Compact input-reflectionless balanced bandpass filter with flexible bandwidth using three-line coupled structure＊

Yahui ZHU ,Jing CAI ,Wei QIN ,Wenwen YANG ,Jianxin CHEN??

1School of Information Science and Technology,Nantong University,Nantong 226019,China

2Research Center for Intelligent Information Technology,Nantong University,Nantong 226019,China

Abstract: A compact input-reflectionless balanced bandpass filter (BPF) with flexible bandwidth (BW) using a three-line coupled structure (TLCS) is presented in this paper.For the differential mode (DM),the TLCS is applied to achieve the bandpass response;meanwhile,the input coupled-feed line of the TLCS is reused in the input absorption network.This design shows a good fusion of the absorptive and BPF sections,effectively reducing the circuit size,and the BWs of the two sections that can be controlled separately result in a flexibly controllable DM response BW of the proposed input-reflectionless balanced BPF.Detailed analyses of the ratio of the two-part BWs have been given for the first time,which is vital for the passband flatness and reflectionless feature.In the codesign of this work,the input-reflectionless DM bandpass response can be optimized easily,while wideband common mode (CM) noise absorption is achieved by the input absorption network.To verify the design method,a prototype with a compact layout (0.52λ×0.36λ) is designed and measured in the 0-7.0 GHz range.The DM center frequency(f0) is 2.45 GHz with a measured 3 dB fractional bandwidth of 31.4%.The simulation and measurement results with good agreement are presented,showing good performance,e.g.,low insertion loss (0.43 dB),wide upper stopband for the DM bandpass response (over 20 dB rejection level up to 2.72f0),and wideband DM reflectionless and CM noise absorption (fractional absorption bandwidth of 285.7%).

Key words: Input-reflectionless filter;Balanced bandpass filter (BPF);Differential mode (DM);Common mode (CM);Three-line coupled structure (TLCS)

1 Introduction

Balanced devices have attracted immense attention due to the urgent requirement of immunity to environmental noise,electromagnetic interference,and crosstalk (Zhou and Chen,2017).On this basis,with the development of chip technology,many balanced circuits have been conceived,such as couplers (Feng et al.,2019;Li HY et al.,2019;Zhang ZQ et al.,2021),power dividers (Shi et al.,2016;Xu et al.,2019;Yu et al.,2022),diplexers (Li YC et al.,2020;Song et al.,2020),and antennas (Cao et al.,2020;Kou et al.,2022;Wang et al.,2022).As an important frequency selection component in radio frequency(RF)/microwave circuits and systems,the balanced implementation of the bandpass filter (BPF) is also very important (Chen JX et al.,2016;Bi et al.,2020;Feng et al.,2021;Wu DS et al.,2022).For these works,desirable common mode (CM) rejection,sharp differential mode (DM) roll-off skirt,and compact layout are competitive indicators,and they have been widely considered.However,the stability of the operating system would inevitably be deteriorated by the unwanted DM signals and CM noise returning to the source.This issue has attracted ever-increasing attention.

Although the traditional adoption of isolators or attenuators alleviates the interference due to undesired reflected signals,it also leads to an inevitable increase in size and insertion loss (IL) (Lee B et al.,2022).Accordingly,the reflectionless technique has been explored recently;it can dissipate the reflected interference energy inside instead of returning it to the source (Morgan and Boyd,2015;Han et al.,2022).Consequently,a large number of single-ended reflectionless filters have been reported (Morgan and Boyd,2015;Gómez-García et al.,2019;Guilabert et al.,2019;Morgan et al.,2019;Wu XH et al.,2020;Fan et al.,2021a,2021b;Lee J et al.,2021;Xu et al.,2022;Zhu YH et al.,2022).Based on this,balanced BPFs with different types have been developed in recent years (Zhang WW et al.,2017;Gómez-García et al.,2018;Lin et al.,2019;Lin and Wu,2020;Yang et al.,2020;Zhu Y et al.,2020;Chen X et al.,2021;Zhang YF et al.,2022) because balanced topology has become popular in modern circuits and systems (Chen JX et al.,2016;Shi et al.,2016;Zhou and Chen,2017;Feng et al.,2019,2021;Li HY et al.,2019;Xu et al.,2019;Bi et al.,2020;Cao et al.,2020;Li YC et al.,2020;Song et al.,2020;Zhang ZQ et al.,2021;Kou et al.,2022;Wang et al.,2022;Wu DS et al.,2022;Yu et al.,2022).

As a common method in the implementation of single-ended reflectionless behavior,the topology of complementary diplexer based behavior (Gómez-García et al.,2019;Wu XH et al.,2020;Fan et al.,2021a,2021b;Xu et al.,2022;Zhu YH et al.,2022)is used in balanced planar BPFs with symmetrical DM quasi-reflectionless characteristics (Gómez-García,et al.,2018).The multilayered vertical transition structure is adopted (Yang et al.,2020) to realize the wideband input-reflectionless response of the DM BPF,and its out-of-band DM signals are dissipated by resistively terminated microstrip branches.In addition,for CM absorption,symmetrically loaded resistors are used (Zhang WW et al.,2017;Lin et al.,2019;Lin and Wu,2020;Zhu Y et al.,2020).The developed balanced BPFs with the characteristic of wideband CM noise absorption are introduced (Lin and Wu,2020;Zhu Y et al.,2020).Although some efforts have been made to absorb DM signals or CM noise,the absorption of unwanted DM and CM signals is rarely considered at the same time.Recently,balanced BPFs(Chen X et al.,2021;Zhang YF et al.,2022) with both DM reflectionless and CM absorption have been reported.However,the large size is a problematic issue.For example,multiple absorption networks in parallel with multiple bandpass sections shown in Fig.1a result in a large size,although the filtering performance is improved (Chen X et al.,2021).However,the limitation of the DM absorptive bandwidth (BW)still exists because of the mismatch in the out-of-band operating ranges.Obviously,it is still a challenge to achieve a balanced BPF that can absorb both DM reflected signals and CM noise with large absorption BW and miniaturized size simultaneously.

To solve the above-mentioned problems,we present an input-reflectionless balanced BPF using the synthesis method.It has the advantages of compact layout and high performance by taking the absorptive section (ABSS) and the BPF section into account simultaneously in a codesign procedure,as shown in Fig.1b.The shared transmission line (STL) acts not only as a key part of the ABSS but also as a coupledfeed line (CFL) of the BPF section based on the threeline coupled structure (TLCS).The relationship between the passband BW of the input-reflectionless balanced BPF and the BWs of the ABSS and BPF section is discussed.This has not been mentioned in detail before,in either diplexer-based single-end or balanced design(Zhang WW et al.,2017;Gómez-García et al.,2018,2019;Lin et al.,2019;Lin and Wu,2020;Wu XH et al.,2020;Yang et al.,2020;Zhu Y et al.,2020;Chen X et al.,2021;Fan et al.,2021a,2021b;Xu et al.,2022;Zhang YF et al.,2022;Zhu YH et al.,2022).Meanwhile,the BW design procedure of the proposed input-reflectionless balanced BPF is given.In addition,the ratio of the two-part BWs and its vital effect on the reflectionless performance and DM passband flatness are analyzed in detail,which has important implications for the diplexer-based reflectionless BPF designs.Accordingly,the seamless integration of ABSS and TLCS-based BPF section provides a compact layout while maintaining good DM filtering performance (such as low IL and a wide upper stopband) and wideband reflectionless for both DM and CM.

Fig.1 Conceptual operation mechanism of the inputreflectionless bandpass filter: (a) traditional cascaded system;(b) fusion design method

2 Theoretical analysis and design

The schematic layout of the proposed inputreflectionless balanced BPF is shown in Fig.2.The whole circuit is symmetrical with respect to planeAA′.It consists of a pair of symmetrical TLCS-based BPFs and absorption networks,in which a pair of STLs are reused,with the electrical lengths of all coupled lines and transmission lines being equal to π/2 (quarter waveguide wavelength:λ/4),i.e.,θa=θb=θc=θd=π/2 at the center frequency (f0=2.45 GHz).Figs.3a and 3b show the DM and CM bisected equivalent circuits of the proposed input-reflectionless balanced BPF,respectively.Detailed theoretical analysis and working mechanism are illustrated as follows.

Fig.2 Schematic of the proposed input-reflectionless balanced bandpass filter

2.1 Differential mode analysis

The DM bisected equivalent circuit of the proposed input-reflectionless balanced BPF is shown in Fig.3a.It can be divided into two parts for analysis,i.e.,ABSS and BPF section.

Fig.3 Equivalent circuits: (a) differential mode;(b) common mode

2.1.1 Absorptive section

For the absorption network,ABSS with double lossy stubs is given in Fig.4,consisting of aλ/4 STL with characteristic impedanceZcand twoλ/4 lossy stubs with characteristic impedancesZaandZb.Theλ/4 lossy stubs can be regarded as transparent atf0;hence,the stopband atf0is provided by the STL.In contrast,the out-of-band energy can be absorbed by the lossy resistors (RaandRb).For the ABSS in Fig.4,the input impedanceZin1and the reflection coefficient |S11| can be given as

Fig.4 Schematic of the proposed absorptive section with double lossy stubs

whereZ0is the port reference impedance.

Fig.5 shows the curves of the proposed ABSS with various parameters.As illustrated in Figs.5a-5f,the values ofZa,Zb,andZcaffect the BW of the reflected signals (whenZin1=0,the reflection coefficient|S11|=0 dB).Figs.5e and 5f show thatZcis the primary influencing factor to determine the reflection BW of the ABSS (BWABSS,i.e.,|S11|＞-10 dB) in Fig.4,and a higherZccan develop a smaller reflection BW.AsZcincreases,the variation trend of reflection BW tends to be flat,but the mismatch (i.e.,the difference between the value ofZin1and 50 Ω) nearf0rises sharply.In addition,the matching performance is affected byZaandRb.A lower mismatch nearf0can be obtained by a smaller value ofZa.In addition,as plotted in Figs.5g and 5h,the matching performances nearf0and at the second harmonic (2f0) are highly dependent onRb,and they increase simultaneously asRbincreases.The absorption resistorRaassembled at the input port 1 is equal toZ0to achieve wideband CM reflectionless performance,which will be discussed in Section 2.2.

Fig.5 Calculated Re(Zin1) and Im(Zin1) of the proposed absorptive section: (a-b) with various Za (Zb=80 Ω, Zc=120 Ω,Rb=150 Ω, Ra=50 Ω);(c-d) with various Zb (Za=40 Ω, Zc=120 Ω,Rb=150 Ω,Ra=50 Ω);(e-f) with various Zc (Za=40 Ω, Zb=80 Ω,Rb=150 Ω,Ra=50 Ω);(g-h) with various Rb (Za=40 Ω, Zb=80 Ω,Zc=120 Ω,Ra=50 Ω)

2.1.2 Bandpass filter section

For the BPF section,a compact and easy-tointegrate TLCS is used.The configuration of the TLCSbased BPF is shown in Fig.6a.The widths of the CFLs and the centerλ/4 resonator arewcandw0,respectively.The gap between them iss.For simplicity,the three coupled lines are regarded as having equal widths(w0=wc).The impedance matrix (Z-matrix) of this sixport network is given by (Yamamoto et al.,1966)

According to Chen CP et al.(2013),the transmission response of the symmetric structure can be precisely described by mode impedancesZoe,Zoo,andkcc.Here,kccrepresents the ratio of the coupling coefficient of nonadjacent lines (k13) to that of adjacent ones (k12):

wherek12andk13can be obtained by the parasitic coupling level (Cin dB) (Chen JX et al.,2015) between two adjacent lines and two nonadjacent lines,respectively.

The modal equations for the configuration of BPF section using TLCS shown in Fig.6a can be derived as

whereVandIare the voltages and currents at ports,respectively.By substituting these conditions into Eqs.(3)and (4),theS-parameter matrix (S-matrix) of this twoport BPF can be directly extracted from the six-portZ-matrix as follows:

According to Eqs.(3)-(9),the calculated frequency response of the TLCS-based BPF is plotted in Fig.6b.There are two transmission zeros (TZs)close to the passband due to the cross-couplingk13of two nonadjacent CFLs (kcc≠0).Meanwhile,three transmission poles (TPs) are generated by the compact TLCS (Feng and Che,2012),which expands the BW and improves the flatness of the passband,avoiding the requirement of multiple resonators.Furthermore,as shown in Fig.7,the BW can be flexibly adjusted bywcands,and it becomes larger aswcandsdecrease.To further improve the roll-off skirt of the passband on the premise of ensuring passband flatness,an additional short stub loaded on the output port CFL,as shown in Fig.8,is proposed.Fig.9 invalidates that the roll-off skirt becomes steeper by this short stub(Zd,θd).It can also enhance the flexibility to adjust the BW of the proposed BPF (BWBPF,i.e.,|S21|＞-3 dB) in Fig.8.

Fig.6 Bandpass filter section using TLCS: (a) configuration;(b) calculated frequency response

Fig.7 TLCS-based bandpass filter design under different s and wc with varied fTPs (a) and 3-dB FBWBPF (b)

Fig.8 Configuration of the TLCS-based bandpass filter with stub (Zd,θd)

Fig.9 Variation of frequency responses with/without stub(Zd,θd) of the TLCS-based bandpass filter (Zoe=175.2 Ω, Zoo=63.3 Ω,kcc=0.53)

2.1.3 Input-reflectionless differential-mode filter design

According to the above analysis,the STL is a key factor for determining the BWABSSand BWBPFin this codesign.WhenZcin Fig.4 increases,BWABSSdecreases;in contrast,whenwcin Fig.6a decreases (corresponding to the increase inZc),BWBPFincreases.To obtain good complementarity of ABSS and BPF section,BWBPFcan be tuned bysandZd,while BWABSScan be tuned byZaandZb.As a result,the proposed fusion design method shown in Fig.3a can be easily realized to obtain miniaturization and good performance simultaneously.

For the DM bisected equivalent circuits of the proposed input-reflectionless balanced BPF shown in Fig.3a,theABCDmatrix of the DM bisected equivalent circuit can be obtained:

whereM1is theABCDmatrix of the lossy stub (Za,θa,Ra),andM2is theABCDmatrix of the remaining part of the DM half circuits without a lossy stub (Za,θa,Ra).They can be expressed as follows (Pozar,2012):

whereM2can be obtained by substituting the conditions into Eqs.(3) and (4),and the conditions can be obtained as

According to Eqs.(10)-(13),theS-matrix of the DM bisected equivalent circuit can be obtained as follows:

Based on this,the calculated DM frequency response can be achieved.

Fig.10 shows the good reflectionless performance when BWABSSis approximately equal to BWBPF.Fusing these two parts by reusing the STL,the BW of the overall circuit (BWDM,i.e.,|Sdd21|＞-3 dB) in Fig.3a is smaller than BWBPFand BWABSS.It is interesting to determine BWDMby BWBPFand BWABSS,which will be discussed below.At the same time,other performances,such as passband IL and absorption of both DM and CM,are evaluated.To facilitate the description of the resultant DM BPF,the BW ratioα=BWABSS/BWBPFis defined.The calculated DM frequency responses under different fractional BWABSS(FBWABSS=BWABSS/f0) and FBWBPF(FBWBPF=BWBPF/f0) in Table 1,whereα=1 is fixed,are plotted in Fig.11.They show good reflectionless performances,as expected,which can be easily controlled byZaandZbof ABSS andZdands(characterized byZoeandZoo) of the BPF section.From this,it can be concluded that BWDMcan be flexibly controlled by different BWABSSand BWBPF.In conclusion,BWDMis always less than BWBPFor BWABSS,and as BWABSSand BWBPFincrease,BWDMincreases.As shown in Fig.11,both DM passband flatness and reflectionless level are varied,which must be studied to optimize the overall performance of the DM filter.

Fig.10 Comparison between the calculated differential mode frequency response of the proposed input-reflectionless balanced BPF and the frequency responses of its ABSS and BPF section (Za=26 Ω,Zb=60 Ω,Zc=120 Ω,Zd=120 Ω,Ra=50 Ω,Rb=150 Ω,Zoe=151.7 Ω,Zoo=80.5 Ω,kcc=0.58)

To evaluate the effect ofα, case 2 in Fig.11 is chosen for study.Fig.12 shows the calculated DM frequency responses of different cases in Table 2.When FBWBPFis fixed at 40%,different values ofαcan be obtained by changingZaandZbof ABSS,and the other parameters are the same as those in case 2 in Table 1.The variableRmaxmarked in Fig.12a is defined as the maximum reflection in the whole band.In addition,the variable PL in Table 2 is defined to quantitatively evaluate the passband flatness (i.e.,distortion at the edges of the passband).The larger the PL,the worse the flatness.PL can be given as follows:

Fig.11 Calculated differential mode frequency responses of different cases in Table 1 (α=1 is fixed) (References to color refer to the online version of this figure)

Table 1 Parameters of the input-reflectionless balanced BPFs (α=1)

Table 2 Parameters of the input-reflectionless balanced BPFs with different α

where 3-dB BWDM(i.e.,BWDM) and 1-dB BWDM(i.e.,|Sdd21|＞-1 dB) can be obtained from Fig.12b.Thus,the reflectionless performance and passband performance of the proposed input-reflectionless balanced BPF can be represented byRmaxand PL,respectively.The curves ofRmaxand PL under differentαvalues are plotted in Fig.13.It shows that the balance between reflectionless performance and passband performance can be adjusted byα.According to the above analysis,the following can be concluded:

1.BWDMis flexibly controlled by BWBPFand BWABSS.Regardless of the value ofα,BWDMis smaller than BWBPFand BWABSS.

2.Whenα=1 (e.g.,case 2),input-reflectionless balanced BPF shows a good reflectionless performance (Rmax=-16.90 dB,which is the optimal value in the interval 0.5-2 ofα),and PL=1.59.

3.Whenα＜1,asαdecreases from 1 to 0.5 in case 2a,Rmaxincreases to -11.74 dB,which manifests a degradation of the reflectionless performance.Moreover,as shown in Fig.12b,the passband produces severe distortion,which is characterized by PL=2.11.

Fig.12 Calculated differential mode frequency responses of different cases in Table 2: (a) transfer coefficient (|Sdd21|) and reflection coefficient (|Sdd11|);(b) |Sdd21| (BWBPF is fixed as 40% with some parameters being the same as in case 2: Zoe=151.7 Ω,Zoo=80.5 Ω,Zd=120 Ω,kcc=0.58,Zc=120 Ω,Ra=50 Ω,Rb=150 Ω) (References to color refer to the online version of this figure)

4.Whenα＞1,the reflectionless performance around the passband is affected.Whenα=1.5 in case 2d,there is a slight effect on the reflectionless performance (Rmax=-13.07 dB),but the passband performance (PL=1.38) is improved.However,whenα=2 in case 2f,the reflectionless performance deteriorates sharply (Rmax=-9.45 dB),although its passband performance is enhanced (PL=1.29).

5.In summary,whenαincreases from 0.5 to 1,Rmaxdecreases from -11.74 dB to -16.90 dB,while whenαincreases from 1 to 2,Rmaxincreases from-16.90 dB to -9.45 dB.In addition,PL decreases asαincreases,which means that the largerαis,the flatter the passband is.According to Fig.13,to obtain a good compromise between reflectionless performance(Rmax＜-10 dB) and passband performance (PL＜1.5),the optimal interval forαis 1.2-1.9.

Fig.13 Performance of the proposed input-reflectionless balanced BPF with varied α in Table 2 (Rmax and PL)

In addition,the BWDMandαare determined by the parametersZa,Zb,Zc,Zd,Zoe,Zoo,andkcc.Rbin Fig.3a can also be used to further optimize the reflectionless performance of the proposed filter.According to Fig.14,although the matching performance of the ABSS nearf0and at the second harmonic (2f0) is improved by increasingRb,as in Figs.5g and 5h,with the variedRb,passband and reflectionless performances have opposite variation trends,and thus a trade-off is needed.Specifically,asRbincreases from 50 Ω to 300 Ω,the reflectionless performance increases (Rmaxdecreases from -5.86 dB to -16.72 dB),but PL increases from 1.19 to 1.56.Accordingly,considering a good compromise between reflectionless performance and passband performance,the range ofRbis 50-150 Ω.

Fig.14 Calculated differential mode frequency responses of case 2d with varied Rb (References to color refer to the online version of this figure)

Through the above analysis,the BWABSSand BWBPFof the proposed input-reflectionless balanced BPF can be easily adjusted to achieve flexible BWDM,and the BW ratioαis a significant indicator to achieve both wideband DM absorption and good passband performance.In addition,the performance can be easily optimized by the codesign method.

2.2 Common mode analysis

When the CM excitation is applied to the proposed input-reflectionless balanced BPF in Fig.2,the symmetrical planeAA′ is equivalent to a magnetic wall.Thus,the CM bisected equivalent circuit can be obtained,as shown in Fig.3b.To obtain wideband CM absorption performance,the absorption behavior at both DC and 2f0is a key indicator.At DC and 2f0,theλ/4 open stubs (ZbandZd) and the absorption resistorRbloaded in the terminal of CFLs can be regarded as transparent,so that most CM noise can be absorbed by the absorption resistorRa.Thus,whenRa=Z0,the ideal absorption behavior at both DC and 2f0can be obtained.Meanwhile,Rbin Fig.3b can be used to optimize CM absorption and suppression levels.The calculated CM frequency responses with the same parameters as in case 2d with variedRbare plotted in Fig.15.AsRbincreases,the CM absorption level increases,but the suppression level atf0worsens.Considering a good balance between the CM suppression level and CM absorption performance,and combined with the requirement of DM reflectionless performance,the final optimization range ofRbis 100-150 Ω.

Fig.15 Calculated common mode frequency responses of case 2d with varied Rb (References to color refer to the online version of this figure)

To summarize the above DM and CM analysis,the main design procedure of the proposed inputreflectionless balanced BPF is as follows:

1.Determine the center frequencyf0and BWDM.According to Fig.10,the relationship between BWDMand BWBPFis BWBPF＞BWDM.On this basis,the approximate BWBPFcan be determined from different cases in Table 1,and it can be easily achieved by adjustingsandZdof the BPF section.

2.Considering the balance between the DM reflectionless performance and passband performance,αcan be determined according to the curves ofRmaxand PL versusαshown in Fig.13.

3.Once BWDM,BWBPF,andαare determined,BWABSScan be determined.This can be easily achieved by adjusting theZaandZbof the ABSS.

4.AdjustRbto obtain a wideband DM and CM reflectionless behavior,minimize DM passband distortion,and improve the CM suppression level.Then,the optimal range ofRb(100-150 Ω) can be obtained.

5.After the initial impedance parameters are obtained by the above design procedure,the proposed input-reflectionless balanced BPF can be constructed and further optimized by the full-wave High-Frequency Structure Simulator (HFSS) once the physical dimensions are converted by Line Calc calculation in the Advanced Design System (ADS).

3 Implementation and discussion

For demonstration,the proposed TLCS-based input-reflectionless balanced BPF is fabricated on a Rogers RO4003 substrate with a relative dielectric constantεr=3.55,dielectric loss tanδ=2.7×10-3,dielectric thicknessh=0.813 mm,and metallization thicknesst=0.035 mm.The center frequencyf0is set at 2.45 GHz.The design specification of the ripple FBWDM=32%is prescribed for the proposed input-reflectionless balanced BPF.With the selected BW ratioα=1.5 and FBWBPF=40%,FBWABSSis 60%.Based on this,the optimized parameters (Za=36 Ω,Zb=80 Ω,Zc=115 Ω,Zd=125 Ω,Ra=50 Ω,Rb=130 Ω) can be easily obtained according to the design procedure in Section 2.2.

Then,the physical model can be built on HFSS,and the layout can be optimized.The photograph and layout of the proposed filter are shown in Fig.16.The simulation is performed with HFSS,and the measurement is conducted by the Agilent N5230A network analyzer,which is a four-port network analyzer that can be used to measure the balanced circuits directly.The measuredS-parameters are plotted in Fig.17 along with the simulation results for comparison.Although the differences between the simulation and measurement results,such as |Sdd11| and |Scc11|,can be observed at approximately 6 GHz,the fractional absorption BWs of both DM and CM in the simulation and measurement are almost the same.The largest deviation comes from the simulated and measured |Sdd11|,which would be caused by the manufacturing tolerances (e.g.,dielectric constant of the employed substrate and implementation of the demonstration board).Overall,the differences between the results in Fig.17 are acceptable.For the DM shown in Fig.17a,the measured FBWDMis approximately 31.4%.Meanwhile,the DM absorptive BW is 285.7%,and the minimum in-band IL (ILmin)is 0.43 dB.The improved roll-off skirt is obtained by four TZs,which are located at 0,1.28,3.28,and 4.72 GHz.Moreover,the rejection levels of over 20 dB at the upper stopband extend to 6.65 GHz (2.72f0).For the CM shown in Fig.17b,it is noted that the absorptive BW is also in a wide range (DC to 7 GHz,285.7%),and over 18.4 dB CM suppression (|Scc21|) is achieved from DC to 4.9 GHz (2f0).

Fig.16 Implementation of the proposed input-reflectionless balanced bandpass filter: (a) photograph;(b) layout (l=18 mm,l0=19.25 mm, la=19.85 mm,lb=19.29 mm,ld=20.3 mm,w=1.78 mm, w0=0.2 mm, wa=2.9 mm,wb=0.74 mm,wc=0.28 mm, wd=0.2 mm,s=0.44 mm)

Fig.17 Simulation (dashed lines) and measurement (solid lines) results of the proposed input-reflectionless balanced BPF: (a) differential mode;(b) common mode (References to color refer to the online version of this figure)

Comparisons with previous reflectionless differential BPFs are summarized in Table 3.Gómez-García et al.(2018) and Yang et al.(2020) did not consider the absorption of the reflected CM noise,which is a key factor for stabilizing the RF system.Moreover,due to the cascaded topology in Gómez-García et al.(2018) and the multi-layered vertical transition structure in Yang et al.(2020),the circuit sizes are large.Some efforts have been made to consider the absorption of unwanted DM and CM signals (Chen X et al.,2021;Zhang YF et al.,2022).DM absorptive BW is approximately 275%,and the CM absorptive BW reaches 200% (Zhang YF et al.,2022).However,its DM upper stopband BW is limited due to the use of theλ/2 coupled ring resonator.In contrast,the proposed filter with a wider upper stopband for DM is due to the adoption of the TLCS.To extend the absorptive BW for the DM and CM,the cascading design is used,resulting in an enlarged circuit size and high IL(Chen X et al.,2021).As seen from Table 3,the proposed input-reflectionless balanced BPF has a more compact circuit layout due to the syncretic working mechanism and the adoption of TLCS.Meanwhile,the proposed filter exhibits larger DM and CM absorptive BWs and lower ILmindue to the design guidelines derived from the detailed analysis.In conclusion,the proposed differential filter exhibits remarkable DM and CM reflectionless performance and filtering performance under the premise of a compact layout.

Table 3 Comparisons with previous reflectionless differential bandpass filters

4 Conclusions

In this paper,a compact input-reflectionless balanced bandpass filter with a flexible bandwidth is presented.It features an innovative conception of the fusion design,especially reusing the shared transmission lines of the absorptive section and bandpass filter section,resulting in a miniaturized circuit and low insertion loss.Meanwhile,the three-line coupled structure introduces the miniaturization of the bandpass filter section with three controllable transmission poles,so that BWBPFcan be easily controlled.In addition,BWABSSand BWBPFcan be adjusted independently,which is helpful for obtaining flexible BWDM,so that the specifications of the differential mode reflectionless filter can be realized in practical applications.In conclusion,the proposed input-reflectionless balanced bandpass filter caters to the development trend of miniaturization and high performance of wireless communication equipment,while eliminating the common mode and differential mode reflected interference signals that are common in the traditional balanced bandpass filter,and is an attractive choice for the radio frequency front end of the wireless communication system.

Contributors

Yahui ZHU designed the research,processed the data,and drafted the paper.Jing CAI,Wei QIN,Wenwen YANG,and Jianxin CHEN helped organize the paper.Yahui ZHU and Jianxin CHEN revised and finalized the paper.

Compliance with ethics guidelines

Yahui ZHU,Jing CAI,Wei QIN,Wenwen YANG,and Jianxin CHEN declare that they have no conflict of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.