Tunable Bandpass and Bandstop Filters Based on Dual-Band Combline Structures

InfoLink DTX8200系列QAM调制器用户指南目录目录1 概述................................................................................................................................................ 1-11.1 简介............................................................................................................................................................... 1-21.2 特性............................................................................................................................................................... 1-31.3 工作原理....................................................................................................................................................... 1-42 设备描述........................................................................................................................................ 2-12.1 设备描述....................................................................................................................................................... 2-22.1.1 设备外观 ............................................................................................................................................. 2-22.1.2 前面板 ................................................................................................................................................. 2-22.1.3 功能键 ................................................................................................................................................. 2-22.1.4 后面板 ................................................................................................................................................. 2-32.2 接口描述....................................................................................................................................................... 2-42.3 设备操作菜单............................................................................................................................................... 2-53 安装指南........................................................................................................................................ 3-13.1 安装流程....................................................................................................................................................... 3-23.2 安装机箱....................................................................................................................................................... 3-23.3 连接线缆....................................................................................................................................................... 3-33.3.1 安装说明 ............................................................................................................................................. 3-33.3.2 连接地线 ............................................................................................................................................. 3-43.3.3 连接DS3输入和输出线缆................................................................................................................. 3-43.3.4 连接ASI输入和输出线缆 ................................................................................................................. 3-53.3.5 连接SPI输入线缆.............................................................................................................................. 3-63.3.6 连接IF中频输入/输出线缆 ............................................................................................................... 3-73.3.7 连接RF射频输出线缆....................................................................................................................... 3-83.3.8 连接10/100M网口 ............................................................................................................................. 3-93.3.9 连接电源线........................................................................................................................................ 3-103.4 启动设备..................................................................................................................................................... 3-114 配置设备参数................................................................................................................................ 4-14.1 配置概述....................................................................................................................................................... 4-24.2 选择输入接口............................................................................................................................................... 4-3目录InfoLink DTX8200系列QAM调制器用户指南4.3 设置DS3模式.............................................................................................................................................. 4-44.3.1 选择模式 ............................................................................................................................................. 4-44.3.2 设置主/备模式号 ................................................................................................................................ 4-54.3.3 搜索模式号.......................................................................................................................................... 4-6 4.4 输出设置....................................................................................................................................................... 4-64.4.1 设置输出频率...................................................................................................................................... 4-64.4.2 设置输出频道...................................................................................................................................... 4-74.4.3 设置QAM调制数 .............................................................................................................................. 4-84.4.4 设置符号率.......................................................................................................................................... 4-94.4.5 设置输出码率...................................................................................................................................... 4-94.4.6 设置射频控制.................................................................................................................................... 4-104.4.7 设置输出增益.................................................................................................................................... 4-114.4.8 设置频谱翻转.................................................................................................................................... 4-11 4.5 码流处理..................................................................................................................................................... 4-124.5.1 设置PID过滤 ................................................................................................................................... 4-124.5.2 设置PID映射 ................................................................................................................................... 4-134.5.3 设置PID插入 ................................................................................................................................... 4-155 配置网络参数................................................................................................................................ 5-15.1 组网简介....................................................................................................................................................... 5-25.2 设置网管IP地址 ......................................................................................................................................... 5-25.3 设置以太网口参数....................................................................................................................................... 5-35.3.1 设置IP地址 ........................................................................................................................................ 5-35.3.2 设置子网掩码...................................................................................................................................... 5-35.3.3 设置网关地址...................................................................................................................................... 5-45.3.4 设置网口模式...................................................................................................................................... 5-55.4 配置TS网口参数 ........................................................................................................................................ 5-55.4.1 打开网口 ............................................................................................................................................. 5-55.4.2 设置IP地址 ........................................................................................................................................ 5-65.4.3 设置子网掩码...................................................................................................................................... 5-65.4.4 设置网管PID ...................................................................................................................................... 5-75.5 配置透明传输网口参数............................................................................................................................... 5-75.5.1 透明传输示例...................................................................................................................................... 5-75.5.2 打开网口 ............................................................................................................................................. 5-85.5.3 设置IP地址 ........................................................................................................................................ 5-85.5.4 设置子网掩码...................................................................................................................................... 5-95.5.5 设置网关地址...................................................................................................................................... 5-95.5.6 设置网元IP ......................................................................................................................................... 5-95.5.7 设置源地址........................................................................................................................................ 5-105.5.8 设置目标地址.................................................................................................................................... 5-11InfoLink DTX8200系列QAM调制器用户指南目录6 典型业务配置................................................................................................................................ 6-16.1 配置复用....................................................................................................................................................... 6-26.2 配置调制....................................................................................................................................................... 6-57 升级指南........................................................................................................................................ 7-17.1 升级准备....................................................................................................................................................... 7-27.2 升级执行....................................................................................................................................................... 7-27.2.1 通过网管系统升级软件...................................................................................................................... 7-37.2.2 通过FTP服务器升级......................................................................................................................... 7-48 例行维护........................................................................................................................................ 8-18.1 设备例行维护项目....................................................................................................................................... 8-28.2 日维护项目................................................................................................................................................... 8-28.3 月维护项目................................................................................................................................................... 8-48.4 年维护项目................................................................................................................................................... 8-68.5 维护表........................................................................................................................................................... 8-78.5.1 日维护表 ............................................................................................................................................. 8-78.5.2 月维护表 ............................................................................................................................................. 8-88.5.3 年维护表 ............................................................................................................................................. 8-99 告警处理........................................................................................................................................ 9-19.1 告警信息处理............................................................................................................................................... 9-29.1.1 查看告警信息...................................................................................................................................... 9-29.1.2 保存告警信息...................................................................................................................................... 9-29.1.3 删除告警信息...................................................................................................................................... 9-29.2 常见告警及处理建议................................................................................................................................... 9-39.2.1 码流类告警.......................................................................................................................................... 9-39.2.2 升级类告警.......................................................................................................................................... 9-49.2.3 其它 ..................................................................................................................................................... 9-410 故障处理.................................................................................................................................... 10-110.1 输入输出故障处理................................................................................................................................... 10-210.1.1 射频信号无输出.............................................................................................................................. 10-210.1.2 射频信号输出偏低.......................................................................................................................... 10-210.1.3 设备输入码流中断.......................................................................................................................... 10-210.2 接收与显示节目故障处理....................................................................................................................... 10-310.2.1 STB不能正常解码节目.................................................................................................................. 10-310.2.2 混频后STB搜索不到节目............................................................................................................. 10-310.2.3 无电视信号...................................................................................................................................... 10-410.2.4 过滤后节目还存在.......................................................................................................................... 10-410.2.5 插入PSI/SI信息导致STB工作异常 ............................................................................................ 10-410.2.6 映射后的节目未能正常播放.......................................................................................................... 10-5目录InfoLink DTX8200系列QAM调制器用户指南10.2.7 图像显示马赛克或定帧.................................................................................................................. 10-5 10.3 网管管理设备故障处理........................................................................................................................... 10-610.3.1 网管不能提取PSI/SI信息 ............................................................................................................. 10-610.3.2 网管不能控制添加的设备.............................................................................................................. 10-610.3.3 网管软件未能成功提取PSI/SI表信息.......................................................................................... 10-711 FAQ ........................................................................................................................................... 11-111.1 名词解释FAQ .......................................................................................................................................... 11-211.2 操作应用FAQ .......................................................................................................................................... 11-3InfoLink DTX8200系列QAM调制器用户指南插图目录插图目录图1-1 DTX8200在数字电视前端的应用......................................................................................................... 1-2图1-2 DTX8200总体结构示意图..................................................................................................................... 1-4图2-1 DTX8200外观示意图............................................................................................................................. 2-2图2-2 DTX8200前面板示意图......................................................................................................................... 2-2图2-3 DTX8208后面板 .................................................................................................................................... 2-3图2-4 DTX8209后面板 .................................................................................................................................... 2-3图2-5 DTX8210后面板 .................................................................................................................................... 2-3图2-6 DTX8211与DTX8211E后面板............................................................................................................. 2-4图2-7 DTX8200接口图 .................................................................................................................................... 2-4图2-8 信息查询项 ............................................................................................................................................. 2-6图2-9 码流处理项 ............................................................................................................................................. 2-6图2-10 输出设置项 ........................................................................................................................................... 2-6图2-11 输入设置项............................................................................................................................................ 2-7图2-12 网络设置 ............................................................................................................................................... 2-7图2-13 系统设置 ............................................................................................................................................... 2-8图3-1 DTX8200安装流程................................................................................................................................. 3-2图3-2 DTX8200的固定 .................................................................................................................................... 3-2图3-3 连接地线 ................................................................................................................................................. 3-4图3-4 75Ω同轴线缆.......................................................................................................................................... 3-4图3-5 DS3输入、输出连接示意图.................................................................................................................. 3-5图3-6 ASI输入、输出连接示意图................................................................................................................... 3-6图3-7 SPI线缆................................................................................................................................................... 3-7图3-8 SPI线缆连接示意图............................................................................................................................... 3-7图3-9 IF输入、IF输出自环连接示意图......................................................................................................... 3-8图3-10 RF射频输出连接示意图...................................................................................................................... 3-9插图目录InfoLink DTX8200系列QAM调制器用户指南图3-11 10/100M网线 ........................................................................................................................................ 3-9图3-12 连接10/100M网口示意图 ................................................................................................................. 3-10图3-13 连接电源和地线.................................................................................................................................. 3-10图3-14 DTX8200启动显示............................................................................................................................. 3-11图4-1 设置过滤参数 ....................................................................................................................................... 4-13图4-2 设置映射参数 ....................................................................................................................................... 4-15图5-1 设置网口IP地址 .................................................................................................................................... 5-3图5-2 设置网口子网掩码.................................................................................................................................. 5-4图5-3 设置网关地址 ......................................................................................................................................... 5-4图5-4 设置网口模式 ......................................................................................................................................... 5-5图5-5 打开TS网口........................................................................................................................................... 5-6图5-6 设置TS网口IP地址.............................................................................................................................. 5-6图5-7 设置TS网口子网掩码 ........................................................................................................................... 5-6图5-8 设置网管PID .......................................................................................................................................... 5-7图5-9 透明传输示例 ......................................................................................................................................... 5-8图5-10 打开透明传输网口................................................................................................................................ 5-8图5-11 设置透明传输网口IP地址 .................................................................................................................. 5-9图5-12 设置透明传输网口子网掩码................................................................................................................ 5-9图5-13 设置透明传输网口网关地址................................................................................................................ 5-9图5-14 设置透明传输网元IP ......................................................................................................................... 5-10图5-15 设置透明传输网口源地址.................................................................................................................. 5-10图5-16 设置透明传输网口目标地址.............................................................................................................. 5-11图6-1 配置组网图 ............................................................................................................................................. 6-2图6-2 基本配置 ................................................................................................................................................. 6-3图6-3 提取表信息 ............................................................................................................................................. 6-4图6-4 复用接口配置 ......................................................................................................................................... 6-5图6-5 配置组网图 ............................................................................................................................................. 6-6图7-1 启动FTP服务器软件............................................................................................................................. 7-2图7-2 升级软件界面 ......................................................................................................................................... 7-3图7-3 选择升级软件 ......................................................................................................................................... 7-4图7-4 设置升级服务器IP地址 ........................................................................................................................ 7-4图7-5 启动程序升级 ......................................................................................................................................... 7-5InfoLink DTX8200系列QAM调制器用户指南表格目录表格目录表2-1 功能及方向键说明.................................................................................................................................. 2-2表2-2 设备接口描述 ......................................................................................................................................... 2-5表3-1 DTX8200安装可选项............................................................................................................................. 3-3表4-1 配置顺序 ................................................................................................................................................. 4-2表4-2 输入接口可选项...................................................................................................................................... 4-3表4-3 模式参数选择 ......................................................................................................................................... 4-5表4-4 DS3模式号.............................................................................................................................................. 4-6表4-5 可选项参数 ............................................................................................................................................. 4-7表4-6 输出频率规划 ......................................................................................................................................... 4-7表4-7 输出频道参数选项.................................................................................................................................. 4-8表4-8 QAM调制数参数选项 ........................................................................................................................... 4-8表4-9 符号率参数选项...................................................................................................................................... 4-9表4-10 输出码率参数选项.............................................................................................................................. 4-10表4-11 射频信号选项...................................................................................................................................... 4-10表4-12 输出增益选项 ..................................................................................................................................... 4-11表4-13 频谱翻转选项 ..................................................................................................................................... 4-12表4-14 PID过滤选项 ...................................................................................................................................... 4-12表4-15 PID映射选项 ...................................................................................................................................... 4-14表4-16 PID插入选项 ...................................................................................................................................... 4-16表5-1 网管组网方式 ......................................................................................................................................... 5-2表6-1 基本流PID .............................................................................................................................................. 6-2表8-1 设备例行维护周期和维护项目.............................................................................................................. 8-2表8-2 设备的日维护项目.................................................................................................................................. 8-3表8-3 指示灯状态及说明.................................................................................................................................. 8-4表8-4 设备的月维护项目.................................................................................................................................. 8-5。

butterworth滤波器的matlab实现-回复Butterworth滤波器的Matlab实现一、介绍Butterworth滤波器是一种常见的滤波器，它是模拟滤波器中最为基础的一种。

它的特点是具有平坦的幅频响应，在通带和阻带之间呈现出平滑的过渡。

在Matlab中，可以使用信号处理工具箱中的函数来实现Butterworth滤波器。

二、Butterworth滤波器的原理Butterworth滤波器的设计是基于将滤波器的传递函数表示为极点和零点的比值的形式。

其传递函数为：H(s) = 1 / ((s/a)^N + 1)其中，s是复变量，a是与滤波器的通带截止频率相关的常数，N是滤波器的阶数。

三、Butterworth滤波器的参数选择在实现Butterworth滤波器之前，我们需要选择一些参数来定义滤波器的特性。

这些参数包括采样率、通带截止频率、阻带截止频率和滤波器的阶数。

首先，采样率是指信号的采样频率，它决定了信号中可以表示的最高频率。

通常情况下，采样率应为信号中最高频率的两倍。

其次，通带截止频率是指滤波器在通带内的最高频率。

我们可以根据信号的频率范围来选择通带截止频率。

一般而言，通带截止频率应低于采样率的一半。

阻带截止频率是指滤波器在阻带内的最低频率。

我们可以根据信号的频率范围来选择阻带截止频率。

一般而言，阻带截止频率应高于通带截止频率。

最后，滤波器的阶数决定了滤波器的陡峭程度。

阶数越高，滤波器越陡峭。

但是，阶数过高可能导致滤波器的相位失真。

四、Matlab中的实现步骤在Matlab中，我们可以使用`butter`函数来设计Butterworth滤波器。

该函数的语法为：[b, a] = butter(阶数, [通带截止频率/采样率, 阻带截止频率/采样率], '滤波器类型')其中，阶数为滤波器的阶数，[通带截止频率/采样率, 阻带截止频率/采样率]为滤波器的截止频率与采样率的比值，'滤波器类型'为滤波器的类型，可以是'low'、'high'、'bandpass'或'bandstop'。

AAbsolutely integrable 绝对可积Absolutely integrable impulse response 绝对可积冲激响应Absolutely summable 绝对可和Absolutely summable impulse response 绝对可和冲激响应Accumulator 累加器Acoustic 声学Adder 加法器Additivity property 可加性Aliasing 混叠现象All-pass systems 全通系统AM (Amplitude modulation ) 幅度调制Amplifier 放大器Amplitude modulation (AM) 幅度调制Amplitude-scaling factor 幅度放大因子Analog-to-digital (A-to-D) converter 模数转换器Analysis equation 分析公式（方程）Angel (phase) of complex number 复数的角度（相位）Angle criterion 角判据Angle modulation 角度调制Anticausality 反因果Aperiodic 非周期Aperiodic convolution 非周期卷积Aperiodic signal 非周期信号Asynchronous 异步的Audio systems 音频（声音）系统Autocorrelation functions 自相关函数Automobile suspension system 汽车减震系统Averaging system 平滑系统BBand-limited 带（宽）限的Band-limited input signals 带限输入信号Band-limited interpolation 带限内插Bandpass filters 带通滤波器Bandpass signal 带通信号Bandpass-sampling techniques 带通采样技术Bandwidth 带宽Bartlett (triangular) window 巴特利特（三角形）窗Bilateral Laplace transform 双边拉普拉斯变换Bilinear 双线性的Bilinear transformation 双线性变换Bit （二进制）位，比特Block diagrams 方框图Bode plots 波特图Bounded 有界限的Break frequency 折转频率Butterworth filters 巴特沃斯滤波器C“Chirp” transform algorithm“鸟声”变换算法Capacitor 电容器Carrier 载波Carrier frequency 载波频率Carrier signal 载波信号Cartesian (rectangular) form 直角坐标形式Cascade (series) interconnection 串联，级联Cascade-form 串联形式Causal LTI system 因果的线性时不变系统Channel 信道，频道Channel equalization 信道均衡Chopper amplifier 斩波器放大器Closed-loop 闭环Closed-loop poles 闭环极点Closed-loop system 闭环系统Closed-loop system function 闭环系统函数Coefficient multiplier 系数乘法器Coefficients 系数Communications systems 通信系统Commutative property 交换性（交换律）Compensation for nonideal elements 非理想元件的补偿Complex conjugate 复数共轭Complex exponential carrier 复指数载波Complex exponential signals 复指数信号Complex exponential(s) 复指数Complex numbers 复数Conditionally stable systems 条件稳定系统Conjugate symmetry 共轭对称Conjugation property 共轭性质Continuous-time delay 连续时间延迟Continuous-time filter 连续时间滤波器Continuous-time Fourier series 连续时间傅立叶级数Continuous-time Fourier transform 连续时间傅立叶变换Continuous-time signals 连续时间信号Continuous-time systems 连续时间系统Continuous-to-discrete-time conversion 连续时间到离散时间转换Convergence 收敛Convolution 卷积Convolution integral 卷积积分Convolution property 卷积性质Convolution sum 卷积和Correlation function 相关函数Critically damped systems 临界阻尼系统Crosss-correlation functions 互相关函数Cutoff frequencies 截至频率DDamped sinusoids 阻尼正弦振荡Damping ratio 阻尼系数Dc offset 直流偏移Dc sequence 直流序列Deadbeat feedback systems 临界阻尼反馈系统Decibels (dB) 分贝Decimation 抽取Decimation and interpolation 抽取和内插Degenerative (negative) feedback 负反馈Delay 延迟Delay time 延迟时间Demodulation 解调Difference equations 差分方程Differencing property 差分性质Differential equations 微分方程Differentiating filters 微分滤波器Differentiation property 微分性质Differentiator 微分器Digital-to-analog (D-to-A) converter 数模转换器Direct Form I realization 直接I型实现Direct form II realization 直接II型实现Direct-form 直接型Dirichlet conditions 狄里赫利条件Dirichlet, P.L. 狄里赫利Discontinuities 间断点，不连续Discrete-time filters 离散时间滤波器Discrete-time Fourier series 离散时间傅立叶级数Discrete-time Fourier series pair 离散时间傅立叶级数对Discrete-time Fourier transform （DFT）离散时间傅立叶变换Discrete-time LTI filters 离散时间线性时不变滤波器Discrete-time modulation 离散时间调制Discrete-time nonrecursive filters 离散时间非递归滤波器Discrete-time signals 离散时间信号Discrete-time systems 离散时间系统Discrete-time to continuous-time conversion 离散时间到连续时间转换Dispersion 弥撒（现象）Distortion 扭曲，失真Distribution theory（property）分配律Dominant time constant 主时间常数Double-sideband modulation (DSB) 双边带调制Downsampling 减采样Duality 对偶性EEcho 回波Eigenfunctions 特征函数Eigenvalue 特征值Elliptic filters 椭圆滤波器Encirclement property 围线性质End points 终点Energy of signals 信号的能量Energy-density spectrum 能量密度谱Envelope detector 包络检波器Envelope function 包络函数Equalization 均衡化Equalizer circuits 均衡器电路Equation for closed-loop poles 闭环极点方程Euler, L. 欧拉Euler’s relation欧拉关系（公式）Even signals 偶信号Exponential signals 指数信号Exponentials 指数FFast Fourier transform (FFT) 快速傅立叶变换Feedback 反馈Feedback interconnection 反馈联结Feedback path 反馈路径Filter(s) 滤波器Final-value theorem 终值定理Finite impulse response (FIR) 有限长脉冲响应Finite impulse response (FIR) filters 有限长脉冲响应滤波器Finite sum formula 有限项和公式Finite-duration signals 有限长信号First difference 一阶差分First harmonic components 基波分量（一次谐波分量）First-order continuous-time systems 一阶连续时间系统First-order discrete-time systems 一阶离散时间系统First-order recursive discrete-time filters 一阶递归离散时间滤波器First-order systems 一阶系统Forced response 受迫响应Forward path 正向通路Fourier series 傅立叶级数Fourier transform 傅立叶变换Fourier transform pairs 傅立叶变换对Fourier, Jean Baptiste Joseph 傅立叶（法国数学家，物理学家）Frequency response 频率响应Frequency response of LTI systems 线性时不变系统的频率响应Frequency scaling of continuous-time Fourier transform 连续时间傅立叶变化的频率尺度（变换性质）Frequency shift keying (FSK) 频移键控Frequency shifting property 频移性质Frequency-division multiplexing (FDM) 频分多路复用Frequency-domain characterization 频域特征Frequency-selective filter 频率选择滤波器Frequency-shaping filters 频率成型滤波器Fundamental components 基波分量Fundamental frequency 基波频率Fundamental period 基波周期GGain 增益Gain and phase margin 增益和相位裕度General complex exponentials 一般复指数信号Generalized functions 广义函数Gibbs phenomenon 吉伯斯现象Group delay 群延迟HHalf-sample delay 半采样间隔时延Hanning window 汉宁窗Harmonic analyzer 谐波分析议Harmonic components 谐波分量Harmonically related 谐波关系Heat propagation and diffusion 热传播和扩散现象Higher order holds 高阶保持Highpass filter 高通滤波器Highpass-to-lowpass transformations 高通到低通变换Hilbert transform 希尔波特滤波器Homogeneity (scaling) property 齐次性（比例性）IIdeal 理想的Ideal bandstop characteristic 理想带阻特征Ideal frequency-selective filter 理想频率选择滤波器Idealization 理想化Identity system 恒等系统Imaginary part 虚部Impulse response 冲激响应Impulse train 冲激串Incrementally linear systems 增量线性系统Independent variable 独立变量Infinite impulse response (IIR) 无限长脉冲响应Infinite impulse response (IIR) filters 无限长脉冲响应滤波器Infinite sum formula 无限项和公式Infinite taylor series 无限项泰勒级数Initial-value theorem 初值定理Inpulse-train sampling 冲激串采样Instantaneous 瞬时的Instantaneous frequency 瞬时频率Integration in time-domain 时域积分Integration property 积分性质Integrator 积分器Interconnection 互联Intermediate-frequency (IF) stage 中频级Intersymbol interference (ISI) 码间干扰Inverse Fourier transform 傅立叶反变换Inverse Laplace transform 拉普拉斯反变换Inverse LTI system 逆线性时不变系统Inverse system design 逆系统设计Inverse z-transform z反变换Inverted pendulum 倒立摆Invertibility of LTI systems 线性时不变系统的可逆性Invertible systems 逆系统LLag network 滞后网络Lagrange, J.L. 拉格朗日（法国数学家，力学家）Laplace transform 拉普拉斯变换Laplace, P.S. de 拉普拉斯（法国天文学家，数学家）lead network 超前网络left-half plane 左半平面left-sided signal 左边信号Linear 线性Linear constant-coefficient difference equations 线性常系数差分方程Linear constant-coefficient differential equations 线性常系数微分方程Linear feedback systems 线性反馈系统Linear interpolation 线性插值Linearity 线性性Log magnitude-phase diagram 对数幅－相图Log-magnitude plots 对数模图Lossless coding 无损失码Lowpass filters 低通滤波器Lowpass-to-highpass transformation 低通到高通的转换LTI system response 线性时不变系统响应LTI systems analysis 线性时不变系统分析MMagnitude and phase 幅度和相位Matched filter 匹配滤波器Measuring devices 测量仪器Memory 记忆Memoryless systems 无记忆系统Modulating signal 调制信号Modulation 调制Modulation index 调制指数Modulation property 调制性质Moving-average filters 移动平均滤波器Multiplexing 多路技术Multiplication property 相乘性质Multiplicities 多样性NNarrowband 窄带Narrowband frequency modulation 窄带频率调制Natural frequency 自然响应频率Natural response 自然响应Negative (degenerative) feedback 负反馈Nonanticipatibe system 不超前系统Noncausal averaging system 非因果平滑系统Nonideal 非理想的Nonideal filters 非理想滤波器Nonmalized functions 归一化函数Nonrecursive 非递归Nonrecursive filters 非递归滤波器Nonrecursive linear constant-coefficient difference非递归线性常系数差分方程equationsNyquist frequency 奈奎斯特频率Nyquist rate 奈奎斯特率Nyquist stability criterion 奈奎斯特稳定性判据OOdd harmonic 奇次谐波Odd signal 奇信号Open-loop 开环Open-loop frequency response 开环频率响应Open-loop system 开环系统Operational amplifier 运算放大器Orthogonal functions 正交函数Orthogonal signals 正交信号Oscilloscope 示波器Overdamped system 过阻尼系统Oversampling 过采样Overshoot 超量PParallel interconnection 并联Parallel-form block diagrams 并联型框图Parity check 奇偶校验检查Parseval’s relatio n 帕斯伐尔关系（定理）Partial-fraction expansion 部分分式展开Particular and homogeneous solution 特解和齐次解Passband 通频带Passband edge 通带边缘Passband frequency 通带频率Passband ripple 通带起伏（或波纹）Pendulum 钟摆Percent modulation 调制百分数Periodic 周期的Periodic complex exponentials 周期复指数Periodic convolution 周期卷积Periodic signals 周期信号Periodic square wave 周期方波Periodic square-wave modulating signal 周期方波调制信号Periodic train of impulses 周期冲激串Phase (angle) of complex number 复数相位（角度）Phase lag 相位滞后Phase lead 相位超前Phase margin 相位裕度Phase shift 相移Phase-reversal 相位倒置Phase modulation 相位调制Plant 工厂Polar form 极坐标形式Poles 极点Pole-zero plot(s) 零极点图Polynomials 多项式Positive (regenerative) feedback 正（再生）反馈Power of signals 信号功率Power-series expansion method 幂级数展开的方法Principal-phase function 主值相位函数Proportional (P) control 比例控制Proportional feedback system 比例反馈系统Proportional-plus-derivative 比例加积分Proportional-plus-derivative feedback 比例加积分反馈Proportional-plus-integral-plus-differential (PID) control 比例－积分－微分控制Pulse-amplitude modulation 脉冲幅度调制Pulse-code modulation 脉冲编码调制Pulse-train carrier 冲激串载波QQuadrature distortion 正交失真Quadrature multiplexing 正交多路复用Quality of circuit 电路品质（因数）RRaised consine frequency response 升余弦频率响应Rational frequency responses 有理型频率响应Rational transform 有理变换RC highpass filter RC 高阶滤波器RC lowpass filter RC 低阶滤波器Real 实数Real exponential signals 实指数信号Real part 实部Rectangular (Cartesian) form 直角（卡笛儿）坐标形式Rectangular pulse 矩形脉冲Rectangular pulse signal 矩形脉冲信号Rectangular window 矩形窗口Recursive (infinite impulse response) filters 递归（无时限脉冲响应）滤波器Recursive linear constant-coefficient difference equations 递归的线性常系数差分方程Regenerative (positive) feedback 再生（正）反馈Region of comvergence 收敛域right-sided signal 右边信号Rise time 上升时间Root-locus analysis 根轨迹分析（方法）Running sum 动求和SS domain S域Sampled-data feedback systems 采样数据反馈系统Sampled-data systems 采样数据系统Sampling 采样Sampling frequency 采样频率Sampling function 采样函数Sampling oscilloscope 采样示波器Sampling period 采样周期Sampling theorem 采样定理Scaling (homogeneity) property 比例性（齐次性）性质Scaling in z domain z域尺度变换Scrambler 扰频器Second harmonic components 二次谐波分量Second-order 二阶Second-order continuous-time system 二阶连续时间系统Second-order discrete-time system 二阶离散时间系统Second-order systems 二阶系统sequence 序列Series (cascade) interconnection 级联（串联）Sifting property 筛选性质Sinc functions sinc函数Single-sideband 单边带Single-sideband sinusoidal amplitude modulation 单边带正弦幅度调制Singularity functions 奇异函数Sinusoidal 正弦（信号）Sinusoidal amplitude modulation 正弦幅度调制Sinusoidal carrier 正弦载波Sinusoidal frequency modulation 正弦频率调制Sliding 滑动Spectral coefficient 频谱系数Spectrum 频谱Speech scrambler 语音加密器S-plane S平面Square wave 方波Stability 稳定性Stabilization of unstable systems 不稳定系统的稳定性（度）Step response 阶跃响应Step-invariant transformation 阶跃响应不定的变换Stopband 阻带Stopband edge 阻带边缘Stopband frequency 阻带频率Stopband ripple 阻带起伏（或波纹）Stroboscopic effect 频闪响应Summer 加法器Superposition integral 叠加积分Superposition property 叠加性质Superposition sum 叠加和Suspension system 减震系统Symmetric periodic 周期对称Symmetry 对称性Synchronous 同步的Synthesis equation 综合方程System function(s) 系统方程TTable of properties 性质列表Taylor series 泰勒级数Time 时间，时域Time advance property of unilateral z-transform 单边z变换的时间超前性质Time constants 时间常数Time delay property of unilateral z-transform 单边z变换的时间延迟性质Time expansion property 时间扩展性质Time invariance 时间变量Time reversal property 时间反转（反褶）性Time scaling property 时间尺度变换性Time shifting property 时移性质Time window 时间窗口Time-division multiplexing (TDM) 时分复用Time-domain 时域Time-domain properties 时域性质Tracking system (s) 跟踪系统Transfer function 转移函数transform pairs 变换对Transformation 变换（变形）Transition band 过渡带Transmodulation (transmultiplexing) 交叉调制Triangular (Barlett) window 三角型（巴特利特）窗口Trigonometric series 三角级数Two-sided signal 双边信号Type l feedback system l 型反馈系统UUint impulse response 单位冲激响应Uint ramp function 单位斜坡函数Undamped natural frequency 无阻尼自然相应Undamped system 无阻尼系统Underdamped systems 欠阻尼系统Undersampling 欠采样Unilateral 单边的Unilateral Laplace transform 单边拉普拉斯变换Unilateral z-transform 单边z变换Unit circle 单位圆Unit delay 单位延迟Unit doublets 单位冲激偶Unit impulse 单位冲激Unit step functions 单位阶跃函数Unit step response 单位阶跃响应Unstable systems 不稳定系统Unwrapped phase 展开的相位特性Upsampling 增采样VVariable 变量WWalsh functions 沃尔什函数Wave 波形Wavelengths 波长Weighted average 加权平均Wideband 宽带Wideband frequency modulation 宽带频率调制Windowing 加窗zZ domain z域Zero force equalizer 置零均衡器Zero-Input response 零输入响应Zero-Order hold 零阶保持Zeros of Laplace transform 拉普拉斯变换的零点Zero-state response 零状态响应z-transform z变换z-transform pairs z变换对。

恒定绝对带宽的紧凑型可重构双频带通滤波器包晓蕾【摘要】A compact dual-band bandpass filter (BPF ) based on stepped impedance resonator (SIR ) and defected-feeding structure is investigated in this paper.The SIR with T-stub centrally loaded provides more degrees of freedom to adjust the dual-band resonant frequencies.By combining the SIR with the defected-feeding structure and adjusting their dimensions,the absolute bandwidth can be easily controlled.Transmission zero is derived through simulation due to the combination of SIR and defected -feeding structure.Finally,simulation results show the second passband switched among 1.55GHz,1.75GHz and 2.05GHz with a constant absolute bandwidth of 230MHz ± 5.6％,and the first passband fixed at 0.90GHz with a constant absolute bandwidth of 32MHz.The measurement of the fabricated example shows good agreement with the simulation.%本文研究了一种基于阶梯阻抗谐振器(SIR)和缺陷馈电结构的小型双频带通滤波器(BPF).具有T型中央加载的SIR可以更自由地调整双频谐振频率,SIR和缺陷馈电结构组合,并进行阶数调整,可以很容易控制绝对带宽,仿真得到传输零点.最后,仿真结果显示,恒定绝对带宽在230MHz±5.6％的情况下,第二通带可以在1.55GHz,1.75GHz和2.05GHz之间切换,恒定绝对带宽为32MHz的情况下,第一通带稳定在0.90GHz.实际加工的滤波器测量结果与仿真结果吻合较好.【期刊名称】《安徽师范大学学报（自然科学版）》【年(卷),期】2017(040)006【总页数】6页(P563-568)【关键词】紧凑型;双频带通滤波器(BPF);阶梯阻抗谐振器(SIR);恒定绝对带宽【作者】包晓蕾【作者单位】上海电子信息职业技术学院通讯与信息工程学院,上海 201411【正文语种】中文【中图分类】TN911随着无线通信系统的快速发展(例如，无线局域网(WLAN)，全球移动通信系统(GSM)，第三代(3G)，第四代(4G)，全球微波接入互操作性(WiMax)，等等).双频通带滤波器(BPF)已经引起了很多关注[1-6].近年来，已经使用阶梯式阻抗谐振器(SIR)的结构实现双频通带滤波器，Makimoto和Yamashita分析了SIR的基本理论，通过控制SIR的阻抗和长度比，可以获得想要的工作频率[7].基于基础理论，一些文章中出现了一些新结构的SIR.Zhang和Sun使用新耦合方案的U形SIR来减少插入损耗[8].采用两个具有缺陷接地结构(DGS)的SIR组成双频带通滤波器，表现出良好的高通带性能[9].并提出了由开环谐振器实现的双频通带滤波器[10-12]，以及由两个级联三重(CT)单元组成的双频带通滤波器[13].RF可重配置双频带滤波器正在成为一个热门研究课题，它可以显著减小现代多频带系统的总体尺寸和复杂性.恒定分数带宽和恒定绝对带宽(ABW)是不同应用的频率可重配置滤波器中的非常重要的特征.以前大多数工作集中在调整中心频率，在保持恒定绝对带宽方面研究较少.有学者采用机械电容器来调节滤波器的频率，通过在相邻的滤波器谐振器之间设置可变耦合衰减器来调谐带宽[14].并引入双模谐振滤波器保持ABW恒定[15，16]，证明了混合电磁耦合方案可以控制带宽[17].在本文中，提出了具有容易控制的第一通带和可重构的第二通带特性的双频通带滤波器.预测第二通带在1.55GHz，1.75GHz和2.05GHz之间切换，改变由T型中央加载的SIR尺寸即可得到.通过改变零欧姆电阻器的位置，可以方便地将第二通带的三个中心频率调谐到期望值，因此本文的滤波器结构提供了更多的自由度来实现可调谐性.将缺陷馈电结构与加载SIR的T型组合，在两个通带之间产生传输零点，从而改善了选择性能.利用缺陷馈电结构调整，可以很容易地控制绝对带宽.去掉多余电路，通带中的低插入损耗性能得到改善，尺寸也更紧凑.为了验证所提出的方法，我们优化设计、制造并测量了可重构双频带通滤波器，仿真和测量结果证明了有效性.谐振器的基本结构如图1(a)所示.由于结构是对称的，可以采用偶模式和奇模式分析获得谐振频率.对于奇模和偶模等效电路，输入阻抗为Zino=jZ2tanθZine=Z2其中Z1和Z2分别是相应传输线的特性阻抗，ZinT是T型负载的输入阻抗.为了简化分析，使内线和外线的电长度相等，定义θ=β1l1=β2l2. 输入阻抗ZinT由下式给出ZinT=-jZ3为了减小谐振的大小，电长度θ小于π/4.由式(1)得出，奇模式谐振频率为fodd=其中l1是物理长度，v1是内线中的相速度. 由式(4)可以看出，当确定l1和v1时，奇模式谐振频率取决于Z2和Z1的比值.偶模式谐振由式(2)得出，feven由式(6)的解确定tan2θ-(1+Z2/Z1)|ZinT|tanθ-Z2/Z1=0tan()=(1+Z2/Z1)+式(6)中，当阶梯阻抗谐振器固定时，受到T型尺寸的影响，偶模式谐振频率由|ZinT|,决定，因此改变T型加载的SIR的尺寸将产生各种偶模谐振频率，而奇模谐振频率不受影响.基于以上分析，本文提出一种双频带通滤波器的结构，由T型加载的SIR和缺陷馈电结构组成，图2所示.该设计中，采用SIR的基本奇模谐振频率作为第一通带频率，将偶模谐振频率作为第二通带频率.为减小尺寸，将谐振器折叠，由两条特性阻抗为50Ω的的微带线路馈电.图3表示T型加载SIR的通带特性和不同参数的频率的变化趋势.预测中心频率的第一通带可以通过优化L2来设计. 如图3(a)所示，L2越小，第一中心频率越高. 实验发现，具有T型尺寸的第二通带的变化对第一通带几乎没有影响.如图3(b)所示，随着L3或L4减小，T型尺寸变小，产生更高的中心频率fo2.显然，第二通带表现出1.88-2.29GHz的调谐范围，而第一通带在运行过程中保持在0.96GHz.在1.88GHz和2.29GHz之间的调谐范围，两个通带的插入损耗都小于1dB，其回波损耗分别大于-20dB.因此，在设计中使用缺陷馈电结构与SIR组合，在主要两个频带之间出现新的通带和传输零点. 同时，新的通带可以通过改变缺陷馈电结构的尺寸来移动，如图4所示.当新的通带和第二通带合并时，可以实现双带BPF的调谐中的中心频率和绝对带宽.如图5所示，随着L7的减小，绝对带宽变窄，位于低阻带的发射零点向第二通带移动，而L7的变化对高阻带处的传输零点几乎没有影响.基于以上分析，我们优化设计了可重构双频带BPF滤波器，其第二通带具有预定义的恒定绝对带宽，第一通带固定.图6为用SIR和基于六个开关的缺陷馈电结构来改变T型尺寸的示意图.根据六个开关的不同状态分成三种组合，状态1：S3断开，S4断开，S6断开，其它接通；状态2：S2断开，S4断开，S6断开，其它接通；状态3：S1断开，S2断开，S5断开，其它接通，相应的S参数如图7所示.在实际应用中，用零欧姆电阻作连接开关.由图7可以看出，第二通带的中心频率在1.55GHz，1.75GHz和2.05GHz之间切换，恒定绝对带宽230MHz和第一通带在调谐过程中保持恒定.随着六个开关的位置改变，将获得其他三个频率，因此所提出的结构提供更多的自由度来实现可调谐性.所提出的可调谐双频带滤波器在单个谐振器结构内集成了两个通带，不仅避免了额外损耗，还实现了尺寸的紧凑. 另外，它大大简化了谐振器的组装和集成，从而节省了时间和成本.在该设计中，所有尺寸选择如下：L0=39.94mm,L1=19.5mm,L2=16.2mm,L3=9mm,L4=5.4mm,L5=5mm,L6=26 mm,L7=13.5mm,W0=1.14mm,W1=0.6mm,W2=2mm,W3=2mm,W4=0.39m m,g1=g1=0.2mm.设计结束后，采用Ansoft HFSS V13进行仿真，用Agilent矢量网络分析仪N5230A进行测量，并制作了紧凑型可重构滤波器，如图8所示.图9比较了仿真和测量结果.制作滤波器的第二通带在1.55/1.75/2.05GH之间切换，3dB绝对带宽为230MHz.所有配置测量到的带内最大插入损耗为2.16/2.18/1.74 dB，其中包含连接器的损耗，带内回波损耗优于-10 dB.第一通带固定在0.91GHz，其3dB绝对带宽约为32MHz.在两个通带之间产生传输零点可以提高通带选择性并提高隔离度.测量与仿真的偏差主要来自连接器和有限衬底的反射.整体尺寸约为20mm×44mm.表1表示滤波器特性与开关配置之间的关系.表2对提出的可重构BPF与其他可重构BPF的性能进行了比较.可以看出，与其他滤波器设计相比，该滤波器设计可以提供独立的可调谐双带通带特性，具有小尺寸和低插入损耗.在本文中，提出了一种基于T型加载SIR和缺陷馈电结构的紧凑可重构双带通滤波器. 通过控制T型尺寸可以方便地将第二通带调谐到期望的值，几乎不影响第一通带.所制作的第二通带实现了230MHz±5.6%的3dB带宽，这可以被明确地看作是ABW.此外，在两个通带之间存在传输零点，这改善了裙部选择性.该设计方法适用于可选择的多频带应用，相关滤波器已经实现.其良好的性能，平面结构和紧凑的尺寸对无线通信也很有吸引力.【相关文献】[1] SUN S, YANG S, WU B, et al. 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Microwave FiltersA filter is a two-port network used to control the frequency response at a certain point in an RF or microwave system by providing transmission at frequencies within the passband of the filter and attenuation in the stopband of the filter. Typical frequency responses include low-pass, high-pass, bandpass, and band-reject characteristics. Applications can be found in virtually any type of RF or microwave communication, radar, or test and measurement system.The development of filter theory and practice began in the years preceding World War II by pioneers such as Mason, Sykes, Darlington, Fano, Lawson, and Richards. The image parameter method of filter design was developed in the late 1930s and was useful for low-frequency filters in radio and telephony. In the early 1950s a group at Stanford Research Institute, consisting of G. Matthaei, L. Young, E. Jones, S. Cohn, and others, became very active in microwave filter and coupler development. A voluminous handbook on filters and couplers resulted from this work and remains a valuable reference . Today, most microwave filter design is done with sophisticated computer-aided design (CAD) packages based on the insertion loss method.Because of continuing advances in network synthesis with distributed elements, the use of low-temperature superconductors and other new materials, and the incorporation of active devices in filter circuits, microwave filter design remains an active research area.We begin our discussion of filter theory and design with the frequency characteristics of periodic structures, which consist of a transmission line or wave guide periodically loaded with reactive elements. These structures are of interest in themselves because of their application to slow-wave components and traveling-wave amplifier design, and also because they exhibit basic passband-stopband responses that lead to the image parameter method of filter design.Filters designed using the image parameter method consist of a cascade of simpler two-port filter sections to provide the desired cutoff frequencies and attenuation characteristics but do not allow the specification of a particular frequency response over the complete operating range. Thus, although the procedure is relatively simple, the design of filters by the image parameter method often must be iterated many times to achieve the desired results.A more modern procedure, called the insertion loss method, uses network synthesis techniques to design filters with a completely specified frequency response.The designs simplified by beginning with low-pass filter prototypes that are normalized in terms of impedance and frequency. Transformations are then applied to convert the prototype designs to the desired frequency range and impedance level.Both the image parameter and insertion loss methods of filter design lead to circuits using lumped elements (capacitors and inductors). For microwave applications such designs usually must be modified to employ distributed elements consisting of transmission line sections. The Richards transformation and the Kuroda identities provide this step.The subject of microwave filters is quite extensive due to the importance of these components in practical systems and the wide variety of possible implementations. Here we can treat only the basic principles and some of the more common filter designs .1、Bandstop and Bandpass Filters Using Quarter-Wave ResonatorsWe know that quarter-wave open-circuited or short-circuited transmission line stubs look like series or parallel resonant circuits, respectively. We can therefore use such stubs in shunt along a transmission line to implement bandpass or bandstop filters,as shown in Figure1. Quarter-wavelength sections of line between the stubs act as admittance inverters to effectively convert alternate shunt resonators to series resonators.The stubs and the transmission line sections are λ/4 long at the center frequency, ω0.For narrow bandwidths the response of such a filter using N stubs is essentially the same as that of a coupled line filter using N + 1 sections. The internal impedance of the Stub filters Z0,while in the case of he coupled line filter end sections are required to transform the impedance level. This makes the stub filter more compact and easier to design.A disadvantage, however, is that a filter using stub resonators often requires characteristic impedances that are difficult to realize in practice.We first consider a bandstop filter using N open-circuited stubs, as shown in Figure 1a. The design equations for the required stub characteristic impedances, Z0n, will be derived in terms of the element values of a low-pass prototype through the use of an equivalent circuit. The analysis of the bandpass version, using short-circuited stubs, follows the same procedure, so the design equations for this case are presented without detailed derivation.FIGURE1 Bandstop and bandpass filters using shunt transmission line resonators (θ= π/2)at the centerfrequency). (a) Bandstop filter. (b) Bandpass filter.As indicated in Figure 2a, an open-circuited stub can be approximated as a series LC resonator when its length is near 90◦. The input impedance of an open-circuitedFIGURE 2 Equivalent circuit for the bandstop filter of Figure 8.47a. (a) Equivalent circuit of an open-circuited stub for θ near π/2. (b) Equivalent filtercircuit using resonatorsand admittance inverters. (c) Equivalent lumped-element bandstop filter.transmission line of characteristic impedance Z0n isZ = −jZ 0n cot θ,where θ = π/2 for ω = ω0. If we let ω = ω0+ ∆ω, where ∆ω<<ω0, then θ = (π/2),(1 + ∆ω/ω0), a nd this impedance can be approximated asZ = jZ 0n tan02ωωπ∆≈0002)(ωωωπ-n jZ (1) for frequencies in the vicinity of the center frequency, ω0. The impedance of a series LC circuit is)(22)(10000ωωωωωωωωωωω-≈-=≈-=+=n n n n n n n jL C L j C L j C j L j Z (2)where LnCn= 1/ω02 .Equating (1) and (2) gives the characteristic impedance of the stub in terms of the resonator parameters:πωn L Z 004= (3) Then, if we consider the quarter-wave sections of line between the stubs as ideal admittance inverters, the bandstop filter of Figure 1a can be represented by the equivalent circuit of Figure 2b. Next, the circuit elements of this equivalent circuit can be related to those of the lumped-element bandstop filter prototype of Figure 2c. With reference to Figure 2b, the admittance Y seen looking toward the L 2C 2 resonator is .10110222)1/11(1)/1(1-++++=Z C j L j C j L j Y Z ωωωω (4)The admittance at the corresponding point in the circuit of Figure 2c is10'1'1'2'2)/11(/11-++++=Z L j C j C j L j Y ωωωω (5) These two results will be equivalent if the following conditions are satisfied:'2'222'1'11120,1C L C L L C C L Z == (6) Since L n C n = L n ’C n ’=1/ω02,these results can be solved for Ln'22'120201,L L L Z L ==ω (7)Using (3) and the impedance-scaled bandstop filter elements gives the stub characteristic impedances as∆==∆==20'200210'10200144,44g Z L Z g Z L Z Z ππωππω (8)where ∆ = (ω2− ω1)/ω0is the fractional bandwidth of the filter. It is easy to show that the general result for the characteristic impedances of abandstop filter is . ∆=n n g Z Z π004 (9)For a bandpass filter using short-circuited stub resonators the corresponding result is n n g Z Z 400∆=π (10)These results only apply to filters having input and output impedances of Z0 and so cannot be used for equal-ripple designs with N even.EXAMPLE 1 BANDSTOP FILTER DESIGNDesign a bandstop filter using three quarter-wave open-circuit stubs. The center frequency is 2.0 GHz, the bandwidth is 15%, and the impedance is 50Ω. Use an equal-ripple response, with a 0.5 dB ripple level.SolutionThe fractional bandwidth is ∆ = 0.15.Then the characteristic impedances of the stubs can befound from (9). The results are listed in the following table:n gn Z0n(Ω)1 1.5963 265.92 1.0967 265.93 1.5963 265.9The filter circuit is shown in Figure1a, with all stubs and transmission line sections λ/4 long at 2.0 GHz. The calculated attenuation forthis filteris shown in Figure 3;the ripplein the passbands is somewhat greaterthan 0.5 dB as aresult of the approximations involved in the development of the design equations.FIGURE3 Amplitude response of the bandstop filterof Example 1.The performance of quarter-wave resonator filters can be improved by allowing the characteristic impedances of the interconnecting lines to be variable; then an exact correspondence with coupled line bandpass or bandstop filters can be demonstrated.2、Bandpass Filters Using Capacitively Coupled Series Resonators Another type of bandpass filter that can be conveniently fabricated in microstrip or stripline form is the capacitive-gap coupled resonator filter shown in Figure 4. An Nth-order filter of this form will use N resonant series sections of transmission line with N + 1 capacitive gaps between them. These gaps can be approximated as series capacitors; The flter can then be modeled as shown in Figure 4（b).FIGURE4 Development of the equivalence of a capacitive-gap coupled resonator bandpass filter to the coupled line bandpass filter (a) The capacitive-gap coupled resonator bandpassfilter. (b)Transmission line model. (c) Transmission line model with nagative-sectionsforming admittance inverters (φi/2 < 0) (d) Equivalent circuit using inverters and λ/2 resonators (φ= πat ω0).The resonators are approximately λ/2 long at the centerfrequency, ω0.Next, we redraw the equivalent circuit of Figure 8.50b with negative-length transmission line sections on either side of the series capacitors. The lines of lengthφ will be λ/2 long at ω0, so the electrical length θiof the ith section in Figures 4a, b is12121+Φ+Φ+=i i i πθ N i ...,3,2,1= （11） with φi< 0. The reason for doing this is that the combination of series capacitor and negative-length transmission lines forms the equivalent circuit of an admittance inverter, as seen from Figure 4c. In order for this equivalence to be valid, the following relationship must hold between the electrical length of the lines and the capacitive susceptance:)2arctan(0i i B Z -=Φ （12）T hen the resulting inverter constant can be related to the capacitive susceptance as 20)(1i i i J Z J B -= （13） T he capacitive-gap coupled filter can then be modeled as shown in Figure 4d. Now consider the equivalent circuit shown in Figure 8.45b for a coupled line bandpass filter.Since these two circuits are identical (as φ = 2θ = π at the center frequency), we can use the results from the coupled line filter analysis to complete the present problem. Thus,we can use (10) to find the admittance inverter constants, Ji, from the low-pass prototype values, gi, and the fractional bandwidth, Ω. As in the case of the coupled line filter,there will be N + 1 inverter constants for an Nth-order filter. Then (13) can be used to find the susceptance, Bi, for the ith coupling gap. Finally, the electrical length of the resonator sections can be found from (11) and (12):)]2arctan()2[arctan(21100++-=i i i B Z B Z πθ EXAMPLE 8.9 CAPACITIVEL Y COUPLED SERIESRESONATOR BANDPASSFILTER DESIGND esign a bandpass filter using capacitive coupled series resonators, with a 0.5 dB equal-ripple passband characteristic. The center frequency is 2.0 GHz, the band-width is 10%, and the impedance is 50Ω. At least 20 dB of attenuation is required at 2.2 GHz.SolutionWe first determine the order of the filter to satisfy the attenuation specification at2.2 GHz. Using formula to convert to normalized frequency gives91.1)2.20.20.22.2(1.01)(100=-=-∆←ωωωωω Then ⎢cωω⎢-1=1.91-1.0=0.91F rom the Figure , we see that N = 3 should satisfy the attenuation specification at2.2 GHz. The low-pass prototype values are given in this Table .The calculated amplitude response is plotted in Figure 5. The specifications of this filter are the same as the coupled line bandpass filter of Example1.FIGURE5 A mplitude response for the capacitive-gap coupled seriesresonator bandpass filter of example 23、Bandpass Filters Using Capacitively Coupled Shunt ResonatorsA related type of bandpass filter is shown in Figure 6, where short-circuited shunt resonators are capacitively coupled with series capacitors.FIGURE6 A bandpass filter using capacitively coupled shunt stub resonatorsAn N th-order filter will use N stubs, which are slightly shorter than λ/4 at the filter center frequency. The short-circuited stub resonators can be made from sections of coaxial line using ceramic materials having a very high dielectric constant and low loss, resulting in a very compact design even at UHF frequencies . Such filters are often referred to as ceramic resonator filters and are among the most common types of RF bandpass filters used in portable wireless systems.Most cellular telephones, GPS receivers, and other wireless devices employ two or more filters of this type.微波滤波器微波滤波器的理论和实践始于第二次世界大战前几年，开拓者有Mason, Sykes, Darlington, Fano, Lawson,和Richards。

butterButterworth filter designSyntax[z,p,k]=butter(n,Wn)[z,p,k] = butter(n,Wn,'ftype')[b,a]=butter(n,Wn)[b,a]=butter(n,Wn,'ftype')[A,B,C,D]=butter(n,Wn)[A,B,C,D] = butter(n,Wn,'ftype')[z,p,k]=butter(n,Wn,'s')[z,p,k] = butter(n,Wn,'ftype','s')[b,a]=butter(n,Wn,'s')[b,a]=butter(n,Wn,'ftype','s')[A,B,C,D]=butter(n,Wn,'s')[A,B,C,D] = butter(n,Wn,'ftype','s')Descriptionbutter designs lowpass, bandpass, highpass, and bandstop digital and analog Butterworth filters. Butterworth filters are characterized by a magnitude response that is maximally flat in the passband and monotonic overall.Butterworth filters sacrifice rolloff steepness for monotonicity in the pass- and stopbands. Unless the smoothness of the Butterworth filter is needed, an elliptic or Chebyshev filter can generally provide steeper rolloff characteristics with a lower filter order.Digital Domain[z,p,k] = butter(n,Wn) designs an order n lowpass digital Butterworth filter with normalized cutoff frequency Wn. It returns the zeros and poles in length n column vectors z and p, and the gain in the scalar k.[z,p,k] = butter(n,Wn,'ftype') designs a highpass, lowpass, or bandstop filter, where the string 'ftype' is one of the following:∙'high' for a highpass digital filter with normalized cutoff frequency Wn ∙'low' for a lowpass digital filter with normalized cutoff frequency Wn'stop' for an order 2*n bandstop digital filter if Wn is a two-element vector, Wn = [w1 w2]. The stopband is w1 < ω < w2.Cutoff frequency is that frequency where the magnitude response of the filter is .For butter, the normalized cutoff frequency Wn must be a number between 0 and 1, where 1 corresponds to the Nyquist frequency, π radians per sample.If Wn is a two-element vector, Wn = [w1 w2], butter returns an order 2*n digital bandpass filter with passband w1 < ω < w2.With different numbers of output arguments, butter directly obtains other realizations of the filter. To obtain the transfer function form, use two output arguments as shown below.[b,a] = butter(n,Wn) designs an order n lowpass digital Butterworth filter with normalized cutoff frequency Wn. It returns the filter coefficients in length n+1 row vectors b and a, with coefficients in descending powers of z.[b,a] = butter(n,Wn,'ftype') designs a highpass, lowpass, or bandstop filter, where the string 'ftype' is 'high', 'low', or 'stop', as described above.To obtain state-space form, use four output arguments as shown below:[A,B,C,D] = butter(n,Wn) or[A,B,C,D] = butter(n,Wn,'ftype') where A, B, C, and D areand u is the input, x is the state vector, and y is the output.Analog Domain[z,p,k] = butter(n,Wn,'s') designs an order n lowpass analog Butterworth filter with angular cutoff frequency Wn rad/s. It returns the zeros and poles in length n or 2*ncolumn vectors z and p and the gain in the scalar k. butter's angular cutoff frequency Wn must be greater than 0 rad/s.If Wn is a two-element vector with w1 < w2, butter(n,Wn,'s') returns an order 2*n bandpass analog filter with passband w1 < ω < w2.[z,p,k] = butter(n,Wn,'ftype','s') designs a highpass, lowpass, or bandstop filter using the ftype values described above.With different numbers of output arguments, butter directly obtains other realizations of the analog filter. To obtain the transfer function form, use two output arguments as shown below:[b,a] = butter(n,Wn,'s') designs an order n lowpass analog Butterworth filter with angular cutoff frequency Wn rad/s. It returns the filter coefficients in the length n+1 row vectors b and a, in descending powers of s,derived from this transfer function:[b,a] = butter(n,Wn,'ftype','s') designs a highpass, lowpass, or bandstop filter using the ftype values described above.To obtain state-space form, use four output arguments as shown below:[A,B,C,D] = butter(n,Wn,'s') or[A,B,C,D] = butter(n,Wn,'ftype','s') where A, B, C, and D areand u is the input, x is the state vector, and y is the output.ExamplesHighpass FilterFor data sampled at 1000 Hz, design a 9th-order highpass Butterworth filter with cutoff frequency of 300 Hz, which corresponds to a normalized value of 0.6:[z,p,k] = butter(9,300/500,'high');[sos,g] = zp2sos(z,p,k); % Convert to SOS formHd = dfilt.df2tsos(sos,g); % Create a dfilt objecth = fvtool(Hd); % Plot magnitude responseset(h,'Analysis','freq') % Display frequency responseLimitationsIn general, you should use the [z,p,k] syntax to design IIR filters. To analyze or implement your filter, you can then use the [z,p,k] output with zp2sos and an sos dfilt structure. For higher order filters (possibly starting as low as order 8), numerical problems due to roundoff errors may occur when forming the transfer function using the [b,a] syntax. The following example illustrates this limitation:n = 6; Wn = [2.5e6 29e6]/500e6;ftype = 'bandpass';% Transfer Function design[b,a] = butter(n,Wn,ftype);h1=dfilt.df2(b,a); % This is an unstable filter.% Zero-Pole-Gain design[z, p, k] = butter(n,Wn,ftype);[sos,g]=zp2sos(z,p,k);h2=dfilt.df2sos(sos,g);% Plot and compare the resultshfvt=fvtool(h1,h2,'FrequencyScale','log'); legend(hfvt,'TF Design','ZPK Design')filter1-D digital filterSyntaxy = filter(b,a,X)[y,zf] = filter(b,a,X)[y,zf] = filter(b,a,X,zi)y = filter(b,a,X,zi,dim)[...] = filter(b,a,X,[],dim)DescriptionThe filter function filters a data sequence using a digital filter which works for both real and complex inputs. The filter is a direct form II transposed implementation of the standard difference equation (see "Algorithm").y = filter(b,a,X) filters the data in vector X with the filter described by numerator coefficient vector b and denominator coefficient vector a. If a(1) is not equal to 1, filter normalizes the filter coefficients by a(1). If a(1) equals 0, filter returns an error.If X is a matrix, filter operates on the columns of X. If X is a multidimensional array, filter operates on the first nonsingleton dimension.[y,zf] = filter(b,a,X) returns the final conditions, zf, of the filter delays. If X is a row or column vector, output zf is a column vector of max(length(a),length(b))-1. If X is a matrix, zf is an array of such vectors, one for each column of X, and similarly for multidimensional arrays.[y,zf] = filter(b,a,X,zi) accepts initial conditions, zi, and returns the final conditions, zf, of the filter delays. Input zi is a vector of lengthmax(length(a),length(b))-1, or an array with the leading dimension of sizemax(length(a),length(b))-1 and with remaining dimensions matching those of X.y = filter(b,a,X,zi,dim) and [...] = filter(b,a,X,[],dim) operate across the dimension dim.ExamplesYou can use filter to find a running average without using a for loop. This example finds the running average of a 16-element vector, using a window size of 5.data = [1:0.2:4]';windowSize = 5;filter(ones(1,windowSize)/windowSize,1,data)ans =0.20000.44000.72001.04001.40001.60001.80002.00002.20002.40002.60002.80003.00003.20003.40003.6000AlgorithmsThe filter function is implemented as a direct form II transposed structure,ory(n) = b(1)*x(n) + b(2)*x(n-1) + ... + b(nb+1)*x(n-nb)- a(2)*y(n-1) - ... - a(na+1)*y(n-na)where n-1 is the filter order, which handles both FIR and IIR filters [1], na is the feedback filter order, and nb is the feedforward filter order.The operation of filter at sample is given by the time domain difference equationsThe input-output description of this filtering operation in the -transform domain is a rational transfer function,。

数字滤波是数字信号处理中的重要环节。

为了用户更好的使用DSP进行数字信号处理，Ti 公司提供了数字滤波器程序模块和相应的matlab滤波器设计函数以加速我们的DSP程序设计。

但是，很不幸的是，该模块附带的说明文档过于简单，程序接口做得不是很好，不利于大家模块化编程。

因此，我写了一下文档，并自己写了一段更方便使用的代码，希望能给大家帮助。

一． M atlab滤波器设计函数的使用首先介绍两种数字滤波器FIR滤波器和IIR滤波器fir滤波器中文全称是有限冲激响应滤波器。

该滤波器是对理想滤波器的高度近似，滤波器的通带增益恒定，阻带增益几乎为零，相位特性好。

iir滤波器中文全称是无限冲激响应滤波器。

该滤波器是实际模拟滤波器的数字实现，通常我们定义在该滤波器的通带有‐3db的增益衰减，并且其相位特性不如fir滤波器。

最常见的iir滤波器有巴特沃思滤波器，切比雪夫滤波器，椭圆滤波器。

在计算量大致相同时，iir滤波器对阻带频率的衰减能力要远高于fir滤波器。

对于电力电子应用来说，数字滤波的目的通常是滤除信号中的部分频率或让信号中的特定频率通过，因此对滤波器的通带增益没有过多要求。

所以选用iir滤波器是合适的。

而在iir滤波器中，又以巴特沃思滤波器最为合适。

TI公司提供了两个基于matlab的IIR数字滤波器设计函数eziir16.m和eziir32.m。

eziir16.m 对应dsp程序内部运算为16位，运算速度较快，但是精度很成问题，所以在使用的时候强烈推荐eziir32.m，其程序内部运算为32位的，运算速度对于电力电子开关电源应用来说也相对可以接受。

现以巴特沃思低通滤波器设计为例，介绍整个设计流程。

1.打开matlab，运行程序 eziir32.m。

（\dsp_tbox\filter\matlab\ezIIR）2.依次选择滤波器类型1，滤波器响应1，采样频率（通常是你的开关频率）10000，通带增益下降3db,阻带增益衰减40db,转折频率，截止频率，最后命名输出文件名。

DSP 专业英语词汇AAbsolutely integrable 绝对可积Absolutely integrable impulse response 绝对可积冲激响应Absolutely summable 绝对可和Absolutely summable impulse response 绝对可和冲激响应Accumulator 累加器Acoustic 声学Adder 加法器Additivity property 可加性Aliasing 混叠现象All—pass systems 全通系统AM （Amplitude modulation ）幅度调制Amplifier 放大器Amplitude modulation （AM) 幅度调制Amplitude-scaling factor 幅度放大因子Analog—to-digital (A-to—D）converter 模数转换器Analysis equation 分析公式（方程）Angel (phase) of complex number 复数的角度（相位）Angle criterion 角判据Angle modulation 角度调制Anticausality 反因果Aperiodic 非周期Aperiodic convolution 非周期卷积Aperiodic signal 非周期信号Asynchronous 异步的Audio systems 音频（声音）系统Autocorrelation functions 自相关函数Automobile suspension system 汽车减震系统Averaging system 平滑系统BBand—limited 带（宽）限的Band—limited input signals 带限输入信号Band—limited interpolation 带限内插Bandpass filters 带通滤波器Bandpass signal 带通信号Bandpass—sampling techniques 带通采样技术Bandwidth 带宽Bartlett (triangular) window 巴特利特（三角形）窗Bilateral Laplace transform 双边拉普拉斯变换Bilinear 双线性的Bilinear transformation 双线性变换Bit （二进制）位，比特Block diagrams 方框图Bode plots 波特图Bounded 有界限的Break frequency 折转频率Butterworth filters 巴特沃斯滤波器C“Chirp" transform algorithm “鸟声”变换算法Capacitor 电容器Carrier 载波Carrier frequency 载波频率Carrier signal 载波信号Cartesian （rectangular) form 直角坐标形式Cascade （series）interconnection 串联，级联Cascade-form 串联形式Causal LTI system 因果的线性时不变系统Channel 信道,频道Channel equalization 信道均衡Chopper amplifier 斩波器放大器Closed-loop 闭环Closed-loop poles 闭环极点Closed-loop system 闭环系统Closed-loop system function 闭环系统函数Coefficient multiplier 系数乘法器Coefficients 系数Communications systems 通信系统Commutative property 交换性（交换律）Compensation for nonideal elements 非理想元件的补偿Complex conjugate 复数共轭Complex exponential carrier 复指数载波Complex exponential signals 复指数信号Complex exponential（s) 复指数Complex numbers 复数Conditionally stable systems 条件稳定系统Conjugate symmetry 共轭对称Conjugation property 共轭性质Continuous—time delay 连续时间延迟Continuous-time filter 连续时间滤波器Continuous-time Fourier series 连续时间傅立叶级数Continuous-time Fourier transform 连续时间傅立叶变换Continuous-time signals 连续时间信号Continuous-time systems 连续时间系统Continuous-to-discrete—time conversion 连续时间到离散时间转换Convergence 收敛Convolution 卷积Convolution integral 卷积积分Convolution property 卷积性质Convolution sum 卷积和Correlation function 相关函数Critically damped systems 临界阻尼系统Crosss—correlation functions 互相关函数Cutoff frequencies 截至频率DDamped sinusoids 阻尼正弦振荡Damping ratio 阻尼系数Dc offset 直流偏移Dc sequence 直流序列Deadbeat feedback systems 临界阻尼反馈系统Decibels (d 分贝Decimation 抽取Decimation and interpolation 抽取和内插Degenerative （negative) feedback 负反馈Delay 延迟Delay time 延迟时间Demodulation 解调Difference equations 差分方程Differencing property 差分性质Differential equations 微分方程Differentiating filters 微分滤波器Differentiation property 微分性质Differentiator 微分器Digital-to-analog (D—to—A) converter 数模转换器Direct Form I realization 直接I型实现Direct form II realization 直接II型实现Direct—form 直接型Dirichlet conditions 狄里赫利条件Dirichlet，P。

A 安培，电流的单位。

ABC 1、自动低音补偿。

2、自动亮度控制。

absolutc pitch 绝对音调、绝对音高。

absorption coefficient 吸声系数absorption loss 吸收损失ac 交流电ac bias 交流偏磁ac voltage 交流电压accentuation 加重、提升access 接近、入口、存取accessory 附属的，附件（形容词）accesspries 附属的、附件、配件、附属设备accmpanimenl 伴奏accordion 手风琴accrescendo 渐强accumulator 1、蓄电池2、累加器、存储器a-channel A通道acoustic 声学的、音响的acoustic backing 吸声衬垫acoustic box 助声箱acoustic color 音色acoustic effect 音响效果acoustic clasticty 声弹性acoustic feedback 声反馈acousticrefeneration 声波的一部分从声频放大系统同这个系统的前置部分或输入电路的机械耦合。

acoustic fidelity 声保真度acoustic filter 声过滤器acoustic generater 声发生器acoustic pressure 声压acoustic reflectivity 声反射率acoustic resonance 声共振acoustics 声学、音响学acoustic system 声系统acoustic trealment 声处理acoustic wave 声波acoustical couping 声耦合acoustical-electrical transducer 声-电转换器actinodielectric 光电介质actionoelectrictiy 光电效应actionoelectricity 光电action 动作、作用activtaion 激活、活化active 有功的、主动的、有源的actual sound 同期声A-D 模拟（电路）-数字（电路）abapter 接续器、连接头、适配器ADC 摸数转换器ADJ 调节、调整ADSR 这是合成器的包络波控制的四个阶段ADT 自动声迹（音）加倍A.DUB 声频复制、配音A.EDIT 自动编辑AES 声频工程师协会af 声频、音频afa 音频放大器A-fade 衰减AFC 自动频率控制AFL 调音台中指监听的声音处在衰减器后面的状态after sound 余音agc 自动增益控制age 老化A-IN 声频输入的缩写A-INSEL 声频输入的选择air coloum 空气拄alarm 告警、警报alc 自动电平控制alignment 调整、校准、校正alkaline cell 碱性电池allen screw 爱林螺钉alligator 接线夹、鳄鱼夹alpha α值alternating current 交流电流alternating current/direct current 交流/直流alternating current erasing head 交流抹音头alternating votltage 交流电压alternation 半周期alternator 交流发电机altitude 高度alto 女低音am 调幅ambience 环境声音ambient noise 环境噪声ambient sound 环境声ambient temperature 环境温度ambiophony 主体混响、环境立体声amp 安培、安；放大器ampere 安培ampere-hour 安培小时amplification 放大amplifier 放大器amplitude 幅度、振幅amplitude distortion 幅度失真amplitude modulation 调幅、幅度调制analog 模拟analog signal 模拟信号analog-to-digital conversion 摸（拟）-数（字）变换器analyser 分析仪、分析器anechoic 无回声的、消声anechoic enclosure 无回声密闭室、消声室anechoic room 无回声室、消声室angle 角、相角angle of incidence 入射角angle of lag(or lerd) 滞后角（或超前角）angular frequency 角频率ANL 自动嗓声限制anode 阳极anode current 阳极电流anodevoltage 阳极电压ANRS 自动嗓声抑制系统、自动降噪系统ANSI 美国国家标准协会antenna 天线antinodes 波腹antinoise microphone 抗噪声传声器antiphase 反相antiresonance 并联谐振antiresonant ciruit 并联谐振电路antiresonant frequency 并联谐振频率APRS 英国专业录音室协会AQL 可接受的质量水平、容许品质等级arpeggio 琶音articulation 清晰度artificial ear 人工耳artificial echo 人工回声artificial voice 仿真口声ASL 美国标准协会assign 分配、指定asynchronous 不同步、异步atmosphere microphone 专门收录空气中的环境声的传声器attack time 启动时间、上升时间ATE 自动测试设备attenuation netwoke 衰减网络attenuator 衰减器audibility 可听度audible 可听的audible tones 正常人耳能够觉察的声音，通常能认同频率范围为30到15000赫兹audio amplifier 音频放大器audio band 音频段audio componet 音频成分andio control cngineer 调音师、录音师audio cue channel 录象机声频提示通道audio equipment 声频设备、伴音设备audio frequency 声频、音频audio-frequency choke 音频扼流圈audio-frequency noise 音频嗓声audio-frequency oscillator 音频振荡器audio-frequency transformer 音频变压器audiogram 闻阀图、听觉阀图audio head 录音头、拾音头、还音头audio-level meter 音频电平表audio patch bay 音频配线架audiophile 音频爱好者、发烧友、讲究音质者audio signal 音频信号audio spectrum 音频频谱audio tape 录音磁带audio-visual 视听的、视听系统auditorium 观众厅aural 听觉的auto-man 自动-人工automatic 自动的automatic bass compensation 自动低音补偿automatic frequency control 自动频率控制(缩写AFC)automatic gain conltrol 自动增益控制(缩写AGC)automatic record changer 自动换片器automatic rewind 自动倒带automatic shutoff 自动停止automatic track shift 自动声道转换装置automatic tuning 自动调谐automatic volume compression 自动音量压缩automatic volume control 自动音量控制autotranstormer 自耦变压器aux 辅助插口auxiliary circuit 辅助电路A-V 视听（装置）、音频-视频A V COMPU 计算机控制A V系统average 平均average value 平均值AWG 美国线规(表示导线直径，号数越大，直径越细)axial lead 轴向引线axis 轴azimuth 方位角、方位b 巴。

matlab function模块实现滤波-概述说明以及解释1.引言1.1 概述概述部分的内容可以包括对该篇长文的主题和背景的简要介绍。

同时，可以说明该篇长文将围绕着MATLAB中的滤波函数展开讨论，并介绍滤波原理及其在信号处理领域中的重要性。

以下为可能的概述部分内容：引言在信号处理领域中，滤波是一项非常重要的技术。

通过滤波，我们可以对信号进行处理和改进，去除噪声、减小干扰，从而得到更好的信号质量。

而MATLAB作为一款强大的科学计算软件，在信号处理方面提供了许多有用的滤波函数和工具。

本篇长文将基于MATLAB function模块，探讨滤波的实现方法。

我们将从滤波原理的基础知识开始，介绍MATLAB中常用的滤波函数，以及如何设计和实现一个滤波模块。

通过学习本文，读者将能够理解滤波的基本原理和实现方法，并能够利用MATLAB的功能进行滤波处理。

本文的目的是为读者提供一个全面的理解MATLAB中滤波函数的能力，并通过实际案例的讲解和代码示例，帮助读者更好地掌握滤波模块的设计和实现技巧。

同时，本文还将评估所实现的滤波模块的效果，并展望该模块在实际应用中的前景。

总结起来，本文将深入探讨MATLAB中的滤波函数，并详细介绍滤波模块的设计与实现。

通过本文的学习，读者将能够掌握滤波的基本原理和实现方法，并具备设计和实现一个滤波模块的能力。

希望本文能为读者在信号处理领域的学习和应用中提供有力的支持。

文章结构部分的内容可以按照以下方式编写：1.2 文章结构本文主要介绍了如何使用Matlab function模块实现滤波功能。

文章的结构如下：引言：在引言部分，我们将对滤波的概念进行简要介绍，并对文章的结构和目的进行说明。

正文：正文部分分为三个主要部分。

2.1 滤波原理：在这一部分，我们将详细介绍滤波的原理，包括滤波的基本概念、滤波的分类以及常用的滤波方法。

2.2 MATLAB中的滤波函数：在这一部分，我们将介绍MATLAB中常用的滤波函数及其使用方法。

matlab中butter的用法Matlab是一种广泛应用于科学计算和工程领域的软件工具，它提供了许多强大的函数和工具箱，用于处理和分析数据。

其中一个常用的函数是butter函数，它用于设计数字滤波器。

数字滤波器是一种用于处理数字信号的工具，它可以去除或改变信号中的某些频率成分。

在实际应用中，我们经常需要对信号进行滤波，以去除噪声或突变，或者提取感兴趣的频率成分。

butter函数是Matlab中用于设计巴特沃斯滤波器的函数。

巴特沃斯滤波器是一种常见的滤波器类型，它具有平坦的幅频响应和最小的相位失真。

使用butter函数可以方便地设计出满足特定要求的巴特沃斯滤波器。

butter函数的基本语法如下：[b, a] = butter(n, Wn, 'ftype')其中，n是滤波器的阶数，Wn是归一化的截止频率，'ftype'是滤波器类型。

滤波器类型可以是'low'（低通滤波器）、'high'（高通滤波器）、'bandpass'（带通滤波器）或'bandstop'（带阻滤波器）。

butter函数返回两个向量b和a，分别表示滤波器的分子和分母系数。

我们可以使用这些系数来实现滤波器的功能。

下面是一个使用butter函数设计低通滤波器的示例：```matlabfs = 1000; % 采样频率fc = 100; % 截止频率Wn = fc / (fs/2); % 归一化的截止频率n = 4; % 滤波器阶数[b, a] = butter(n, Wn, 'low'); % 设计低通滤波器% 生成一个测试信号t = 0:1/fs:1; % 时间向量x = sin(2*pi*50*t) + sin(2*pi*150*t) + randn(size(t)); % 带有噪声的信号% 使用滤波器对信号进行滤波y = filter(b, a, x);% 绘制原始信号和滤波后的信号figure;subplot(2,1,1);plot(t, x);title('原始信号');subplot(2,1,2);plot(t, y);title('滤波后的信号');```在上面的示例中，我们首先定义了采样频率fs和截止频率fc。

结构紧凑的高选择性宽带带通滤波器钱颖;张凤娟;靳静【摘要】为实现结构紧凑和高选择性的宽带滤波器，在传统平行耦合线结构的基础上，作了适当改进，设计了3种结构新颖的三线耦合结构，均能够实现具有3个传输零点的宽带响应，且其中两个零点分别紧靠通带的上下边缘。

加工并测试了基于其中一种结构的宽带滤波器，工作频率为2.6 GHz，3 dB相对带宽为63%，3个传输零点分别位于1.46 GHz，3.77 GHz和5.13 GHz，介质基板采用Rogers 4003，厚度0.813 mm。

实测结果与仿真结果吻合良好，验证了结构的有效性。

%To achieve compact and highly selective wideband filter,on the basis of the traditional parallel coupled line structure,we make the appropriate improvements. Three novel coupled line structures are designed. All struc⁃tures exhibit a wideband response to three transmission zeros and two of them are close to the upper and lower edges of the passband. One filter has been designed,fabricated and measured. The operating frequency of filter is 2.6 GHz,3 dB fractional bandwidth(FBW)of the filter is 63%,transmission zeros are located at 1.46 GHz,3.77 GHz and 5.13 GHz respectively. The filter is designed on a Rogers 4003 dielectric substrate and the thickness of filter is 0.813 mm. Good agreement between the measured results and simulation ones is obtained,verifying the validity of structures.【期刊名称】《电子器件》【年(卷),期】2016(039)005【总页数】4页(P1059-1062)【关键词】宽带带通滤波器;三线耦合结构;奇偶模分析法;阶梯阻抗谐振器;传输零点【作者】钱颖;张凤娟;靳静【作者单位】无锡科技职业学院电子技术学院，江苏无锡214028;无锡科技职业学院电子技术学院，江苏无锡214028;中国电子科技集团第五十五研究所，南京210016【正文语种】中文【中图分类】TN713宽带滤波器作为微波通信系统中的关键无源器件，不仅在工业界引起了广泛的关注，在学术界也有非常高的研究价值。

振铃现象汇总找个数字电路，接上电源让它跑起来，然后⽤⽰波器去看看有规则波形的信号。

把⽰波器的采样率调到⾜够⾼，并利⽤沿触发模式捕捉波形，你能观察到波形在沿(不管是上升还是下降)之后有振幅很快衰减的⾼频振荡，那就是数字电路永远甩不掉的“振铃”。

振铃和过冲什么是过冲（overshoot）？过冲（Overshoot）就是第⼀个峰值或⾕值超过设定电压――对于上升沿是指最⾼电压⽽对于下降沿是指最低电压。

下冲（Undershoot）是指下⼀个⾕值或峰值。

过分的过冲（overshoot）能够引起保护⼆级管⼯作，导致过早地失效。

什么是下冲（undershoot）（ringback）？过冲（Overshoot）是第⼆个峰值或⾕值超过设定电压――对于上升沿过度地⾕值或对于下降沿太⼤地峰值。

过分地下冲（undershoot）能够引起假的时钟或数据错误（误操作）。

什么是振荡（ringing）？振荡（ringing）就是在反复出现过冲（overshoots）和下冲（undershoots）。

信号的振铃（ringing）和环绕振荡（rounding）由线上过度的电感和电容引起，振铃属于⽋阻尼状态⽽环绕振荡属于过阻尼状态。

信号完整性问题通常发⽣在周期信号中，如时钟等，振荡和环绕振荡同反射⼀样也是由多种因素引起的，振荡可以通过适当的端接予以减⼩，但是不可能完全消除。

⼀般指LC回路的⾃由衰减振荡。

如在开关电源中，变压器漏感与开关管（或整流⼆极管）结电容就会产⽣振铃。

例如某个频率信号，上升沿的顶峰超过平均⾼电平很多就是过冲，下降沿的顶峰超过平均低电平很活就是负冲，上升或下降产⽣波浪就叫振铃这类现像多数与电路中分布参数有关，例如电路板上两线之间的分布电容，导线⾃⾝的电感，芯⽚输⼊和输出端对地的电容，等等，很难完全避免。

在含电感的电路中更有电感⾃⾝的分布电容、变压器漏感等等。

频率较⾼时还需要考虑传输线的反射。

每个电路，电原理图可能完全相同，但实际制作时元器件布局不同，电路板布线不同，这种振铃和过冲也不同，没有具体布局布线，很难分析。

Switchable Wide Tuning Range Bandstop Filters for Frequency-Agile Radios Zhengzheng Wu, Yonghyun Shim, and Mina Rais-ZadehDepartment of Electrical Engineering & Computer Science, University of Michigan, Ann Arbor, MI 48109, USAAbstractThis paper reports on micromachined tunable bandstop filters that exhibit an octave frequency tuning range with high stopband rejection and low out-of-band loss. In addition to continuous frequency tuning, stopband switch on-off capability is realized by employing ohmic switches along with tunable capacitors. The fully re-configurable filters in this work are fabricated using a silicon-based integrated passive device technology and are the smallest-size bandstop filters reported in the low SHF range.IntroductionReconfigurable and cognitive radios require frequency-agile RF front-end modules to cover a wide range of wireless spectrum. Tunable filters are imperative components of cognitive radios and have been the focus of much research in the past [1], [2]. In the presence of strong out-of-band interferers, pre-select RF filters can protect the receiver from gain desensitization, and the receiver linearity requirement is significantly relaxed. Filters with high rejection provide Tx/Rx isolation and are needed in frequency-division duplexing (FDD) transceivers and transmitter spurious emission control. Compared to bandpass filters, bandstop filters exhibit lower passband insertion loss, minimizing the degradation of receiver noise figure, while providing high rejection level for removing spurious signals. Therefore, tunable bandstop filters have the potential to replace more complicated and higher loss switched bandpass filter banks used in multi-band RF front-ends. In this paper, we report on a switchable wide tuning range bandstop filter. Filters are realized in a silicon-based integrated passive device (IP D) technology intended for multi-chip module integration.IPD Fabrication ProcessThe silicon-based IP D technology developed in this work offers both high-Q fixed RF passive components and tunable RF micro-electromechanical systems (MEMS) [3]. Fig. 1 shows the fabrication process steps. It offers three metal layers, one dielectric layer and a sacrificial layer. The process starts with passivating the substrate which is high resistivity (>1 k·cm) silicon. The bottom metal is deposited and patterned. The sacrificial layer is then deposited and step etched to allow the formation of dual air-gaps (as shown in Fig. 1(d)) for realizing high analog tuning range (>5:1) MEMS capacitors, and contact dimples used in MEMS ohmic switches. An electroplated gold layer is utilized as the structural layer for RF MEMS devices, and a thick electroplated copper layer is utilized for forming high-Q inductive components and low-loss transmission lines. The sacrificial layer is removed to release the tunable capacitors and RF switches. Finally, silicon is selectively removed under inductive components to reduce the substrate loss.Fig. 1. Fabrication process flow of the IPD. (a): Deposit oxynitride dielectric as surface passivation layer and evaporate bottom metal layer; (b): Deposit and pattern dielectric layer for MIM capacitors; (c): Deposit a sacrificial layer; (d): Step etch the sacrificial layer; (e): Electroplate 2nd metal layer for MIM capacitors and RF MEMS structural layer; (f): Electroplate thick metal for high-Q inductors; (g): Sacrificial layer removal and substrate micromachining to create air-suspended inductors.Tunable Bandstop FiltersThe design of tunable bandstop filter is based on coupled transmission line configuration, as shown in Fig. 2. The transmission line is loaded with a capacitor for reduced electrical length. A pair of lumped coupled inductors (layout shown in Fig. 2) is used to imitate the coupled transmission lines in the band of interest. The advantage of using lumped components over transmission lines is that they occupy a smaller area. Using this filter design, narrow bandwidth bandstop filters with performances superior to conventional LC type filters can be implemented using low-value and high-Q inductors. Wide tuning range MEMS capacitors are employed to tune the filter center frequency. As shown in Fig. 3, a fabricated MEMS capacitor can be tuned from 0.38 pF to 2.1 pF with applying a voltage of up to 35 V, demonstrating a tuning range of 5.5:1. The MEMS capacitor is modeled considering the resistive (Rseries) and inductive parasitic (Lseries), as shown in Fig. 4. Recalling from Fig. 2, the capacitor is connected in series with an inductor to form the resonator tank in the bandstop filter. The parasitic inductance of the capacitor (Lseries) is absorbed into the main inductor of the tank. Therefore, the overall Q of the LC tank is improved and its usable frequency range is extended.20.5.1IEDM11-493 978-1-4577-0505-2/11/$26.00 ©2011 IEEE123Fig. 2. Circuit implementation of the bandstop filterlumped coupled inductor pair.Fig. 3. Measured tuning range of a fabricated MEMS caFig. 4. Circuit model of the RF MEMS capacitor.A two-pole tunable bandstop filter is realiztwo 1st-order bandstop filter cells. Fig. 5 showof a fabricated two-pole tunable bandstop fithe filter is 2.2 mm × 2.6 mm. The measureof the bandstop filter are plotted in Fig.frequency is tuned from 6.5 GHz to 3.1more than an octave frequency coverage. Atuning range, the insertion loss at both lopassbands is measured to be less than 1 dB.0510*******0.30.60.91.21.51.82.1Capacitance(pF)Bias Voltage (V)4r and layout of theapacitor.zed by cascadingws a SEM imageilter. The size ofed tuning results. 6. The centerGHz, achievingAcross the entireower and higherThe filter shapeshows significant improvementreported lumped LC filter impleme[6]. The stopband rejection level isfrequency range of 5−6.5 GHz. Afrequencies, the filter bandwidcapacitance of the tank is incrbandwidth reduction and also thefrequencies, the filter rejectionfrequencies below 5 GHz.Fig. 5. A SEM image of a tunable bandstopFig. 6. Measured frequency response of thbias voltage shown). (a) Insertion loss; (b) reThe linearity of the tunable bandsusing a two-tone test. A two-frequency of 5.25 GHz and inpuapplied to the bandstop filter when5.25 GHz. Figs. 7(a) and (b) showan input frequency offset of 1 kHz30350246-35-30-25-20-15-10-5InsertionLoss(dB)Frequency (G0246-40-30-20-100V5V9V11V13V14V15V16V17V18V29VReturnLoss(dB)Frequency (Gcompared with otherentations in this range [4]–s better than 20 dB in theAt lower stopband centerdth is reduced as thereased. Because of thislower inductor Q at lown level is degraded atfilter.he tunable bandstop filter (witheturn loss.stop filter is characterized-tone input with centerut power of -10 dBm isn the stopband is tuned tothe output spectrum withand 1 MHz, respectively.810120V5V9V11V13V14V15V16V17V18V29VGHz)81012GHz)20.5.2IEDM11-494The extracted 3rd–order input intercept point (IIP3) from the measurement is 3.6 dBm at 1 kHz frequency offset, as is shown in Fig. 8. At a higher two-tone frequency offset the 3rd-order inter-modulation output signals are below the noise floor, and the IIP3 cannot be extracted. This is because the MEMS capacitor has a lowpass response [1] that filters out the inter-modulation products with offset frequencies higher than the mechanical resonance frequency of the movable membrane. Therefore, inter-modulation products are highly attenuated if they fall in the lower and higher passbands of the bandstop filter, showing benefit of using MEMS devices as part of a filter.Fig. 7. Measured output spectrum with a two-tone test at 5.25 GHz and -10 dBm input power; (a) 1 kHz offset, and (b) 1 MHz offset.O u t p u t P o w e r (d B m )Input Power (dBm)Fig. 8. Extraction of IIP3 with a two-tone input frequency offset of 1 kHz.The tuning speed of the bandstop filter is measured by applying a step-function actuation bias to the MEMS capacitors. The measured tuning speed of the tunable bandstop filter is better than 80 μs as shown in Fig. 9.A p p l i e d Vo l t a g e (V )Time (μs)D e t e c t e d V o l t a g e (V )Fig. 9. Measured tuning speed of the tunable bandstop filter. The tuning speed is better than 80 µs.Switchable Bandstop FiltersIn a cognitive spectrum utilization scheme, it is useful to switch off the bandstop filter in case no interference is present. When the filter is switched off, additional channel loss introduced by the filter will be minimized and the available wireless spectrum will be fully utilized. In this work, a MEMS ohmic switch is exploited to add switch on/off capability to the wide tuning range bandstop filters. As shown in the circuit schematic of Fig. 10, a MEMS ohmic switch is connected in parallel with the tunable capacitor. When the RF MEMS ohmic switch is in contact, it shorts the capacitive load port to the ground. In this switched-off state, the filter becomes an all-pass network.Fig. 10. Circuit model of the tunable bandstop filter with switch on/off capability and the electrical model of the MEMS ohmic switch.In the proposed switchable bandstop filter design, the MEMS switch is placed in the coupled line section instead of in the main RF signal path (Fig. 10). Therefore, the filter loss is less sensitive to the contact resistance of the ohmic switch. The pass-band insertion loss of the filter having different contact resistance (R contact ) for the switch is simulated and shown in Fig. 11. Simulation results indicate that even with a contact resistance of 10Ω, the insertion loss is less than 0.83 dB up to 10 GHz. Because of the low sensitivity to contact resistance, the switchable filter can also employ RF MEMS switches that use hard metals (e.g. Ru) as the contact material. Such switches offer good reliability [7].Fig. 11. Insertion loss of the filter path when the bandstop filter is switched off using a MEMS ohmic switch.(a)(b)-4-224-120-80-400O u t p u t P o w e r (d B m )Frequency Offset (kHz)-4-224-120-80-40Frequency Offset (MHz)I n s e r t i o n L o s s (d B )Frequency (GHz)20.5.3IEDM11-495A SEM image of a fabricated switchable filter is shown in Fig. 12. The RF MEMS ohmic switch is embedded in the capacitive load port, as can be seen in the close-up view show in Fig. 12. The size of the switchable filter is 2.2 mm × 2.6 mm, similar to the size of the tunable bandstop filter. The measured response of the filtering path when the bandstop filter is switched off is shown in Fig. 13. With increasing actuation voltage on the switch, the contact resistance of the RF MEMS switch is reduced and the insertion loss of the switched-off bandstop filter is improved. The measured insertion loss is less than 0.84 dB up to 10 GHz. The higher insertion loss in measured results is due to the higher resistance of the electroplated metal and fabrication imperfections that cause non-ideal electrical performance for the lumped coupled inductors. The bandstop filter responses at switch on/off states are compared in Fig. 14.Fig. 12. A SEM image of the fabricated tunable bandstop filter with closed-up view and circuit model of the RF MEMS ohmic switch (up-state).I n s e r t i o n L o s s (d B )Frequency (GHz)6R e t u r n L o s s (d B )Frequency (GHz)Fig. 13. Measured responses of the switched-off bandstop filter with varied DC bias on MEMS ohmic switch; (a) Insertion loss, and (b) return loss.I n s e r t i o n L o s s (d B )Frequency (GHz)R e t u r n L o s s (d B )Fig. 14. Insertion loss and return loss when the bandstop filter is switched-on and switched-off (a 30 V bias on ohmic switch).ConclusionIn this paper, wide tuning range miniaturized bandstop filters are implemented. These tunable filters provide high interference rejection capability and low passband insertion loss. A stopband switch on-off technique is proposed which is tolerant to contact resistance of ohmic switches. Filters are fabricated using a silicon-based IP D technology which can be used to realize other miniaturized frequency-agile RF front-ends.AcknowledgementThe authors would like to acknowledge the staff of the Lurie Nanofabrication Facility at the University of Michigan for their assistance with fabrication. This work is supported by National Science Foundation under award number1055308.References[1] G.M. Rebeiz, et al., "Tuning in to RF MEMS," IEEE Microw. Mag.,vol. 10, no. 6, pp. 55-72, Oct. 2009.[2] H.A.C. Tilmans, W. De Raedt, and E. Beyne, "MEMS for wirelesscommunications: 'from RF-MEMS components to RF-MEMS-SiP'," Journal of Micromechanics and Microengineering , vol. 13, pp. S139-163, July 2003.[3] Z. Wu, Y. Shim, and M. Rais-Zadeh, "Miniaturized UWB bandpassfilters integrated with notch filters using a silicon-based integrated passive device technology," 2011 IEEE MTT-S International Microwave Symposium , June 2011.[4] M. Fernandez-Bolaos, T. Lisec, C. Dehollain, D. Tsamados, P. Nicole,and A.M. Ionescu, "Highly tunable band-stop filters based on AlN RF MEM capacitive switches with inductive arms and zipping capacitive coupling," 2009 IEEE International Electron Devices Meeting , Dec. 2009.[5] P. Ekkels, et al., "Air gap-based MEMS switch technology usingnickel surface micromachining," Sensors and Actuators A: Physical , vol. 166, no. 2, pp. 256-263, Apr. 2011.[6] H.S. Lee, D.H. Choi, and J.B. Yoon, "MEMS-based tunable LCbandstop filter with an ultra-wide continuous tuning range," IEEE Microw. Wireless Compon. Lett., vol. 19, no. 11, pp. 710-712, Nov. 2009. [7] C.D. Patel and G.M. Rebeiz, "An RF-MEMS switch with mN contactforces," 2010 IEEE MTT-S International Microwave Symposium , May 2010.20.5.4IEDM11-496。

滤波器设计向导[注]：滤波器向导能够帮助你设计出初步满足条件的各类滤波器，在此基础上，加上具体设计要求（通带或阻带特性的优化目标），就可以快速完成特定期间的设计。

The Microwave Office Filter Wizard is a filter synthesis plug-in application that accesses the simulation routines of MWO through a standard COM/API interface. Using the Filter Wizard, you can synthesize Bandpass, Bandstop, Highpass and Lowpass filters（带通、带阻、高通和低通） utilizing a variety of transmission response approximations including Butterworth, Chebyshev, and Bessel-Thomson.（响应类型）进入向导：在设计界面的左下方“project”按钮的最下方选“Wizards”你可以看到画面：点击下一步：上面的图形非常形象的给你提供可选择的各类滤波器。

There are four broad categories that transmission response shape requirements typically fall under:LowpassHighpassBandpassBandstop (also called Band-reject or Notch).You select one of these transmission response shapes when you begin the wizard.选取你所需要设计的类型及可再点击下一步开始向导设计。

级联法实现宽带LC带通滤波器设计赵兰;刘伟【摘要】利用高通、低通滤波器级联可以实现宽带带通滤波器,利用此方法设计了一个工作频段在100～400 MHz的LC宽带带通滤波器.将所设计的截止频率为100 MHz的高通滤波器HPF以及截止频率为400 MHz的低通滤波器LPF级联实现滤波器的宽带化设计.通过分别对HPF和LPF设置带外陷波点使该带通滤波器具有较好的矩形系数、带外抑制效果.ADS仿真结果验证了理论设计的可行性,并通过优化使滤波器带宽达到4倍频程,带内平坦,输入、输出端口匹配良好,滤波器矩形系数达到1.2.【期刊名称】《无线电工程》【年(卷),期】2010(040)008【总页数】4页(P42-45)【关键词】宽带滤波器;级联法;陷波点;ADS仿真【作者】赵兰;刘伟【作者单位】上海师范大学,天华学院,上海,201815;上海师范大学,天华学院,上海,201815【正文语种】中文【中图分类】TN713.50 引言滤波器是通信工程中常用的重要器件,它对信号具有频率选择性,在通信系统中通过或阻断、分开或合成某些频率的信号,被广泛地应用于各种电信设备和控制系统中[1]。

随着计算机技术、集成工艺和材料工业的迅速发展,各国越来越重视滤波器的性能及应用范围的提高,并致力于将其应用到更多产品的开发和研制。

滤波器已经成为所有电子部件中使用最广、技术最复杂的器件之一。

宽频带、小型化、低功耗器件一直以来是微波射频电路的研究热点,带通滤波器中如果上截止频率对下截止频率的比超过2(一个倍频程),则为宽带型带通滤波器[2]。

滤波器宽带化的研究主要集中在LC带通滤波器和微带带通滤波器宽带化两方面。

将高通滤波器、低通滤波器级联实现滤波器的宽带化设计,用这种方法构成的带通滤波器带宽较宽,且频带截止频率容易调整。

本文设计了一个工作频段在100～400 MHz的LC宽带带通滤波器实例。

1 滤波器理论设计方法在传统设计理论的基础上,现今滤波器的设计方法更为多样化。