Asymmetric Shunt Inductance Iris Rectangular Waveguide Filters for Satellite Communication Systems

. This paper presents the design, simulation and manufacture of two Asymmetrical filters based respectively on standard rectangular waveguides WR90 and WR75 in which resonant irises are inserted, operating respectively in the X-Band [9-11GHz] and Ku-Band [11-13GHz].The filter parameters were simulated by the MMM modal matching method (MMM) implemented in the Microwave-Wizard software, and that obtained by the CST-MWS software. The simulated results are in good agreement with those obtained by the experimental measurements.


Introduction
The microwave frequency domain is widely used by telecommunications networks.Optimal use of the frequency spectrum requires very high channel selectivity, which has enabled an increasing number of users of the frequency spectrum.Filters are essential devices that are key elements in determining the performance of telecommunications systems; they represent a major and very important part in the field of modern fixed or mobile communications, land or space.This has created both very demanding performance specifications for filters and commercial pressures to reduce costs.In the design of microwave or millimeter wave components, discontinuities play a particularly important role.These discontinuities are used to perform various types of functions: filtering, phase shifting, power matching, etc.In the case of our evanescent mode filters, the discontinuities are created by obstacles made up of symmetrical or asymmetrical rectangular irises.Many methods have been used to model the uniaxial discontinuities in cascade [1] - [7], the dispersion matrix of the set will be obtained by carrying out the scattering of the individual discontinuities, assimilated to multipoles and separated from each other by waveguide sections of lengths equal to the distances between the discontinuities.We present the procedure for designing and producing iris filters.The modeling of the various discontinuities is analyzed by the modal Matching method (MMM).The scattering of the set will be obtained by chaining the generalized scattering (GSMs) of the individual discontinuities [8], [9] - [15].We propose in this paper, two band-pass filters in waveguide technology having rectangular symmetrical discontinuities, designed and tested respectively in the band [9][10][11] GHz and the band [11][12][13] GHz.These filters consist of 8 irises placed asymmetrically respectively in a standard WR90 and WR 75 waveguide.These irises are used to very strongly couple the sections in this filter, which allows to increase the bandwidth and to control the matching.

Design of Asymmetrical Iris Filter
Rectangular waveguide microwave bandpass filters composed of coupling irises are used extensively in telecommunications systems today.Their main quality is to withstand very high powers by creating low insertion losses.The conventional procedure for producing this type of filter is based on the fundamental TE mode which resonates n times in the structure (n resonant cavities coupled by irises).The Ki+1 element simulate the coupling irises.These inverters cannot be produced using passive elements alone.Their implementation requires the use of elements with distributed constants of negative electrical length, which are absorbed by the adjacent resonant cavities.The coupling irises have purely inductive impedance.The equivalent electrical circuit must be equivalent to an impedance inverter [16].Taking into account the normalized susceptance B � = 0, the ABCD matrix is the product of the ABCD matrix of these three elements [18].
By comparing the equality of the two terms of the above equation, the equality is checked if: The expression for Φ shows that the electrical lengths introduced by the irises are negative and therefore absorbed by the lengths of the adjacent cavities.The negative phase shift introduced by the irises Φi-1/2 and Φi + 1/2 is compensated by the electrical length θi; of the ith cavity of the filter.This is illustrated in the following figure [16]: The electrical lengths θi are adjusted so that the electrical length between two consecutive inverters is equal to: This corresponds to: The physical length of the cavities depends on the electrical length and the wavelength in the guide.
θ � π In other words : When designing waveguide filters with discontinuities, one will need to use many analytical models modeling these discontinuities.For the sizing of these discontinuities, approximation equations valid for zero iris width have been given in this article to determine the dimensions of asymmetric irises.The passage from the localized bandpass filter to the volume filter and the analytical iris models will be used during the synthesis of the inductive iris bandpass filters.The negative component introduced by the irises is negligible compared to the length of the resonant cavity.
For the current design, E plane Asymmetrical iris structure is preferred as shunt inductors which is also known as H plane waveguide filter [17].This structure is named as shunt inductance asymmetrical iris and the most accurate one in terms of bandwidth, return loss and center frequency responses and also it is easy to implement [18].Thus, it is mostly chosen in waveguide filter applications.
li is the distance between two consecutive irises waveguide cavity, can be found using the formula given in Eq. ( *  [18].
The topology of the asymmetric inductive iris bandpass filter is shown in figure 4. The inductive irises appear as non-symmetrical openings at the ends of the guide cavities after each half wavelength λ / 2.

Simulation and Experimental Results
In the two prototypes we tested, we used 8 iris discontinuities separated by quarter-wavelength cavities.
Figure 5 shows a mechanical prototype of one of the two symmetrical filters.The two filters that we have analyzed are asymmetrical and consist respectively of rectangular waveguides WR90 and WR75 in which resonant irises are inserted.Figure 6 and figure 7 show the comparison between theoretical and experimental results.
From the previous figures comparing the theoretical and experimental results of the parameters of the diffraction matrix S11 and S21, it can be seen very clearly, on these curves, that the measurements give results almost similar to the theoretical results over the entire frequency range of interest; the slight increase in the reflection coefficient in the passband is due to the problem of miniaturization during the mechanical manufacture of filters.In the modal adaptation method that we used to characterize the four filters, we used a number of modes N between 30 and 60.As we can observe in both cases, we obtained a good agreement between the theoretical and experimental results.
We notice that the results obtained using the two tools simulation is in agreement with those resulting from the experimental results.We note a good consistency between the results.This also demonstrates the ability of Mician and CST to design this type of filter.The bandwidth of this filter is on the order of 1 GHz and its center frequency is close to 9.9 and 12.18 GHz respectively.We notice a good matching characterized by a reflection coefficient around (-30 dB), and insertion loss around (-0.05 dB) in the band of interest.IL: Insertion loss over the whole pass-band.RL: Return loss over the whole pass-band.Fc: The central frequency.
To further demonstrate the performance of these filters, table 1 is provided for comparison of this work with other works which are all based on wide band pass filter category.A comparison of the main performances of waveguide filters is listed.

Conclusion
In summary, we have presented two asymmetrical filters based respectively on standard rectangular waveguides WR90 and WR75 in which resonant irises are inserted, operating respectively in the X-Band  and Ku-Band .The simulated results are in good agreement with those obtained by the experimental tests.The bandwidth of this filter is on the order of 1 GHz and its center frequency is close to 12.18 and 9.9 GHz respectively.We notice a good ports matching characterized by a reflection coefficient around (-30 dB) in two bands.

Fig 1 .
Fig 1. Electrical diagram equivalent to the impedance inverterAn iris is equivalent to a pure reactance and two sections of line of characteristic impedance Z0 and of total electrical length Φ.

Fig 2 .
Fig 2. Resonant cavity surrounded by irises at its ends Resonant cavities are half-wave lines; their electrical length is equal to: . (*) are the electrical lengths of transmission line sections with negative lengths at two sides of shunt inductances shown in Figure2.The total electrical lengths between two consecutive irises are π shunt inductor asymmetrical iris structure is given in Figure3.In the case of an asymmetric inductive iris, a single metal plate is inserted on one side of the waveguide.The equivalent electrical diagram and the geometry of this obstacle which produces an inductive effect are shown in figure3.

Fig 3 .
Fig 3. Asymmetric inductive iris The relation between the normalized susceptance B � and the distance d shown in the figure above is given by [16]:

Fig 4 :
Fig 4: Geometric structure of the asymmetric inductive iris filter

Fig 5 :
Fig 5: Prototype of a symmetrical filter formed by 8 symmetrical iris discontinuities.

Fig 6 :
Fig 6: Comparison of theoretical reflection coefficients and those obtained by measurements, X band (WR90).

Fig 7 :
Fig 7: Comparison of theoretical reflection coefficients and those obtained by measurements, Ku band (WR75).