диафрагмированные волноводные фильтры / 6db37d6b-5a42-4b5a-9ec5-c4bc3938c519

BANDPASS FILTERS WITH IMPROVED STOPBAND PERFORMANCE

GEORGE GOUSSETIS

Wireless Communications Research Group, Department of Electronic Systems, Westminster

University

115 New Cavendish Street, London WIM 81S, UK

E-mail: gousseg@cmsa.wmin.ac.uk

DJURADJ BUDIMIR

Wireless Communications Research Group, Department of Electronic Systems, Westminster

University

115 New Cavendish Street, London WIM 81S, UK

E-mail: budimid@cmsa.wmin.ac.uk

Waveguide bandpass filters with improved stopband performance are investigated. The predicted filters performance show improved stopband performance and reduced filter dimensions compared with conventional E-plane bandpass filters. The validity of the method is confirmed by the measurement of a fabricated five resonator ridged waveguide bandpass filter, for which measured response shows good agreement with simulated results.

1Introduction

All-metal inserts placed in the E-plane of a rectangular waveguide along the waveguide axis offer the potential of realising low cost, mass producible and low dissipation loss millimetre-wave filters. However, despite their favourable characteristics, the attenuation in the second stopband may often be too low and too narrow for many applications, such as multiplexers, when frequency selectivity and high stopband attenuation are considered to be important ftltering properties. This is due to the following effect, which is characteristic for the common single insert design: beyond the cutoff frequency of the fundamental mode within the septum section, which is determined by the distance between the septa and the waveguide sidewalls, the power is

increasingly transported directly by propagating waves [ 1], causing degradation of the selective properties of resonators based on two septa and the waveguide between them. This paper investigates a solution for improvement in the second stopband and stopband selectivity. Improved stopband performance may be met by the ridged waveguide filter configuration [2] (Fig. 2). Improvement is achieved due to the nonlinear relation between guide-wavelength and frequency for a ridged waveguide (Fig. 1), which can be favourably influenced by a suitable reduction of the cutofffrequency of the fundamental mode within the ftlter resonators. A further increase of the thickness of the ridges and the metal inserts will improve furthermore the stopband performance [3]..

The generalised transverse resonance technique [4] can produce a rigorous description of the ftled distribution for propagation in a ridged waveguide. This result is suitable for the application of the mode-matching method in order to specify the scattering matrix of the discontinuities that involve the ridged waveguide. Implementing the procedure described by [5, 2], the K-inverter approach for the design of E-plane filters and optimisation is applied for the design of an improved stopband ridged waveguide E-plane filter.

Fig. 2: Waveguide Filter with Improved Stopband Performance

2 Theory

The transverse resonance field-matching technique lies into theoretical division of the cross section under consideration into discrete regions, where it will be easy to formulate the x- and y-dependence of the fields. The electric and magnetic fields in each region can be derived by two independent

Hertzian vector potentials [4,6], corresponding to TE and TM modes. Hertzian potentials can be expressed as Fourrier sum. Continuity of the tangential components of the fields at the boundary surface is then applied and a homogeneous set of linear equations for each type of vector potential is obtained upon use of orthogonality properties. The roots of the determinant of each system correspond to the cutoff frequencies of propagating modes for TE or TM propagation. The Fourrier coefficients of each mode can be derived upon solution of the linear system for a particular mode [4]. Power normalisation is then applied, so that the power transferred by each mode of amplitude I to be equal to

I [4, 7]. This condition will determine the free constant of the homogeneous system and is necessary in order to apply the mode matching method. Due to the x-symmetry of the structure, the analysis can be carried out assuming only half of the structure's cross-section.

The application of the transverse resonance technique for the ridged waveguide will thus return the field distribution as a sum of trigonometric functions. This rigorous analysis is convenient for the application of the mode-matching method in order to solve the ridged to rectangular waveguide discontinuity. The electric and magnetic fields, expressed in terms of Hertzian potentials, are written in the form of Fourrier series. Upon matching the tangential field components and using the orthogonality properties of the trigonometric functions, the scattering matrix for the surface discontinuity ridged-rectangular waveguide is obtained. Similarly we can derive the scattering matrix for the ridged waveguide to metal septum discontinuity (waveguide bifurcation, [7]).

Although cascaded discontinuities can be modelled by multiplying sub-groups represented by generalised transmission matrices, this procedure is potentially unstable due to exponentials with positive real arguments, which appear in the transmission matrix of a homogeneous waveguide section of finite length. Therefore the S-matrix representation is used for cascaded discontinuities [7). An accurate tool for the simulation of structures of Fig. 2 is thus obtained.

In order to design an improved stopband performance filter, the synthesis procedure described in [2, 5] is implemented. The power-voltage definition of the ridged waveguide impedance, which is used for normalisation purposes, can be derived as the integral of the electric field component along the middle of the waveguide [8, 9]. After the design of the filter, an optimisation procedure is applied in order to specify dimensions that ensure specified passband ripple level.

3 Numerical and Experimental results

In order to demonstrate the improvement at stopband performance of this filter compared to conventional E-plane filter, a five-resonator X band ridged waveguide filter with Imrn gap height and

O.lmm gap width has been designed. The insertion loss of this filter is compared with that of a conventional E-plane filter of the same passband, same ripple and same septa thickness. The dimensions are given in Table 1. 20 TEmo modes were used for the design and simulation of the conventional E-plane filter while 20 TE and 20 TM modes were used for the design and simulation of the improved stopband performance filter. The comparison between calculated insertion loss of the

matching method. Two Imm ridged waveguide filters with ridge thickness 0.1 and 0.5mm have been designed and simulated. The stopband performance of the latter is compared to a conventional E-plane filter of the same passband. A shift of the second passband of approximately I GHz towards higher frequencies is achieved. Improvement of the out of band selectivity as well as reduced physical dimensions are among the advantages of the proposed filters.

Furthermore, an 8mm ridged waveguide filter was fabricated. Measured S parameters were in good agreement with the simulated S parameters, which illustrates the accuracy of the developed tool.

Acknowledgements

The authors would like to acknowledge Engineering and Physical Sciences Research Council (GRJK58634), UK for their support.

References

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