFSSTM and frequency responses have been obtained. Then from each curve, two peak frequencies have been identified as low mode flow and high mode fhigh frequencies. Coupling coefficient can be extracted using a well-known expression [14]:

The filter contains three positive coupling structures which produce the main path for the signal in combination with all four resonators. Among the resonators, two (1 and 4), between which negative coupling is to be realized, have been chosen to be halfwavelength for the reason of easier organization of input and output transitions. The rest (2 and 3) have been chosen to be quarter-wavelength due to their location at the bend of the waveguide.

Thus, coefficients k12 and k34 can be obtained from analysis of coupled pair of halfand quarter-wave resonators. In this case, direct iris coupling without septum is used, and the coupling is controlled by the width W12 of the iris. Curve obtained as a result of the analysis is built in Figure 7.

Analysis of a pair of directly coupled quarter-wave resonators (depicted in Fig. 3) gives a similar curve for the coefficient

Figure 8 Coupling coefficient k23 versus iris width W23

Figure 9 Coupling coefficient k14 versus slot length Lslot

k23 (Fig. 8). Here, coupling control is performed by the iris of the width W23.

As it has been mentioned in Section 3, negative coupling structure (Fig. 4) is also based on magnetically coupled pair, but, in this case, coupling element is a rectangular slot of length Lslot between top layer of resonator 1 and bottom layer of

Figure 10 External quality factor Qext versus input iris width Win

TABLE 2 Dimensions of the Bandpass Filter (Fig. 11)

resonator 4. Dependence of coupling coefficient k14 on the Lslot is shown in Figure 9.

It can be noticed from Figures 7–9 that the wider the coupling element, the stronger the coupling and the larger the value of coupling coefficient. Such behavior is characteristic to the cavities coupled magnetically: in this case, high-mode frequency drifts slightly, whereas low frequency moves significantly. On contrary, for electric coupling the behavior of low and high modes is opposite and thus coupling coefficient decreases with widening coupling element.

To control the external quality factor, changing of the width Win of input iris with a fixed width of the input stripline is utilized. The parameter Qext can be extracted from frequency response of doubly loaded resonator using the expression:

where fres—a frequency where transmission coefficient reaches its maximum; Df3 dB—bandwidth of the resonator for which transmission is reduced by 3 dB from its maximum value |S21| taken in dB. The resulting curve with the dependence of external quality factor on the width of the input iris is presented in Figure 10.

4.3. Results

Filter layout consists of two layers of Taconic RF-35TM (er ¼ 3.5; tan d ¼ 0.0018) on which two half-wavelength and two square quarter-wavelength substrate integrated folded resonators are organized. A view of the filter with dimensions marked is presented in Figure 11. Dimensions data is collected in Table 2.

Coplanar waveguide (CPW) input and output pads are located on the top layer. They are connected to the stripline on the middle layer using a metallic post. This input stripline connects to the resonator 1; resonator 4 is connected to the output stripline, respectively. The dimensions of the whole structure are 17 22 mm2.

Transmission characteristics of the designed cross-coupled filter simulated in Ansoft HFSSTM are presented in Figure 12. It is seen that the filter exhibits about 0.95 dB insertion loss and return loss is better than 30 dB in the passband. The second passband of the filter appears at about 15 GHz, but it is suppressed by 23 dB. It can be noticed that an extra transmission zero has been obtained in upper stopband at about 13.8 GHz. Theoretical analysis shows that the transmission zero appears because of very slight coupling available between source and load. At the same time, the source-load coupling creates another transmission zero in lower stopband which cannot be caught by the simulator. Increase of source-load coupling leads to drifting of the extra transmission zeros closer to the passband.

5. CONCLUSIONS

A compact fourth-order pseudoelliptic multilayer substrate integrated cross-coupled filter with two finite transmission zeros based on halfand quarter-wavelength folded resonators was designed using multilayer PCB technology. The filter adjusted for the central frequency of 10 GHz has a bandwidth of 800 MHz, exhibits insertion loss of better than 1 dB and return loss of 30 dB. It has a small size and can be integrated with other filters into diplexers and multiplexers. The approach used in this design can be easily applied for the other multilayer substrates, for example, LTCC.

REFERENCES

1.D. Deslandes and K. Wu, Integrated microstrip and rectangular waveguide in planar form, IEEE Microwave Wireless Comp Lett 1 (2001), 68–70.

2.S.T. Choi, K.S. Yang, K. Tokuda, and Y.H. Kim, A V-band planar narrow bandpass filter using a new type integrated waveguide transition, IEEE Microwave Wireless Comp Lett 14 (2004), 545–547.

3.X.-P. Chen and K. Wu, Substrate integrated waveguide crosscoupled filter with negative coupling structure, IEEE Trans Microwave Theory Tech 56 (2008), 142–149.

4.J.A. Ruiz-Cruz, M.A.E. Sabbagh, K.A. Zaki, J.M. Rebollar, and Y. Zhang, Canonical ridge waveguide filters in LTCC or metallic resonators, IEEE Trans Microwave Theory Tech 53 (2005), 174–182.

5.A. Shelkovnikov and D. Budimir, Novel compact EBG waveguide resonators in planar form, European Microwave Conference, Vol. 2, Paris, France, 4–6 October 2005.

6.N. Grigoropoulos, B. Sanz Izquierdo, and P.R. Young, Substrate integrated folded waveguides (SIFW) and filters, IEEE Microwave Wireless Comp Lett 15 (2005), 829–831.

7.J.-S. Hong, Compact folded-waveguide resonators, IEEE MTTS Digest, Fort Worth, TX, 2004, 213–216.

8.S.K. Alotaibi and J.-S. Hong, Novel substrate integrated waveguide filter, Microwave Opt Technol Lett 50 (2008), 1111–1114.

9.H. Lin, Novel folded resonators and filters, IEEE MTT-S Digest 2007, 1277–1280.

10.R. Wang, L.-S. Wu, and X.-L. Zhou, Compact folded substrate integrated waveguide cavities and bandpass filter, Prog Electromagn Res PIER 84 (2008), 135–147.

11.D. Budimir, Optimized E-plane bandpass filters with improved stopband performance, IEEE Trans Microwave Theory Tech 45 (1997), 212–220.

12.J.B. Thomas, Cross-coupling in coaxial cavity filters—A tutorial overview, IEEE Trans Microwave Theory Tech 51 (2003), 1368–1376.

13.S. Amari, Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique, IEEE Trans Microwave Theory Tech 48 (2000), 1559–1564.

14.J.-S. Hong and M.J. Lancaster, Microstrip filters for RF/microwave applications. Wiley, New York, 2001.

VC 2011 Wiley Periodicals, Inc.

FABRICATION AND CHARACTERISTICS OF PHASE-SHIFTED BEAT GRATINGS INDUCED BY CO2 LASER

Yan-en Fan,1 Tao Zhu,1 Leilei Shi,1 and Yun-Jiang Rao2

1 Key Lab of Optoelectronic Technology and Systems (Education Ministry of China), Chongqing University, Chongqing 400044, China; Corresponding author: zhutao@cqu.edu.cn

2 Key Lab of Broadband Optical Fiber Transmission and Communication Networks Technology (Education Ministry of China), University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Received 22 January 2011

ABSTRACT: We propose and investigate a phase-shifted long-period

fiber grating (LPFG) written by CO2 laser in twisted single-mode fibers (SMFs). For the beating effect, two peaks of LPFG derived from phase-shift further split into two peaks, respectively. The evolution and characterization of the transmission spectra were investigated. The channel spacing of the phase-shifted LPFGs written in twisted Er-doped fiber could be much narrower than that of which written in twisted normal SMF. Polarization dependent loss of the phase-shifted beat-gratings is less than 0.6 dB. This type of gratings provides potential applications in optical communication systems, such as course wavelength division multiplexing devices. VC 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:2526–2530, 2011; View this article online at wileyonlinelibrary.com.

DOI 10.1002/mop.26340

Key words: long-period fiber gratings; optical fiber devices; optical communication systems; fiber waveguide

1. INTRODUCTION

Long-period fiber gratings (LPFGs) are band-rejection transmissive filters which couple light from the core of a single-mode fiber (SMF) into the cladding, thus producing attenuation bands in the fiber transmission spectrum. Because of their unique features such as a low insertion loss, a low back-reflection, and strong immunity to electromagnetic wave, the LPFGs have attracted great interest with regard to optical telecommunication and sensor applications [1]. In most practical applications, multiple peaks and special spectral profile are required. A reported technique for tailoring the LPFG spectrum is by cascading two independent LPFGs, which has been demonstrated as a multichannel filter for multiwavelength signal generation in wavelength division multiplexer (WDM) system [2]. To flatten a gain spectrum that contains several peaks, a compact module based on using several concatenated uniform LPFGs has been proposed [3]. However, extra insertion loss is usually introduced due to the sidelobes on both sides of the attenuation peak loss. The application of phase shifted LPFG with multiattenuation peaks may reduce the need for cascaded LPFGs [4]. To further reduce insertion loss, the use of apodization technique is demonstrated [5]. Another technique to design the LPFG spectrum is chirping the period of a grating. Several types of period chirped LPFGs (CLPFGs) have been demonstrated, such as, linearly chirp, peak-shape chirp, and cascaded linearly chirp. CLPFGs