# The Novel Microwave Stop-Band Filter

Authors: R. E. Chernobrovkin; I. V. Ivanchenko; A. M. Korolev; N. A. Popenko; K. Yu. Sirenko
Journal: Active and Passive Electronic Components
 (2008)

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## Abstract

The stop-band filter with the new band-rejection element is proposed. The element is a coaxial waveguide with the slot in the centre conductor. In the frame of this research, the numerical and experimental investigations of the amplitude-frequency characteristics of the filter are carried out. It is noted that according to the slot parameters the two typical resonances (half-wave and quarter-wave) can be excited. The rejection band of the single element is defined by the width, depth, and dielectric filling of the slot. Fifth-order Chebyshev filter utilizing the aforementioned element is also synthesized, manufactured, and tested. The measured and simulated results are in good agreement. The experimental filter prototype exhibits the rejection band 0.86 GHz at the level −40 dB.


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## Body

## 1. Introduction

Review of the microwave
filters technology, applications perspective, as well as filter designs is described in [1]. The narrow-band tunable filters are usually realized by using
the rectangular waveguide with the dielectric resonator [2] or microstrip
resonators [3]. In order to provide the wideband filter, the resonators with
low Q-factor such as the ring resonator with direct-connected orthogonal feed
lines [4] or coplanar stripline resonators [5] are applied.The slot resonator as a basic
element of the microwave filter has been proposed earlier in the paper [6]. The
main advantages of this resonator are the small sizes, the simplicity of
manufacturing, as well as a possibility of its natural integration into the coaxial
line. In this paper, the slot resonators on the TEM waves are used in designing the stop-X-band filter.The paper is organized as
follows. In Section2, the different designs of the band-rejection element as
well as the EM field distributions in the slot are considered. Furthermore, the
behavior of the resonance frequency and the loaded Q-factor is studied
depending on the slot dimensions. The results of experimental investigations of
the rejection filter with a single slot are discussed in Section 3 and point to
the capability of developing the more complicated filter designs. Section 4 is
devoted to the synthesis and experimental investigations of the Chebyshev rejection
filter prototype.


## 2. Band-Rejection Element

Schematic view of the novel
band-rejection element is presented in Figure1. The band-rejection element is the
axial-symmetrical
structure which consists of the coaxial waveguide with the centre conductor radius a, and outer conductor b, respectively. The coaxial waveguide is filled by the dielectric with permittivity
ε1. The slot in the centre conductor has the width w and the depth d (Figure 1) and it is filled by the dielectric with permittivity ε2.
Two different filter designs can be realized by means of both the complete slot d=a (Figure 1(1)) and the partial slot d<a (Figure 1(2)).Figure 1
The problem geometry: (1)a=d; (2) a>d.In order to excite the
resonance with the componentHρ=0 in this structure, the condition  w≪d has to be realized [6]. In this case, the magnetic field
distribution is the axial-symmetrical one. It
should be noted that the two types of resonance can be excited in this
structure depending on the relation between the slot depth d and the centre conductor radius a (Figure 1). The maximal magnitude is located in the slot centre for d=a (Figure 2(a)); whereas for d<a, the maximal magnitude is located on
the centre conductor surface (Figure 2(b)). Based on the amplitude distributions
of the magnetic field noted above, the authors of [6] called “half-wave
resonance” when  d=a (Figure 2(a)) and “quarter-wave resonance” when d<a (Figure 2(b)).The magnetic field distribution in the slot: (a)d=a; (b) d<a.
(a)(b)From the beginning, let us analyze the influence of the depth (d), width
(w), and permittivity (ε2)
on the single-slot
performance. For the quarter-wave resonance (d<a), the slot-depth increase
leads to moving the resonance frequency from f0=9 GHz to f0=11 GHz
(Figures 3(a)  and 3(b), Table 1). In this case, the slot-width variation from 0.5 mm to 1.5 mm results
in the Q-factor changing about 72% whereas the resonant frequency is slightly
changed (Figures 3(b) and 3(c), Table 1).Table 1
Geometrical and physical parameters of the band-rejection element.
w=0.5 mm d=6.0 mm
ε2=1w=0.5 mm
d=5.0 mm  ε2=1w=1.5 mm d=5.0 mm
ε2=1w=0.5 mm
d=9.0 mm   ε2=3.78w=1.5 mm d=9.0 mm
ε2=3.78f0 GHz91110.710.310.27Q-factor171759137Quarter-wave resonanceHalf-wave resonanceAmplitude-frequency characteristics of the band-rejection element in
the case of the quarter-wave resonance.
(a)(b)(c)We note that for the half-wave
resonance (a=d), the slot width variation points to the similar results (Figures
4(a) and 4(b)). It is quite clear that the dielectric filling of the slot leads to
changing the resonant frequency of the single element. So, the dielectric filling
of the slot allows reducing the radius of the centre conductor of the given
coaxial waveguide. In this case, there is a possibility to provide the efficient
rejection-band control of the aforementioned filter.Amplitude-frequency characteristics of the band-rejection element in
the case of the half-wave resonance.
(a)(b)With these remarks in mind,
one may summarize that the resonance frequency is defined by the slot depth and
the dielectric permittivity ε2. At the same time, the Q-factor
depends on the slot width and dissipations in the dielectric and the metal. For
the illustration of these statements, the dependences of numbered above parameters
on the slot dimensions are shown for both the half-wave (d=a) and quarter-wave (d<a) (Figures 5 and 6) resonances. In both cases, the radius of centre and outer
conductors are constant. We have chosen the permittivity ε2=1
for the slot when d<a and ε2=3.78,
tanδ = 0.0001 for the slot when d=a. The
choice of such values of dielectric permittivity ε2 allows us to
remain in the same frequency band. For both slots, the resonance frequency has
the linear dependence on the slot depth (Figure 5). Q-factor reduction is
explained by increasing the radiation losses with the slot-width increase (Figure 6). The highest value of Q-factor can be achieved by using the slot-width
parameter d=a.Figure 5
The dependence of the resonance frequency on the slot depth: (1)a=9 mm, b=15 mm, w=0.5 mm,   ε1=ε2=1;
(2) a=d, b=15 mm, w=0.5 mm, ε1=1,    ε2=3.78.Figure 6
The dependence of the loaded Q-factor on the slot width: (1)a=9 mm, b=15 mm, d=5.5 mm,  ε1=ε2=1;  (2) a=d=9 mm, b=15 mm,   ε1=1,   ε2=3.78.


## 3. Experimental Verification

Experimental investigations of
characteristics of the single-slot filter prototypes were carried out on the
Agilent network analyzer PNA-L N5230A in the frequency band 8–14 GHz. The manufactured
filter prototype is shown in Figure7. The filter parameters are as follows: d=a=9 mm, b=15 mm, ε1=1, and ε2=3.78.
A fair agreement between the measured and simulated S12-parameters
for the single slot with different widths (w=1 mm
and w=2 mm) is observed (Figure 8). The
dissimilarity at the resonance frequency is less than 0.05 GHz and can be
explained by the manufacturing inaccuracy of the filter as well as by the difference
between the real dielectric permittivity in the experiment and that used in the
simulations.Figure 7
General view of the filter prototype with the single slot.S12-parameter of the filter prototype with the single slot: (a) w=1 mm; (b) w=2 mm.
(a)(b)


## 4. Synthesis of the Chebyshev Filter

The stop-band filter with initial parameters
mentioned in Table2 will be synthesized below. The slots filled with the air
(ε2=1) in the case of quarter-wave resonance were chosen as a basic
element of this filter. Equivalent circuit of the filter is shown in Figure 9
(top). Based on the simulated results, the values of all  elements of the
equivalent circuit as well as the resonant frequency and Q-factor of each
resonator were determined. The initial values of the geometric parameters of slots
(w and d) were chosen from Figures 5 and 6. The desirable impedances were
provided by the changing of centre conductor radius a. Further filter optimization was carried out by means of the
full wave simulator developed by us earlier [6]. In this case, the resonators
are located at the distance 3λ/4 (λ = 30 mm) from each other to provide the
minimal coupling between resonators (Figure 9, bottom).  As the goal function, the S-parameters were
chosen, and the slot width w and the slot
depth d were varied within the limits
±5%.Table 2
The parameters of the Chebyshev
filter.
The number of resonatorsRipple [dB]f1 [GHz]f2 [GHz]f0 [GHz]f2−f1 [GHz]Source and load [OH]50.19.510.510150Figure 9
Low-pass block diagram and
the general view of the Chebyshev filter prototype.The optimized filter with parameters
highlighted in Table3 was designed, manufactured, and investigated. The
S-parameters of the filter prototype noted above are shown in Figure 10. Based
on the analysis of these data, we can formulate some conclusions, namely, (i)
the measured S-parameters are in good agreement with the simulated ones at the
most frequency points over the entire pass-band and stop-band; (ii) the
rejection band is 0.86 GHz at the leve −40 dB.Table 3
The geometrical parameters of the filter.
The number of resonators12345w0.29 mm1.0 mm1.25 mm1.0 mm0.29 mmd5.6 mm5.6 mm5.6 mm5.6 mm5.6 mma9 mm10.7 mm11.72 mm10.7 mm9 mmFigure 10
The measured
and simulated S-parameters of the Chebyshev filter prototype.


## 5. Conclusions

The original band-rejection
element as the slot in the centre conductor of the coaxial waveguide for designing
the microwave stop-band filters is presented. The half-wave and quarter-wave
resonances which are excited in this element have been studied and analyzed. The
band-rejection element has been designed and manufactured. It has been found
that for both cases the slot-width increase fromw/a=0.056 to w/a=0.23
leads to decreasing the loaded Q-factor on 22%. The  resonance frequency depends
on the slot depth. The good coincidence of calculated and measured data is
observed. Fifth-order Chebyshev filter with the given band-rejection element has
been also synthesized, manufactured, and investigated. The measured S-parameters
are in good agreement with the numerical ones at the most frequency points over
the entire pass-band and stop-band. Notice that the filter characteristics are close to the simulated
ones without any trimming elements. The rejection band is 0.86 GHz at the level
−40 dB. The proposed stop-band filter can be naturally
integrated into the coaxial waveguides and seems to be very attractive in
different applications.



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*Source: 745368-2008-06-17.xml*