диафрагмированные волноводные фильтры / 9bb12ebc-5cfb-4dfc-a019-366207307a83
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The Analysis of E-plane Filters with Loaded Resonators with Mode Matching Method
Meysam Sabahi1, Nader Komjani2
1,2 Electrical Department of Iran University of Science & Technology meisam_sabahi@ee.iust.ac.ir, n_komjani@iust.ac.ir.
Abstract - This paper presents the analysis of an E- plane filter with loaded resonators. Using these structures, not only solves the problem of excessive length of conventional E-plane filters, but also leads to a great improvement in rejection of upper stop band. This method has a high accuracy in wide frequency range. In order to demonstrate the validity of this method, the results of construction and simulation are compared; and this comparison has a good compatibility.
Keywords: Waveguide Filter; E-plane; Mode Matching;
Ridge Waveguide;
1. Introduction
E-plane filters are one of the methods of enacting waveguide filters. For the first time, this structure was reported by Konishi [1] in 1974. Until 1997 these structures were the center of researchers' attention. Especially in 1982-1985 a lot of papers about the analysis of these filters and similar structures were presented [2]. The advantages of these filters are the ability of mass producing, low price, and also it is not necessary to adjust them. Despite these advantages, they have two disadvantages: excessive length and low insertion loss in upper stop band. In order to solve these two problems, it is suggested to apply a set of ridge discontinuity in the resonators of these filters [3].
Because of inability to adjust these filters after construction, it is necessary to simulate them carefully, so having an accurate simulator is very important. As the boundary conditions are clear and there are some discontinuities in the direction of propagation, mode matching method is used in this paper.
First of all, the method used to simulate this structure is explained. Then, in order to verify the validity of this method, the results of simulation and measurement of a constructed sample are compared. Finally in order to show the advantages of this structure, the results are compared with conventional E-plane filter.
2. Mode Matching Method
Figure 1 shows the general structure of E-plane filter with loaded and unloaded resonators. According
to figure 2, this structure is consisted of two fundamental discontinuities, ridge waveguide to rectangular waveguide junction and bifurcation discontinuity.
(a)
(b)
Figure 1: (a) General image of E-plane filter with loaded resonators. (b) Loaded and unloaded resonator.
In order to calculate the generalized scattering matrix (GSM) in each discontinuity, electrical and magnetic fields, in all regions of discontinuity, due to cross sectional functions of that region, T(x,y), is extended[4].
Figure 2: Fundamental discontinuities of the structure.
(a) Bifurcation discontinuity. (b) Discontinuity of ridge waveguide to rectangular waveguide.
E = ×(Ahz e$z ) |
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Nh |
exp(− jkzhq z)+ Bhq exp(+ jkzhq z)} |
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Ahz = ∑ Zhq Thq (x, y){Fhq |
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q=1
1-4244-1435-0/07/$25.00©2007 IEEE
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Aez = ∑ Yep Tep (x, y){Fep exp(− jkzep z)−Bep exp(+ jkzep z)} |
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Where, A |
and A are potential vectors of TE and |
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TM modes respectively. Y and Z are admittance and impedance of the modes respectively, and kz is
propagation constant in z direction. Fhq,ep and Bhqep, are
forward and backward wave amplitude of all modes, which should be normalized according to the following relation.
E =×(Ahz e$z )+ |
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× ×(Aez e$z ) |
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By matching tangential field components in common face of discontinuity regions, GSM of discontinuity is calculated by relations of:
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where M is described as:
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The GSM of a septum from achieved scattering matrix of bifurcation discontinuity is calculated according to the following relations:
W =(I −D S22f |
D S22f )−1 D S21f |
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S21s = S12f W |
L } |
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In the above relations i =I, II and L is the length of the septum. S f relates to GSM of bifurcation
ij
discontinuity. In order to calculate the scattering matrix of a ridge section that is made of two discontinuities (ridge waveguide to rectangular waveguide junction) and a length of ridge waveguide and also to cascade different parts of filter, we apply the following relations. (See figure 5)
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F =(I −S22a DS11b D)−1 |
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D = Diag {e− jkzmn L } |
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diag |
Yhq }JHH diag { |
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M = |
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hu } |
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T means transpose, U is unit matrix and diag{} is |
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diagonal matrix. Modal coupling matrix is calculated |
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by the following relations: |
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Figure 5: The technique of cascading two 2-ports with a |
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(JHH )qu |
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middle waveguide. |
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In the ridge section, the middle part is a ridge |
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F II |
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(JEH )pu = ∫ (−TepI )( ThuII ×e$z )dF |
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waveguide but in other cases it is rectangular |
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waveguide. In diagonal matrix of D, L indicates the |
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length of the middle part and kzmn is the propagation |
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constant of considered modes in it. |
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F II
4. Simulation and Measurement Results
It is note worthy that (JHE)qv ≡0 , so M12 argument
spontaneously vanishes. Due to existence of ridge discontinuity in this structure, it is necessary to consider TEmn and TMmn modes for analysis.
Due to the symmetry in the discontinuities of the structure, using image theory, it can be shown that the only odd modes with cut off frequency less than fc, are considered.
To clarify the validity of this simulation method, an E-plane filter with three loaded resonators is considered in X-band. The shape of this filter's middle plate is shown in figure 6 and its dimensions are in table 1. To simulate this filter, the frequency for omitting the modes (fc) is 250 GHz.
3. Generalized Scattering Matrix
Considering achieved scattering matrix for each discontinuity and cascading them, we can calculate the GSM of the whole structure.
Figure 6: The middle plate structure of a three loaded resonators filter.
Table 1: The dimensions of three loaded resonators filter with the center frequency of 10 GHz and the 400 MHz bandwidth.
a = 22.86 mm |
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Ls4 =1.7 mm |
Ls3 =6.547 mm |
Ls3 =6.547 mm |
Ls1 =1.7 mm |
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L2 = 0.802 mm |
res1 |
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9.8 |
9.9 |
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Frequency ( GHz ) |
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Figure 7: Scattering coefficients of the designed filter.
In figure 7, the filter simulation results are shown. As it can be seen, the center frequency of this filter is 10 GHz and the bandwidth is 400 MHz. For a better comparison between the designed filter and conventional E-plane filter with the same characteristics, the dimensions of the two structures are compared in table 2. It is clear that in the new structure, length of filter reduces about 40%. To verify the validity and accuracy of this method, two kinds of E-plane filters (conventional and loaded resonators) were constructed.
Figure 8 shows the structure of these two filters. The results of simulation and measurement of these two filters are in figures 9 and 10. It can be seen, there is a good compatibility between the results of measurement and simulation, and the difference between insertion loss of this structure and conventional E-plane filter in upper stop band and the improvement is completely obvious. Also the simulation of this filter has been done in HFSS [7] and there is a good compatibility between results of this software and the technique used in this paper.
5. Summary
This paper presented the technique of analyzing one kind of improved E-plane filter that has a smaller length and a better upper stop band. Also by improving upper stop band of filter the decrease in the length of the new filter is 40%.
The accuracy of the analysis technique is not only valid in filter pass band, but also it is so accurate in the extended frequency band. Regarding these comparison, there is a good compatibility between the results of simulation by the written code and HFSS, and measurement.
Table 2: The comparison of conventional and loaded E-plane filter dimensions.(dimensions is in mm)
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With Loaded |
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Resonators |
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22.86 |
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B |
10.16 |
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T |
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1.41 |
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S1= b |
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13.815 |
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S1= b |
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Filter Length |
58.26 |
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(a) |
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Figure 8: (a) The structure of the two constructed filters.
(b) The comparison of these filters from the view point of dimension.
Figure 9: The measurement of Loaded E-plane filter with HP8720B network analyzer.
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9 .7 |
9.8 |
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10.1 |
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Frequency ( GHz ) |
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(b) |
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Resonators,” Int. J. Numerical Modeling, vol. 4, pp. 63-73, Mar. 1991.
J. Uher, J. Bornemann, and U. Rosenberg,
Waveguide Components for Antenna Feed Systems: Theory and CAD, Norwood, Artech House, 1993.
H. Patzelt and F. Arndt, “Double-plane steps in rectangular waveguides and their application for transformers, irises, and filters”, IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 771776, May 1982.
“Ansoft High-Frequency Structure Simulator,” Ansoft Corporation, Pittsburgh, PA.
Figure 10: (a) Comparing the results of construction and simulation of these two filters. (b) Comparing the results of simulation and measurement of loaded resonator filter's pass band.
Acknowledgement
The authors would like to thank the financial support provided by Iran Telecommunication Research Center (ITRC).
References
[1]Y. Konishi, K. Uenakada, “The Design of a Bandpass Filter with Inductive Strip-Planar Circuit Mounted in Waveguide,” IEEE Trans. Microwave Theory, Tech., vol. MTT-22, pp. 869873, Oct. 1974.
[2]Y. C. Shih, “Design of waveguide E-plane filters with all-metal inserts,” IEEE Trans. Microwave Theory Tech., vol. 32, no. 7, pp. 695–704, 1984.
[3]G. Goussetis, D. Budimir, “ Novel Periodically Loaded E-Plane Filters,” IEEE Microwave and Wireless Components Letters, vol. 13, no. 6, pp. 193-195, June 2003.
[4]J. Bornemann, “Comparison between Different Formulations of the Transverse Resonance Field-
Matching Technique for the Three-Dimensional Analysis of Metal-Finned Waveguide