# Compact Bandstop Filters with Extended Upper Passbands

Authors: Majeed A. S. Alkanhal
Journal: Active and Passive Electronic Components
 (2008)

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## Abstract

This paper presents new compact bandstop filters (BSFs) with extended upper passbands. In the basic proposed filter configuration, the conventional quarter-wavelength open-stub resonators are replaced with equivalent two-section stepped impedance resonators. Transmission line analysis is used to determine the dimensions of the equivalent stepped impedance sections. The filter structure is analyzed using a full wave electromagnetic (EM) simulator and then realized at 2.3 GHz band. Experiments have also been done to validate the performance of the design concept. Compared with the conventional quarter-wavelength-based bandstop filter, significant extensions of the upper passband beyond 9 GHz and 40% size reduction are achieved. Two other variations of the proposed basic BSF with further size reduction (more than 60%) are implemented and their measured performances are verified.


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## Body

## 1. Introduction

Bandstop filters (BSFs) are
key building blocks in modern RF/microwave communication systems. Such filters
play the main role of filtering out the unwanted signals and passing the
desired signals. In RF/microwave systems, active devices, such as oscillators
and mixers, are systematically followed by bandpass/bandstop filters to remove
harmonics and other spurious signals. BSFs have found many applications in
microwave/millimeter-wave systems where numerous components including diplexers
and switches are comprised of BSFs. Moreover, a BSF can be used as a
radio-frequency (RF) choke to conduct bias current and to choke off RF
transmission over its lower stopbands [1–4].Microstrip circuits, in general, and specifically filters
have the advantages of low-cost, low-weight, and ease of implementation. Conventional
microstrip BSF [2–4] is composed of shunt open-circuited resonators that are
quarter-wavelength long and with connecting lines that are also
quarter-wavelength long. Conventional bandstop filters that consist of transmission
lines or uniform distributed elements encounter a severe restriction on the
extent of the upper passband imposed by the periodicity of the distributed
elements. This causes the stopbands to repeat at odd multiples of the
fundamental stopband center frequency. Bandstop filters with quarter-wavelength
resonators give a first-upper
stopband center frequency located at three times the fundamental stopband.
Numerous efforts have been contributed to enhance and control the size, the
rejection bandwidth, and the passbands of the microstrip bandstop filters
[4–7]. In [8], a modern synthesis technique is employed to design an extended
upper passband multi-compound resonator commensurate-line microwave bandstop
filter with possible lumped elements. The
upper stopband center frequency has been extended to six times the fundamental
stopband center frequency by a new design procedure that uses coupled line
configuration with the open stubs replaced by loading capacitors. More
recently, this ratio has been improved to 18 times the main stopband with
realizable element values [9]. In the basic design of [9], resonators made up
from commensurate open circuit (OC) and short circuit (SC) stubs coupled by
inverters are used. The inverters are, then, converted into proper number of
unit elements (UE) which increase the degree of the filter and contributes to
the filter response considerably upon optimization. L-type inductively loaded
and capacitively loaded parallel coupled line (PCL) resonators are proposed as
possible configurations of the new banstop filter design as well. Optimization is
executed to attain the targeted responses of the high-degree filters. The total
number of UEs affects the filter total length as well as the required values of
the impedances of the PCL resonators. The main limitation for realization of
such filter circuits seems to be coming from the implementation of lumped
capacitors which should operate up to the targeted upper-edge frequency.The transmission zeroes formed by the distributed resonators
in the BSF basic circuit shape the stopband response of the filter [1, 2, 9, 10]. Based
on that, new shaped structures of compact bandstop filter sections are
presented in this paper. The proposed designs remove the repeated odd-multiple
resonance limitation using nonuniform stepped impedance resonators that have
shorter electrical lengths. These simple filter-configurations that incorporate
no lumped elements have more degrees of freedom for the dimensions of the stepped
resonators and accomplish wider upper passbands. These structures feature
compact size BSFs and avoid using shorted stubs or via holes as well. The
desired operation is accomplished by using stepped impedance shaped sections [11, 12].
Each branch with quarter-wave length (λ/4)
is converted to its equivalent two-section stepped impedance shaped section.
The resulted basic filter configuration will have a significant more than 40%
area-size reduction. The proposed filter structures have their classical
stopbands besides wide extended passband regions. To facilitate the design of
the proposed basic filter, closed forms are depicted utilizing transmission
line analysis of the stepped impedance sections. The final layout of the basic filter
structure is designed based on these formulas, and then analyzed using a full
wave electromagnetic (EM) simulator. To verify the design concept, a microstrip
bandstop filter element exhibiting extended upper passband operation is
realized on FR4 substrate (εr=4.6, thickness (h)=1.4986mm) at
2.3 GHz band. The measured results are in a very good agreement with the
theoretical results for the rejection and passband operations of the proposed
structure. Two other variants of the proposed basic stepped impedance BSF that
achieve more than 60% surface size-reduction are simulated and implemented and
their measurements ensure their good performances as compared to the covenantal
BSF. These filter structures can be used as a stand alone simple bandstop
filter or as a section in a higher order multisection filter.


## 2. Analysis

The conventional microstrip-based bandstop filter can be
derived from the lowpass filter (LPF) prototype. The design starts with
n-section low pass filter in the form of shunt capacitors and admittance inverters
[1, 9, 10] as shown in Figure 1. A suitable frequency transformation [1, 10]
converts the shunt capacitors of the LPF prototype circuit to a series
resonance circuit at the fundamental frequency that could be implemented by
open circuit microstrip stubs as shown in Figure 2. All stubs and transmission
line inverters connecting the stubs are with the commensurate length of (λ/4) at the center frequency (f0) of the bandstop filter.Figure 1
LPF prototype based on shunt capacitors and admittance inverters.Figure 2
Conventional commensurate microstrip BSF derived from the LPF prototype.LP prototype to distributed element BSF mapping resulting in
circuit made up of OC and SC stubs and ideal inverters could be, effectively, employed
as described in [9]. This transformation converts the shunt capacitors into
shunt arm series OC and SC stubs. The series combinations of SC and OC stubs
form distributed resonators of finite transmission zero (FTZs) which shape the
stopband of the filter. The resonators (FTZs) can also be formed by parallel
combination of SC and OC stubs in series arms [9]. The use of quarter wavelength open-stub resonators causes the stopband behavior to
be repeated at odd multiples of the center frequency of the fundamental response. In particular, the nearest
spurious stopband is located at three times the fundamental stopband.Figure3 depicts one section of the conventional
distributed microstrip BSF [2–4]. In the present work, each quarter wave length (λ/4) open-stub section of the conventional BSF of is converted to a  stepped-impedance shaped transmission line section. The
stepped (shaped) transmission line model shown in Figure 2 is consisted of two connected series transmission line sections. The equivalence
between the uniform quarter-wavelength long open-stub section and the nonuniform stepped impedance section is
investigated using transmission line theory.Figure 3
Conventional one-section BSF with two resonators structure.Figure 4
Equivalence of stepped impedance and open circuit quarter-wave sections.Letθ1 and θ2 denote the effective electrical lengths of the
lines with Z1 and Z2 characteristic impedances, respectively.
Investigating the input impedance of the stepped impedance section at
resonance, the following equation can be derived [8, 11]: (1)K=Z2Z1=tanθ1tanθ2, where K equals to Z2/Z1.
Design curves are drawn in Figure 3 for different values of K. The total
electrical length of the resonator is given by (2)θt=θ1+θ2. It is noted that for K=1 (uniform
resonator), the total electrical length is 90° and the total length
of the nonuniform resonator decreases as the impedance ratio K decreases.
A quarter-wavelength uniform resonator will resonate at its fundamental frequency
and repeats at odd
multiples of the fundamental frequency whereas the nonuniform stepped impedance
resonator will effectively remove this resonance (odd multiples) repetition.For practical realization of microstrip lines, the
characteristic impedances should be bounded in the region(25Ω≤Z≤150Ω).
Consequently, the corresponding practical impedance ratio must be in the range (0.17≤K≤4).Utilizing (1), the first spurious frequency (fs1) of the stepped impedance resonator can be deduced since
the equality will be repeated
at each spurious frequency. The ratio of the first spurious response to the
center frequency (fs1/f0) depends on the
values of the impedance ratio K as well as the stepped-sections
electrical lengths. Figure 6 illustrates the control of the first spurious
frequency by the impedance ratio K for varying θ1 value while Figure 7 compares the frequency responses of the conventional and
the modified (stepped resonator based, K=0.25 and θ1= 25°) BSFs. It is manifested from these
figures that the smaller the impedance ratio K, the wider is the upper passband
region for compact BSFs. As inferred from these figures, reentrant responses in
a realizable single-section stepped impedance resonator can be delayed up to
eight times the center frequency.Investigating Figure5 for the relation of θ1 and θ2 for different values of K, the symmetry of θ1 and θ2 values around the line θ1=θ2 can be noticed. This permits the advantage of interchanging θ1 and θ2 values without changing the impedances Z1 and Z2, that is, keeping K unchanged. This advantage
gives another degree of freedom in selecting the proper line lengths according
to the geometry constrains. In the next section, design and implementations of the
stepped impedance BSF in different configurations utilizing the above analysis along
with numerical optimization to compensate for edge and proximity effects are
carried out. For compact design, the following parameters are chosen, Z1=120Ω,Z2=30Ω and hence K=0.25.Figure 5
θ1 versus θ2 for different values of K.Figure 6
Variation of the first spurious frequency
with the impedance ratioK.Figure 7
The first spurious frequency of conventional and modified BSFs.


## 3. Design, Simulation, and Experimental Results

A compact BSF is designed for the 2.3 GHz band. Based on the
previously outlined design procedures withZ0=50Ω, the filter parameters will be Z1=120Ω,Z2=30Ω,
θ1= 18°, and θ2= 36°. The designed BSF is simulated using a full wave EM
software package and then realized on FR4 substrate (εr=4.6,h=1.4986mm). Figure 8 shows the layout of the designed BSF.
Further optimization to yield the desired performance has been carried out. The
wider lower impedance transmission line sections are brought inside the filter inner space
to save space, and then further optimization for the dimensions of all filter
sections are carried out numerically. The inverter section impedance is tuned
to improve the return loss of the upper passband. The fabricated bandstop
filter resulted in a more than 40% size reduction as compared to the
conventional all-quarter-wave length-based filter.Figure 8
The proposed bandstop filter with stepped resonator structure.The measurement results of the realized BSF filter are
compared with the simulation results in Figure9.
From Figure 9, it is evident that the measurement results are in a very good
agreement with the simulated results. In the rejection band, the measured
coupling S21 maintains a very low value around −46 dB
with the reflection coefficient S11 in its maximum value
around 1 dB. In
the passband, the coupling S21 is within (−2 dB) over a wide
extended passband up to 9 GHz. Actually, the slight loss-increase at the higher
frequencies is obviously attributed to the lesser quality FR4 substrate at
frequencies higher than 2 GHz. The simulation results show almost a perfect
insertion loss over the entire extended upper passband. The reflection
coefficient S11 maintains a value less than −13 dB in the extended
passband. The proposed compact BSF does not have the repeated stopbands at odd
multiples of the operating frequency and, hence, demonstrates a well-extended passband
region up to 9 GHz with enhanced performance in terms of the insertion
loss and the return loss values.Figure 9
Simulation and measurement results of the proposed stepped impedance bandstop filter.The second BSF configuration is similar to the first one but
with the series 90° line shaped and bended and with the section
lengths θ1 and θ2 interchanged to have a better space utilization efficiency. More
optimization is applied to compensate for edge discontinuity and proximity coupling
effects of the structure. This configuration shown in Figure 10 is implemented
on Duroid substrate (εr=2.33, substrate thickness (h)=0.508mm, loss tangent (tanδ)=0.004). Figure 11 demonstrates the good performance of this
shaped configuration as presented by the simulation and measurement S-parameters of the BSF structure. S11 and S21 maintain
quite good values in the stopband and in the passband.Figure 10
The shaped stepped impedance bandstop filter with dimensions in mm.Figure 11
Simulation and measurement results of the shaped stepped impedance bandstop filter.The third configuration investigated and implemented at 2 GHz
is that of Figure12. This configuration has a straight (unshaped) series line
but with a shorter length. The length of the series branch is kept around 52° in this structure to get more than 30% additional surface reduction on the BSF
design. The effect of this shorter series line in the BSF performance is inconsequential. The slower (smoother and wider) fall of the S21 after the
transmission zero is the only noticeable effect of this modification as shown in Figure 13. This effect is compensated by the perfect transmission behavior
represented by the S21 values in the passband region of the BSF.Figure 12
The shortened stepped impedance bandstop filter with dimensions in mm.Figure 13
Simulation and measurement results of the shortened stepped impedance bandstop filter.The three presented structures can be classified as medium
stop-bandwidth filters in their basic section-forms. A better performance in
terms of deeper rejection and a wider rejection bandwidth can be achieved by
cascading more identical stepped impedance sections in the filter structure but
at the expense of increasing circuit size and complexity. Numerical optimization
incorporating the stubs as well as the unit-elements in multisection filters is
successfully used to obtain the required design insertion loss and rejection
bandwidth [8–10].


## 4. Conclusions

This paper presents analysis and design of new compact
bandstop filters with wide extended upper passband regions. The basic design configuration
uses stepped impedance section transformation of the quarter wavelength
open-stub resonator sections of the filter with no short circuit stubs, lumped
elements, or via holes. Practical and simple design procedures are depicted.
The design of a basic compact bandstop filter with extended upper passband is examined
using a full wave EM software simulator and then realized on FR4 substrate. The
measurements of the realized basic filter structure are in a very good
agreement with the simulated results and demonstrate the quality of the
presented design. Two other variations of this basic stepped impedance BSF
design that accomplish more than 60% size-reduction are implemented and
measured as well. Simulation and measurements of these reduced size BSFs prove
their good performance as compared to the covenantal BSF. The proposed designs
can serve as standalone simple BSFs or as filter sections that can be cascaded
in multisection optimized bandstop filter configurations.



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*Source: 356049-2008-07-17.xml*