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作为无线通信系统中的重要组件,可调带通滤波器由于其灵活性高、尺寸紧凑等优点引起了人们的广泛关注[1-2]。可调滤波器的调谐方案众多[3],以变容二极管作为调谐器件的可调方案具有调谐速度快、制造成本低的优点,成为众多可调方案中应用最为广泛的一种[4-5]。文献[6-10]中提出了一系列基于均匀阻抗谐振器的频率可调带通滤波器设计,通过引入源和负载端耦合,在通带两侧产生两个传输零点,改善了滤波器的选择性。为了实现滤波器频率及带宽同时可调,文献[11-13]中在均匀阻抗谐振器之间增加变容二极管或PIN开关,实现谐振器间耦合系数可调。除了均匀阻抗谐振器,基于变容二极管加载的阶跃阻抗谐振器由于其调谐范围宽和尺寸紧凑的优点,在文献[14-17]中也被用于频率可调滤波器的设计,除了这些基于耦合谐振器的滤波器外,文献[18-21]中还介绍了基于双模谐振器的频率可调滤波器设计,与基于耦合谐振腔的滤波器相比,这些滤波器通常具有更加紧凑的尺寸。然而,上述介绍的频率可调滤波器由于其阶数较低,只有两个极点,其选择性比较差。为改善滤波器的选择性,文献[23-26]中提出了一些基于均匀阻抗谐振器的四阶可调滤波器设计,上述滤波器的选择性显著增强,但是这些滤波器的调谐范围较窄。因此,为改善高选择性频率可调滤波器的调谐范围,本文采用VL-SIR设计一款4阶4零点的频率可调滤波器,该滤波器采用级联四元组(Cascaded Quadruplet, CQ)拓扑结构,通过引入交叉耦合,在通带近端产生一对传输零点,显著改善滤波器的选择性,同时引入源和负载端耦合,在通带远端产生一对交叉零点,改善了阻带抑制性。谐振器之间采用频变耦合结构,实现了频率调谐过程中绝对带宽保持稳定。
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图1为所提出的可调滤波器的结构示意图。滤波器由四个阶跃阻抗谐振器(R1,R2,R3,R4)和输入/输出馈电微带线组成。变容二极管作为调谐元件的加载在阶跃阻抗谐振器的高阻抗线路中,通过改变直流偏置电压VC1/VC2来改变变容二极管的有效电容,实现谐振器谐振频率可调谐。4个VL-SIRs通过直径为0.4 mm的金属过孔连接到地。滤波器具有左右对称结构,有助于简化设计和优化过程。
滤波器拓扑为经典CQ结构,如图1中框图所示。基于经典滤波器理论[27],在谐振器R1和R4之间引入感性交叉耦合可以在通带近端产生两个传输零点,从而改善滤波器的选择性,零点距离通带越近,滤波器矩形系数越小。此外,在滤波器源和负载端引入容性交叉耦合,还可以在通带远端产生两个传输零点,以提高阻带的抑制水平。
滤波器设计指标如下,频率调谐范围0.8~1.1 GHz,3dB绝对带宽50 MHz,回波损耗:20 dB,传输零点位置:±1.7和±20(归一化频率[28])
使用文献[21]中所介绍的耦合矩阵综合方法得到(N+2)阶归一化耦合矩阵M:
$$ \left[ M \right] = \left[ {\begin{array}{*{20}{c}} 0&{1.02}&0&0&{\text{0}}&{0.000{\text{6}}} \\ {1.02}&0&{0.8{\text{5}}}&0&{ - 0.{\text{25}}}&0 \\ 0&{0.8{\text{5}}}&0&{0.{\text{8}}}&0&0 \\ 0&0&{0.{\text{8}}}&0&{0.8{\text{5}}}&0 \\ 0&{ - 0.{\text{25}}}&0&{0.8{\text{5}}}&0&{1.02} \\ {0.{\text{0006}}}&{\text{0}}&0&0&{1.02}&0 \end{array}} \right] $$ (1) 则滤波器耦合矩阵[m]和外部品质因数Qe可由式(2)和(3)计算得到,在式(2)、(3)中,fo为可调滤波器的中心频率,ABW为滤波器绝对带宽,Ms1为滤波器源端与第一个谐振器之间的归一化耦合系数,其中,fo= 0.8~1.1 GHz,ABW=50 MHz。
$$ \left[m\right]=\left[M\right]·\frac{ABW}{{f}_{o}} $$ (2) $$ {\text{Q}}_{e}=\frac{{f}_{o}}{{M}_{\text{S}1}^{\text{2}}·ABW} $$ (3) 根据式(2)和(3)计算得到理论耦合系数和外部品质因数Qe与谐振频率的关系曲线如图2所示,其中,m_sl为源端和负载端的耦合系数。由下图可知,在滤波器中心频率调谐过程中,为保持滤波器绝对带宽稳定不变,谐振器间的耦合系数应该与中心频率成反比,外部品质因数与中心频率成正比。
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变容二极管加载的阶跃阻抗谐振器结构如图3所示,谐振器由一段低阻抗线和一段高阻抗线串联而成,低阻抗线和高阻抗线的特性导纳和电长度分别为Y1, Y2和θ1, θ2。高阻抗线一端接地,低阻抗线一端为开路状态。在高阻抗线中间加载变容二极管,距离高阻抗线接地端的距离为θc,变容二极管的有效电容用Cv表示。此外,VL-SIR的电长度比和特性导纳比用α和β表示,
$ \alpha {\text{ = }}{{{\theta _{\text{2}}}} \mathord{\left/ {\vphantom {{{\theta _{\text{2}}}} {({\theta _{\text{1}}} + {\theta _{\text{2}}})}}} \right. } {({\theta _{\text{1}}} + {\theta _{\text{2}}})}} $ ,$ \beta {\text{ = }}{{{Y_{\text{1}}}} \mathord{\left/ {\vphantom {{{Y_{\text{1}}}} {{Y_{\text{2}}}}}} \right. } {{Y_{\text{2}}}}} $ 。根据传输线理论[28],输入导纳Yin可以通过以下式(4)-式(6)计算。谐振器的谐振条件是输入导纳的虚部必须为零[29],即 Im(Yin) = 0,因此式(3)-式(5)可用于计算VL-SIR的谐振频率:
$$ {Y_A} = \frac{{{Y_2}}}{{jtan{\theta _c}}} $$ (4) $$ {Y_B} = \frac{{j{Y_1}{Y_2}tan{\theta _1} + jY_{\text{2}}^{\text{2}}tan({\theta _{\text{2}}} - {\theta _{\text{c}}})}}{{{Y_2}{\text{ - }}j{Y_1}tan{\theta _1}tan({\theta _{\text{2}}} - {\theta _{\text{c}}})}} $$ (5) $$ {Y_{in}} = \frac{{jw{C_v}{Y_A}}}{{{Y_A} + jw{C_v}}} + {Y_B} $$ (6) 调谐范围(Tuning Range, TR)是频率可调滤波器的关键指标,调谐范围TR定义如式(7)所示。在(7)中,f(Cv_min)和f(Cv_max)分别表示当有效电容Cv为最小值和最大值时VL-SIR的谐振频率:
$$ TR = \frac{{f({C_{v\_\min }}) - f({C_{v\_\max }})}}{{{{(f({C_{v\_\min }}) + f({C_{v\_\max }}))} \mathord{\left/ {\vphantom {{(f({C_{v\_\min }}) + f({C_{v\_\max }}))} 2}} \right. } 2}}} $$ (7) 不同特性导纳比β下调谐范围和电长度比α之间的关系如图4所示,此时,Y1=0.03S, θ1+θ2=180°,变容二级管加载位置θc=20°,电长度参考频率为1 GHz。当特性导纳β为1时,谐振器为均匀阻抗谐振器,当电长度比α改变时,调谐范围TR保持不变。当特性导纳β不为1时,随着电长度比α的增加,调谐范围TR先增大后减小,当电长度比α为0.6时,调谐范围TR达到最大值。随着特性导纳β增加,调谐范围TR也会变宽,这意味着与均匀阻抗谐振器相比,阶跃阻抗谐振器可以实现更宽的调谐范围。
基于以上分析,与均匀阻抗谐振器相比,所提出的VL-SIR可以实现更宽的调谐范围。因此,本文采用VL-SIR来实现具有高选择性和恒定绝对带宽的频率可调四阶带通滤波器。
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所提出的4阶4零点频率可调带通滤波器加工实物如图11所示,滤波器使用Rogers 5880进行加工,介质基板相对介电常数εr为2.2,厚度为0.787 mm。使用全波仿真软件HFSS对滤波器进行优化和仿真,滤波器最终尺寸为l1=12.1 mm, l2=20.3 mm, l3=13.1 mm, l4=11.2 mm, l5=13.3 mm, l6=23.2 mm, l7=27.4 mm, w0=2.4 mm, w1=2.5 mm, w2=0.9 mm, S01=0.12 mm, S12=1.42 mm, S23=0.46 m,滤波器整体尺寸为46.8 mm × 70 mm。使用Skyworks公司的商用变容二极管管SMV1413-SC79作为调谐器件,该变容二极管电容调谐范围从1.77 pf(30 V)到9.6 pf(0 V)。变容二极管的有效电容可以通过直流偏置电压VC1和VC2进行控制。直流偏置线使用0402封装的470 nH电感与谐振器相连,该扼流电感可以减少偏置电路对谐振器电路的影响。
使用Keysight公司的N5244A型号矢量网络分析仪对加工的滤波器进行测试,仿真和测试的频率响应如图12所示,测试结果和仿真结果吻合良好,两者存在的偏差主要由加工误差导致。图12中5条曲线中心频率分别为0.79 GHz,0.89 GHz,0.96 GHz,1.06 GHz,1.14 GHz,对应的偏置电压VC1/VC2分别为0/0 V,2.1/2.2 V,6.5/6.6 V,13.4/14.2 V,27.2/30 V。结果表明,滤波器中心频率可以在0.79 ~ 1.14GHz之间连续调谐,滤波器调谐率约为36.2%。在整个调谐范围内,滤波器的回波损耗优于10 dB,插入损耗为2.8~3.3 dB。同时,在频率调谐过程中,该滤波器3 dB绝对带宽保持在55±3 MHz,实现了恒定的恒定绝对带宽特性。滤波器在通带近端产生两个传输零点,有效提高了滤波器的选择性,另外在通带远端产生了另外两个传输零点,改善了阻带性能。以下图中蓝色曲线为例对滤波器零点分布进行说明。下图蓝色曲线S21的中心频率fo为0.963 GHz,三个传输零点fz1=0.915 GHz,fz2=1.013 GHz和fz3=1.713 GHz,3 dB绝对带宽为55 MHz。因此,fz1、fz2、fz3的归一化频率分别为−1.79、1.77、21.3。fz3的归一化频率大于20,因为源和负载的实际耦合可能小于0.0006,由于测量仪器的量程限制,通带远端左侧的传输零点在图12中未显示。
表1给出了本文所设计的频率可调滤波器与一些之前相似工作典型性能的比较。由下表可以看出,与其他一些基于均匀阻抗谐振器和双模谐振器的可调滤波器相比,本文所提出基于VL-SIR的可调滤波器实现了更宽的调谐范围。同时,该滤波器通过引入交叉耦合,实现了四传输零点的特性,滤波器的选择性和阻带性能都得到了改善。此外,在滤波器频率调谐过程中,滤波器的绝对带宽可以保持稳定,这一特性在一些实际应用中非常有用。
表 1 滤波器典型性能对比
参考文献 频率/GHZ 调谐率/% 带宽/MHZ 插损/dB 阶数 零点个数 谐振器 恒定绝对带宽 尺寸(λg×λg) [10] 1.5-1.8 18.1 119 2.5 2 0 UIR YES 0.18x0.13 [13] 0.57-0.79 32 51 4.1 2 2 UIR YES 0.1 x 0.1 [18] 2.5-3 21 630 1.1 3 2 DMR NO NG [24] 1.21-1.58 26.8 133 3 4 4 UIR YES 0.73 x 0.11 [25] 0.89-1.13 23.8 46.8 4.3 4 2 UIR YES 0.23 x 0.19 Proposed 0.79-1.14 36.2 55 3.3 4 4 VL-SIR YES 0.16 x 0.25 备注: NG: 未给出; DMR: 双模谐振器。
Design of fourth-order frequency tunable bandpass filter using varactor-loaded step-impedance resonators
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摘要: 本文提出一种基于阶跃阻抗谐振器的紧凑型四阶四零点频率可调滤波器设计。滤波器使用变容二极管加载的阶跃阻抗谐振器(VL-SIR),有效拓宽了滤波器的调谐范围。在VL -SIR之间引入交叉耦合,从而在滤波器通带近端产生一对传输零点,显著提高了滤波器的选择性。同时,引入源和负载端的交叉耦合,在通带远端生成一对传输零点,以提高带外抑制。此外,采用基于VL-SIR的频变耦合结构来实现恒定绝对带宽。仿真结果与实测结果吻合良好。测量结果显示,可调滤波器频率调谐范围为0.78至1.15 GHz,3 dB绝对带宽约为55±3 MHz,滤波器的回波损耗大于10 dB,插入损耗约为2.8~3.3 dB。
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关键词:
- 带通滤波器 /
- 微带 /
- 可调滤波器 /
- 变容管加载的阶跃阻抗谐振器
Abstract: In this article, a compact fourth-order frequency tunable bandpass filter (BPF) with four Transmission Zeros (TZs) based on Varactor-Loaded Step-Impedance Resonators (VL-SIRs) is presented. With the utilization of VL-SIRs, the Tuning Range (TR) of the proposed fourth-order BPF is improved. Besides, by introducing cross coupling between VL-SIRs, a pair of TZs close to the passband are produced and the selectivity of the filter is enhanced significantly. Another pair of TZs are generated to improve the out-of-band rejection by using source-load coupling. Moreover, the Frequency-Dependent Coupling (FDC) structures based on VL-SIRs are employed to realize constant Absolute Bandwidth (ABW). The simulated and measured results are presented and show good agreement. The measured results exhibit a tuning range from 0.78 GHz to 1.15 GHz with a 3-dB constant ABW of about 55±3 MHz, the return loss of the filter is greater than 10 dB and the insertion loss is about 2.8 dB to 3.3 dB.-
Key words:
- Bandpass filter /
- microstip /
- tunable filter /
- varactor-loaded step impedance resonator
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表 1 滤波器典型性能对比
参考文献 频率/GHZ 调谐率/% 带宽/MHZ 插损/dB 阶数 零点个数 谐振器 恒定绝对带宽 尺寸(λg×λg) [10] 1.5-1.8 18.1 119 2.5 2 0 UIR YES 0.18x0.13 [13] 0.57-0.79 32 51 4.1 2 2 UIR YES 0.1 x 0.1 [18] 2.5-3 21 630 1.1 3 2 DMR NO NG [24] 1.21-1.58 26.8 133 3 4 4 UIR YES 0.73 x 0.11 [25] 0.89-1.13 23.8 46.8 4.3 4 2 UIR YES 0.23 x 0.19 Proposed 0.79-1.14 36.2 55 3.3 4 4 VL-SIR YES 0.16 x 0.25 备注: NG: 未给出; DMR: 双模谐振器。 -
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