диафрагмированные волноводные фильтры / 9dfe2185-423e-486b-98c7-63a8cf98f652

Abstract: In this paper, a new partial H-plane filter with half-wavelength resonators and periodic slow-wave structure is presented. The proposed filter makes use of the slow-wave effect to improve the frequency characteristics and considerably reduce the filter length. Using partial H- plane waveguides reduces the filter's cross section to onequarter of that of a conventional E-plane filter. Although because of their compactness, the insertion loss of the proposed H-plane filters is larger than that of the E-plane filters, they have lower cost and are mass producible. Also by using the periodic slow-wave structure the stop-band slope has been improved and the length has been reduced by 22 percent. These partial H-plane filters have been designed along with coaxial to partial H-plane waveguide transition.

Keywords: E-plane filters, folded waveguide, H-plane filters, slow-wave structure.

I. INTRODUCTION

Radio frequency and microwave band-pass filters are basic components in a wide spectrum of communication systems.

Passive Components at microwave frequencies, especially at lower frequency bands, are still bulky and occupy a lot of space so in order to reduce the cost it’s desirable to reduce the size.

Waveguide filters like E-plane, H-plane, and finline filters have been used extensively since they have low cost, are mass producible and easy to fabricate.[1-3] Embedding Metal inserts in the E-plane of a metal waveguide, is a reasonable technique to achieve low cost and mass producible structures such as band-pass filters.

However, in spite of their desirable characteristics, conventional E-plane filters are bulky and have undesirable stop-band performance, large cross section and big length. These filters are not suitable for many applications such as multiplexers.[4-10]

By using a periodic slow-wave structure in a partial H-plane waveguide, which is a rectangular waveguide that is transversely folded, in addition to reducing the cross section to one-quarter of conventional E-plane filters, the stop-band performance can be improved and the filter length can be reduced. As a result, the three main problems of the conventional E-plane filters will be solved [10-14].

There is no need to further tune the presented numerical design method to achieve the desirable properties, except for fractional bandwidth. The results show that the frequency response of the partial H-plane filter without the slow wave periodic structure is the same as conventional E-plane filters. However, the slow-wave partial H-plane filter has a better frequency response and less length.

II. THEORY AND DESIGN

In the past, various filters made by hollow metal waveguides were designed as microwave and millimeterwave filters. Still they were quite large at lower frequency bands and didn't have an appropriate stop-band performance [15].

In this paper, a partial H-plane filter using a periodic slow-wave structure is proposed as a new type of compact direct-coupled resonator filter using a partial H- plane waveguide. Different slow wave periodic structures have always been an interesting research subject in the microwave field since these structures can be used to achieve high performance microwave and millimeter wave devices. For example filters with superior frequency characteristics, harmonic tuning in power amplifiers and leakage suppression in stripline circuits are only a few of their applications in the microwave and millimeter wave regime.[10-15]

A partial H-plane waveguide is a rectangular waveguide which is transversely folded and for the two first dominant modes, has the same dispersion characteristic as the rectangular waveguide; however it's cross section has been reduced to one-quarter of that of conventional rectangular waveguide [16,17].

The partial H-plane filter without the periodic slowwave structure is comparable to a conventional E-plane filter; because H-plane filter metal vanes are located in the waveguide H-plane, and E-plane filter metal vanes are located in the waveguide E-plane, and both filters have inductive-coupled structures.

It will be shown that the partial H-plane filter without the slow-wave structure has the same frequency response as the conventional E-plane filter; while it's cross section is one-quarter [18]. However, the stop-band of neither of the mentioned filters is steep enough.

Consequently, a periodic slow-wave structure has been used in the partial H-plane filter, which in addition to reducing the size, gives a better frequency response.

A. Partial H-plane waveguide analysis.

The dominant and second modes of the rectangular waveguide are TE10 and TE20 respectively. These

modes do not depend on the y-direction therefore the reduction of height does not affect them. Consequently, the waveguide can be transversely folded to achieve a more compact structure. A partial H-plane waveguide has a shape of a rectangular waveguide with a metal vane insert (Fig.1). As shown in Fig.1, the waveguide cross section includes three regions.

H-plane metal vane

3

2

1

Fig.1: Schematic of partial H-plane waveguide

To find the appropriate modes of a partial H-plane waveguide, Maxwell's equations have been solved using a vector potential. It has been assumed that only TE modes will propagate in the partial H-plane waveguide since it only has one metal vane. In the simulations, the H-plane vane thickness has been considered to be very small. Afterward, the electric and magnetic field for the TE mode of regions (1) and (2) can be obtained using equations (1) and (2). The term exp(− jβz z ) has been

omitted. Regions (1) and (2) are shown with indices (1) and (2). βx and β y are wave numbers in the x and y

directions respectively, A is an arbitrary amplitude constant and β0 is the free space wave number.

Since Ey and Hx are continuous at x=d, the

characteristic equation for the TE mode can be obtained from equation (3). βx1 is obtained from equations (3)

and (4). The propagation constant and cutoff frequency, are derived from equations (5) and (6) respectively, where c is the light velocity and wave impedance is derived from equation (7). After solving equations 1-7, the proper TE modes should be represented as TEl(mn) .

TEl(mn) has uncommon mode indices. Indices l, m, and n,

represent the number of half-cycles of the sinusoidal variation of the wave in the x-direction for the whole structure, y-direction of region (1), and y-direction of region (2) respectively. Notice, that TM modes are of higher than 9th order of the TE mode. Therefore, only TE modes are investigated in this paper.

B. Analysis of Partial H-plane filter without the slow-wave structure

The structure of a partial H-plane filter using a partial H-plane waveguide is shown in Fig.2, which consists of resonators interchanged with evanescent regions. Evanescent regions are created by replacing H-plane septa in region (2) of Fig.1. Fig.3 shows an admittance inverter, the evanescent waveguide region, and the π- equivalent circuit [19].

Fig.3: Admittance inverter for evanescent waveguide

jβa and jβb are evanescent region components and a function of evanescent region length. Normalized inverter values and negative electrical lengthφ can be derived

from equations (8) and (9) respectively. Yg is the wave

admittance of the partial H-plane waveguide. Normalized admittance values for each evanescent region can be

derived from equation (10). g , g ,..., gn+1 are the low-

0 1

pass equi-ripple prototype element values and ω1′ is the normalized cutoff frequency. λg0 , λg1 , λg2 are the

center frequency and lower and upper pass-band edge guided wavelengths andωλ is the relative bandwidth

guide wavelength. The designed partial H-plane filter in the H-plane has 4.925GHz center frequency, 0.01 dB pass-band ripple, and 5% relative bandwidth. Filter design based on simulation is carried out in four steps [15,17]:

1. First a unit cell is considered to extract its S- parameters (Fig. 4). The unit cell consists of propagating regions on both sides of an H-plane Septum. The unit cell is simulated by changing the septum length w and extracting the S-parameters for the center frequency, assuming that the only propagating mode in the unit cell is the dominant TE0(01) mode.

2. For each septum length, the S-parameters have been converted to ABCD matrices (by using equation 11). A[TOTAL] is the ABCD matrix of the entire unit cell. Since the unit cell is symmetrical, we have

S11 = S22 , S12 = S21 and A=D.

3.Using equation (12), the ABCD matrix of the evanescent region has been derived. [PROPA] and [EVA] matrices, are ABCD matrices of propagation and evanescent regions respectively. Afterwards, using equation (13), the exact values of evanescent region versus the septum length has been obtained.

4.Finally, by making use of equations (8) and (10),

the calculated values for jβa and jβb can be derived as a function of septum length. the evanescent region length

3

Fig.4: Frequency response of partial H-plane filter without the slow-wave structure

The H-plane filter simulation results in H-band are shown in Fig.4. These results will be compared to the H-plane filter with slow-wave structure. The metal vane thickness is 0.1 mm. The partial H-plane filter has the same frequency response as the E-plane filter, while its cross section is one-quarter. According to the simulation

S4-1

results, this filter suffers from very small slope of transition band. Next a solution to this problem will be given and the length will also be reduced.

III. PARTIAL H-PLANE FILTER WITH SLOW WAVE

STRUCTURE

Various periodic structures have always been a favorite research subject, and nowadays they are a matter of interest again. In filter applications, periodic structures reduce the size and improve the stop-band performance. This is due to the slow-wave effect. The phase velocity and guided wavelength of the slow-wave are reduced largely relative to those of a wave propagating in a comparable homogenous line. Because of the dispersion relation of slow-waves, the stop-band performance improves [20-22].

Using periodic slow wave structures for microwave filters not only improves the frequency characteristics but also the slow-wave characteristics exhibited by the periodic structures can be used to reduce the size of microwave filters. In the proposed filter a novel periodic slow wave structure has been used to improve the stop band performance and reduce the size of the filter without introducing much complexity in the filter structure. The design procedure is also straight forward.

The slow-wave structure could be used to optimize different delay times between various transmission lines and reduce their length. A standard way to improve the stop-band of filters is to create a structure to produce slow-wave. When the number of unit cells increases, the performance of the periodic structure improves. Also, when the number of unit cells increases to some degree, its characteristics, including cutoff frequency, dispersion, and group delay, get better slightly because of the influence of parasitic parameters.

2012 IEEE Student Conference on Research and Development

In order to eliminate the disadvantages of common E-plane filters and the H-plane filter, a slow-wave structure has been used. For this purpose, using the steps mentioned in the previous section, we obtain the dimensions of the resonator and evanescent regions. Also, the proper dimensions for the periodic structure can be obtained by using finite element simulation software, high frequency structure simulator, HFSS13 [23] optimization. The filter structure is shown in Fig.5 and its frequency response is shown in Fig.6.

To show the stop-band performance improvement and the length reduction, a periodic slow-wave structure has been designed and its performance has been compared with E-plane and partial H-plane filter mentioned before. Dimensions of this filter and the periodic slow-wave parts are presented in TABLE1. By comparing the dimensions and frequency response of the two filters, it can be observed that this filter has a cross section of one-quarter of conventional E-plane filters, and the filter introduced before. Also, the partial H-plane filter with slow-wave structure has a considerably steeper stop-band compared to the conventional partial H-plane filter, as shown in Fig.7. The length is also reduced by 22% compared to the filter introduced in 2.2.

TABLE 1: Partial H-plane Filter Sizes (mm)

IV. CONCLUSIONS

In this paper, a partial H-plane filter with slow-wave structure is proposed as a new type of filters with smaller cross section and length, and improved frequency response. This filter is more compact, has lower cost, and is mass producible. The H-plane filter proposed in 2.2 has the same frequency response as the conventional E-plane filter therefore; it has a small stop-band slope. However, its cross section is one-quarter of conventional E-plane filters. While having the advantages of the H-plane filter without slow-wave structure, the partial H-plane filter with slow-wave structure improves the stop-band slope and reduces the length of the filter.

References

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