低通滤波器

应用报告 ZHCA0�� – �00�年��月 FilterProTM MFB及Sallen-Key 低通滤波器程序 运算放大器应用, 高性能线性产品John Bishop, Bruce Trump, R. Mark Stitt FilterPro低通滤波器设计程序 2 巴特沃兹（最大幅度平坦度） 3 切比雪夫（等纹波幅度） 3 贝塞尔（最大时间延迟平坦度） 3 概述 5 巴特沃兹响应 5 切比雪夫响应 5 贝塞尔响应 5 电路实现 6 MFB拓扑 6 Sallen-Key拓扑 7 使用FilterPro程序 7 计算机要求 7 安装 7 入门 7 程序特点 9 打印结果 9 敏感度 9 MFB及Sallen-Key拓扑的fn敏感度 9 Q值敏感度 9 使用敏感度显示特性 10 使用籽电阻(Seed Resistor)设定 10 电容值 11 针对运算放大器输入电容进行补偿——仅用于Sallen-Key拓扑 11 电容选择 11 使用fn及Q值显示 12 运算放大器选择 12 运算放大器带宽 12 运算放大器转换频率 12 UAF42通用有源滤波器 13 摘要 尽管低通滤波器在现代电子学领域的地位越来越重要，但其设计及定型工作仍是冗长乏味且耗时巨 大的。FilterPro程序设计用于辅助低通滤波器设计，以实现多反馈(MFB)及Sallen-Key拓扑。本报告可作 为FilterPro操作指南，同时还包括了其他方面的问题，记述了设计人员涉足该程序的必备信息以及程序 所交付的功能。 目录 FilterPro 是德州仪器的注册商标。 � � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn 电流反馈放大器 13 全差分放大器 13 MFB滤波器响应示例 14 结论 15 图片目录 图1. 偶数阶（4极点）、3 dB纹波切比雪夫滤波器的频率响应（截止于0 dB） 4 图2. 奇数阶（5极点）、3 dB纹波切比雪夫滤波器的频率响应（截止于-3 dB） 4 图3. 图3. 实极点部件（单位增益、一阶巴特沃兹；f-3dB=1/2π×R1×C1） 4 图4. 二阶低通滤波器 4 图5. 三阶低通滤波器 4 图6. 采用层叠复极点对部件的偶数阶低通滤波器 5 图7. 采用层叠复极点对部件+单实极点部件的奇数阶低通滤波器 5 图8. MFB复极点对部件（增益= - R2/R1） 6 图9. Sallen-Key复极点对部件，单位增益（增益=1） 6 图10. Sallen-Key复极点对部件（增益= 1+ R4/R3） 6 图11. FilterPro的屏幕显示，展示了40 dB了益的9极点MFB滤波器 8 图12. 三阶低通滤波器驱动ADC 13 图13. 5阶20 kHz巴特沃兹、切比雪夫及贝赛尔单位增益MFB低通滤波器的增益随频率的变化， 所示为总体滤波器响应 14 图14. 5阶20 kHz巴特沃兹、切比雪夫及贝赛尔单位增益MFB低通滤波器的增益随频率的变化，所示为过渡带 (Transition-band)的详细情况 14 图15. 5阶20 kHz巴特沃兹低通MFB滤波器的阶跃响应 14 图16. 5阶20 kHz 切比雪夫低通MFB滤波器的阶跃响应 14 图17. 5阶20 kHz贝赛尔低通MFB滤波器的阶跃响应 15 图18. 三种20 kHz MFB低通滤波器的实测失真 15 格目录 表1. 滤波器电路vs.滤波器介数 6 FilterPro低通滤波器设计程序 源自德州仪器的FilterPro程序使有源低通滤波器的设计工作变得更为轻松。该程序可辅助设计低通 滤波器并实现多反馈点(MFB)拓扑。由于在某些场合Sallen-Key滤波器拓扑更为优秀，因此该程序也支持 Sallen-Key低通滤波器的设计。 理想的低通滤波器将完全消除截至频率以上的信号，并使得低于截至频率（处于通带内）的信号完好 的通过。但对实际的滤波器来说，需要做不同的折衷以逼近理想的状态。某些滤波器类型针对通带内的增 益平坦度作了优化，另一些则以通带内的增益变化（纹波）作为代价，折衷获取陡峭的滚降；还具有其他 的滤波器类型，为了获取较好的脉冲响应保真度而同时对平坦度及滚降速率做了折衷。FilterPro支持三种 最常见的全极点滤波器类型：巴特沃兹、切比雪夫及贝塞尔。 � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn 巴特沃兹（最大幅度平坦度） 该类型的滤波器具有尽可能平坦的通带幅度响应。截止频率的衰减设计为–3 dB。高于截止频率的频带衰减 具有适中的斜率—— 20 dB滚降每十倍频程每极点。巴特沃兹滤波器的脉冲响应具有适当的过冲(overshoot)及振 铃(ring)。 切比雪夫（等纹波幅度） 注释：切比雪夫(Chebyshev)先生的名字还被音译为Tschebychev、Tschebyscheff或Tchevysheff. 与巴特沃兹滤波器相比，此类型的滤波器在通带以外的衰减更为陡峭——该优点是以牺牲通带内的幅度变化 量（纹波）为代价的。与巴特沃兹及贝赛尔响应（3 dB 衰减位于截止频率处）不同，切比雪夫滤波器的截止频率 定义为响应滚降至低于纹波带的频点。对于偶数阶滤波器而言，所有纹波均高于0 dB了益的直流响应，因此截止 频点位于0 dB 衰减处，如图1所示。对于奇数阶滤波器来说，所有的纹波均低于0 dB了益的直流响应，截止频率 则定义为低于纹波带最大衰减点（- ripple dB的频点），如图2所示。在极点数量一定时，增加通带纹波可实现更 陡峭截止。相对于巴特沃兹滤波器而言，切比雪夫滤波器的脉冲响应具有更大的振铃。 贝赛尔（最大延迟时间平坦度） 也称为汤姆逊(Thomson)型滤波器。由于其线性相位响应特性，使得此类滤波器具有最优的脉冲响应（最小 化过冲及振铃）性能。对于给定的极点数量而言，贝赛尔的幅频响应并不如巴特沃兹平坦，-3 dB 截止频率以外 频带的衰减也不如巴特沃兹陡峭。尽管须采用更高阶的贝赛尔滤波器来逼近给定的巴特沃兹滤波器的幅频响应， 但考虑到贝赛尔滤波器的脉冲响应保真度，增加一定的复杂性（源于附加的滤波器部件）也是物有所值的。 � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cnSBFA001A � FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program Figure 1. Response vs Frequency of Even-Order (4-pole), 3 dB Ripple Chebychev Filter Showing Cutoff at 0 dB. Figure 2. Response vs. Frequency of Even-Order (5-pole), 3 dB Ripple Chebychev Filter Showing Cutoff at -3 dB Figure 3. Real Pole Section (Unity-Gain, First-Order Butterworth; f-3dB = 1/2·ππππ·R1·C1) Figure 4. Second-Order Low-Pass Filter. Figure 5. Third-Order Low-Pass Filter. 图1. 偶数阶（4极点）、3dB纹波切比雪夫滤 波器的频率响应（截止于0dB） 图2. 奇数阶（5极点）、3dB纹波切比雪夫滤 波器的频率响应（截止于-3dB） SBFA001A � FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program Figure 1. Response vs Frequency of Even-Order (4-pole), 3 dB Ripple Chebychev Filter Showing Cutoff at 0 dB. Figure 2. Response vs. Frequency of Even-Order (5-pole), 3 dB Ripple Chebychev Filter Showing Cutoff at -3 dB Figure 3. Real Pole Section (Unity-Gain, First-Order Butterworth; f-3dB = 1/2·ππππ·R1·C1) Figure 4. Second-Order Low-Pass Filter. Figure 5. Third-Order Low-Pass Filter. 图3. 实极点部件（单位增益、一阶巴特沃兹； f-3dB=1/2π×R1×C1） 图4. 二阶低通滤波器 SBFA001A � FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program Figure 1. Response vs Frequency of Even-Order (4-pole), 3 dB Ripple Chebychev Filter Showing Cutoff at 0 dB. Figure 2. Response vs. Frequency of Even-Order (5-pole), 3 dB Ripple Chebychev Filter Showing Cutoff at -3 dB Figure 3. Real Pole Section (Unity-Gain, First-Order Butterworth; f-3dB = 1/2·ππππ·R1·C1) Figure 4. Second-Order Low-Pass Filter. Figure 5. Third-Order Low-Pass Filter.图5. 三阶低通滤波器 � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn 图6. 采用层叠复极点对部件的偶数阶低通滤波器 SBFA001A FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program 5 Figure 6. Even-Order Low-Pass Filter Using Cascaded Complex Pole-Pair Sections. Figure 7. Odd-Order Low-Pass Filter Using Cascaded Complex Pole-Pair Sections Plus One Real-Pole Section. Summary Butterworth Response Advantages: It provides maximally flat magnitude response in the pass-band. It has good all- around performance. Its pulse response is better than Chebyshev. Its rate of attenuation is better than that of Bessel. Disadvantages: Some overshoot and ringing is exhibited in step response. Chebyshev Response Advantages: It provides better attenuation beyond the pass-band than Butterworth. Disadvantages: Ripple in pass-band may be objectionable. There is considerable ringing in step response. Bessel Response Advantages: It provides best step response: very little overshoot or ringing. Disadvantages: It exhibits slower rate of attenuation beyond the pass-band than Butterworth. SBFA001A FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program 5 Figure 6. Even-Order Low-Pass Filter Using Cascaded Complex Pole-Pair Sections. Figure 7. Odd-Order Low-Pass Filter Using Cascaded Complex Pole-Pair Sections Plus One Real-Pole Section. Summary Butterworth Response Advantages: It provides maximally flat magnitude response in the pass-band. It has good all- around performance. Its pulse response is better than Chebyshev. Its rate of attenuation is better than that of Bessel. Disadvantages: Some overshoot and ringing is exhibited in step response. Chebyshev Response Advantages: It provides better attenuation beyond the pass-band than Butterworth. Disadvantages: Ripple in pass-band may be objectionable. There is considerable ringing in step response. Bessel Response Advantages: It provides best step response: very little overshoot or ringing. Disadvantages: It exhibits slower rate of attenuation beyond the pass-band than Butterworth. 图7. 采用层叠复极点对部件+单实极点部件的奇数阶低通滤波器 概述 巴特沃兹响应 优点：巴特沃兹滤波器提供了最大的通带幅度响应平坦度，具有良好的综合性能，其脉冲响应优于切比雪夫，衰 减速度优于贝赛尔。 缺点：阶跃响应存在一定的过冲及振荡。 切比雪夫响应 优点：与巴特沃兹相比，切比雪夫滤波器具有了更良好的通带外衰减。 缺点：通带内纹波令人不满，阶跃响应的振铃较严重。 贝赛尔响应 优点：贝赛尔滤波器具有最优的阶跃响应——非常小的过冲及振铃。 缺点：与巴特沃兹相比，贝赛尔滤波器的通带外衰减较为缓慢。 � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn 电路实现 此程序的偶数阶滤波器设计由层叠的复极点对(pole-pair)组成。奇数阶滤波器则包含了额外的实极点部件。图 3至图7 展示了推荐的堆叠排列方式。图示的附加实极点部件位于其他部件之前，但在某些配置中，实极点部件后 置可获得更好的效果（敬请参见图12）。此程序将自动的将低 Q值的层级排列于高Q值的层级之前，以避免运算 放大器的输出因增益过高而饱和。程序所能设计的滤波器最高为10阶。 表1. 滤波器电路vs滤波器阶数 SBFA001A � FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program Circuit Implementation Even-order filters designed with this program consist of cascaded sections of complex pole- pairs. Odd-order filters contain an additional real-pole section. Figures � through � show the recommended cascading arrangement. The figures show the additional real-pole section ahead of the other sections, but some configurations are better with the real-pole section following (see Figure ��). The program automatically places lower Q stages ahead of higher Q stages to prevent op amp output saturation due to gain peaking. The program can be used to design filters up to �0th order. FILTER ORDER FIGURE � pole Figure � � poles Figure � � poles Figure � � or more poles (even order) Figure � � or more poles (odd poles Figure � Table 1. Filter Circuit vs Filter Order Complex Pole-Pair Circuit The choice of a complex pole-pair circuit depends on performance requirements. FilterPro supports the two most commonly used active pole-pair circuit topologies: • Multiple Feedback (MFB)—shown in Figure �. • Sallen-Key—shown in Figures � and �0. Figure 8. MFB Complex Pole-Pair Section. (Gain = — R2/R1) Figure 9. Sallen-Key Complex Pole-Pair Section. (Gain = 1) Unity Gain Figure 10. Sallen-Key Complex Pole-Pair Section. (Gain = 1+ R4/R3) MFB Topology The MFB topology (sometimes called Infinite Gain or Rauch) is often preferred due to assured low sensitivity to component variations—see sensitivity section. 滤波器阶次 图 单极点1 图3 双极点2 图4 三极点3 图5 4极点或更多（偶数阶） 图6 5极点或更多（奇数极点） 图7 复极点对电路 复极点对电路的选择取决于所需的性能。 FilterPro可支持两类最常用的有源极点对电路拓扑： 多反馈 (MFB)——如图8所示。 Sallen-Key——如图9及图10所示。 • • 图8. MFB复极点对部件 （增益= - R2/R1） 图9. Sallen-Key复极点对部件， 单位增益（增益=1） 图10. Sallen-Key复极点对部件 （增益= 1+ R4/R3） MFB拓扑 MFB拓扑（也称为无限增益拓扑或Rauch拓扑）对元件值改变的敏感度较低，因此较为常用——敬请参见敏 感度部分。 � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn Sallen-Key拓扑 在某些例子中，Sallen-Key拓扑证明更为优秀。就经验法则而言，下列情况时，Sallen-Key拓扑更佳： 1)了益精度较为重要，以及 2)采用了单位增益滤波器，以及 3)极点对Q值较低（例如，Q <3） 在单位增益时，由于运算放大器被用作单位增益缓冲器，使得 Sallen-Key拓扑具有了与生俱来的卓越增益精 度。对MFB拓扑而言，增益则取决于R2/R1的电阻比值。单位增益Sallen-key拓扑还具有元件需求较少的优势（仅 需两个电阻，MFB需三个电阻）。 在应用于高Q值高频率滤波器部件之时，Sallen-Key拓扑也是可取的。在此类部件中，若采用MFB设计，C1 值必需很低以得到合理的电阻值。而由于寄生电容干扰使得低电容值将导致极大的误差。 最佳的滤波器设计将是MFB及Sallen-Key部件的结合。为了实现该目标，可使用FliterPro分别基于两种电路类 型针对同一设计定义的两套元件值，而后在设计的不同部分采用不同的元件值，以构建你的滤波器设计。 使用FilterPro程序 将每个数据逐一输入之后，程序将自动计算出滤波器的性能及所有的滤波器元件值。从而允许你采用试凑 (what if)的程序表型设计方法。例如，你可以通过试验及误差结果，快速的得到给定滚降条件下所需的极点数 量。 计算机要求 FilterPro需求windows 95、NT 3.5或更高的操作系统。显示分辨率的最低配置为800x600。打印机（可批量 的打印屏幕截图）——本地的或网络的，可予以辅助，但并非必备的。 安装 运行硬盘或CD上setup.exe 即可将 FilterPro 安装到您的电脑之上。 入门 初次使用该程序，你可以点击桌面上的FilterPro图表进入。另一途径是点击Start（开始），Programs（所 有程序），而后点击FliterPro。此时，你已经默认设计了一个3极点、1 kHz的巴特沃兹型滤波器，元件值如示意 图所示。如需进行不同的设计，点击下列选项的任一单选按钮(radio button)。屏幕响应图的左侧将出现提示， 以指导你使用程序。如有需要，可参照此处的程序表以获取详细信息。所需的全部设定均包含在设置框(Setting frame)之内。 1) 在电路类型选框内选择极点对电路：MFB或Sallen-Key 2) 在滤波器类型选框内选择滤波器类型：Butterworth（巴特沃兹）、Chebyshev（切比雪夫） 贝赛尔(Bessel)。 � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn 3) 切比雪夫型滤波器须输入纹波数值：0.0001 dB至10 dB 4) 输入所需的极点数：1 to 10（对贝赛尔或切比雪夫型而言，至少 2极点） 5) 输入滤波器截止频率：1 mHz至100 MHz 6) 如果希望在特定的频率点上查看当前所设计的滤波器的增益/相位响应（默认值为截止频率的10倍）。可在 Response Freq输入框填入所感兴趣的频率。增益/相位值将在fn、Q、响应显示区域给出。 7) 如果希望改变电阻量值(resistor scaling)，可在R1 Seed输入框输入。电容值也会做相应的改变。 8) 如果希望改变部件的增益，可在相应的增益输入框内填入所期望的数值。默认增益值为1.0-V/V每部件。 9) 如果希望自定义的电容值，可在C1或C2输入框内输入。该操作将导致籽电阻(seed resistor)输入无效。 10) 如果希望采用标准的1%误差电阻（取代严格精准的电阻）进行设计，可点选1% Resistors确认框。 SBFA001A � FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program �) For the Chebyshev filter type, enter ripple amount: 0.000� dB to �0 dB �) Enter the desired number of poles: � to �0 (� min. for Bessel or Chebychev) �) Enter the filter cutoff frequency: � mHz to �00 MHz �) If you want to view the gain/phase response of the current filter design at a particular frequency (the default value is �0 times the cutoff frequency), enter the frequency of interest on the response entry box. The gain/phase values are displayed on the fn, Q, Response display fields. �) If you want to change the resistor scaling, enter a value on the R� Seed entry. This will also change the capacitor values accordingly. �) If you want to change the gain of a section, enter the desired value into the appropriate gain entry box. Default value for gain is �.0-V/V in each section. �) If you want to enter your own capacitor values, enter them into the appropriate C� or C� entry boxes. This will cause the seed resistor entry to be ignored. �0) If you want to design with standard �% resistors instead of exact resistors, click the 1% Resistors check box. Figure 11. Screen Display of FilterPro Showing a 9 Pole MFB Filter With a Gain of 40 dB.图11. FilterPro的屏幕显示，展示了40 dB了益的9极点MFB滤波器 � ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn 程序特点 打印结果 可选择打印(Print)菜单栏的选项进行结果打印。所显示的对话框将用于打印屏幕。在打印开始时，常规的屏 幕尺寸将扩大以容纳一个信息表——包含了示意图中未显示的信息，如敏感度数据或元件值。扩大的屏幕将被截 取并发送至打印机。如果由于位置或分辨率的关系使得屏幕不完全可见，则仅有可见部分会被打印。 敏感度 敏感度是当元件值改变时，滤波器性能受影响的度量。所考虑的重要参数为自然频率(fn)及Q值。 MFB and Sallen-Key的fn敏感度 不管采用MFB 还是Sallen-Key滤波器拓扑，fn对电阻、电容及滤波器增益变化的敏感度始终不高。 SBFA001A FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program 9 Program Features To Print Results To print results select the Print menu item. It displays a dialog box that can be used to print the screen. When printing is started, the normal screen size increases to include a table containing information not shown on the schematic (sensitivity data or component values). The larger screen is then captured and sent to the printer. If the screen is not fully visible, due to position or size, only what is visible is printed. Sensitivity Sensitivity is the measure of the vulnerability of a filter’s performance to changes in component values. The important filter parameters to consider are natural frequency (fn ) and Q. fn Sensitivity for Both MFB and Sallen-Key Sensitivity of fn to resistor, capacitor, and amplifier gain variations is always low for both the Sallen-Key and MFB filter topologies. %/%5.0±== fCfR SS where: =fCfCfR SSS ,, Sensitivity of fn to resistor, capacitor, and gain variations Q Sensitivity For the MFB topology, sensitivities to Q are also always low, but sensitivities for the Sallen-Key topology can be quite high—exceeding � • K • Q�. K is the variable used here for gain. At unity gain, the Sallen-Key Q sensitivity to resistor and capacitor variations is always low. Unfortunately, however, the sensitivity of the unity-gain Sallen-Key pole-pair to op amp gain can be high. Q Sensitivity for MFB Pole-Pair %/%5.0±=QCS )(2 332 332 RKRR RKRRS QR ⋅++ ⋅−−±= (MFB complex pole-pair) 332 3 RKRR RKS QK ⋅++ ⋅±= (MFB complex pole-pair) Notice, by inspection: QRS is always less than ±0.�%/%, and Q KS is always less than �.0%/%. 0=fKS 此处： =fkfCfR SSS ,, 分别为fn对电阻、电容及滤波器增益变化的敏感度。 Q值敏感度 对于MFB拓扑而言，Q值敏感度依然较低，但 Sallen-Key的Q值敏感度却可能会很高——超过2 • K • Q2。此 处的K 是增益相关的变量。在单位增益时，Sallen-Key拓扑对电阻及电容变化的Q值敏感度依然较低，然而令人遗 憾，单位增益Sallen-Key极点对对运算放大器增益变化的敏感度有可能较高。 MFB极点对的Q值敏感度 SBFA001A FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program 9 Program Features To Print Results To print results select the Print menu item. It displays a dialog box that can be used to print the screen. When printing is started, the normal screen size increases to include a table containing information not shown on the schematic (sensitivity data or component values). The larger screen is then captured and sent to the printer. If the screen is not fully visible, due to position or size, only what is visible is printed. Sensitivity Sensitivity is the measure of the vulnerability of a filter’s performance to changes in component values. The important filter parameters to consider are natural frequency (fn ) and Q. fn Sensitivity for Both MFB and Sallen-Key Sensitivity of fn to resistor, capacitor, and amplifier gain variations is always low for both the Sallen-Key and MFB filter topologies. %/%5.0±== fCfR SS where: =fCfCfR SSS ,, Sensitivity of fn to resistor, capacitor, and gain variations Q Sensitivity For the MFB topology, sensitivities to Q are also always low, but sensitivities for the Sallen-Key topology can be quite high—exceeding � • K • Q�. K is the variable used here for gain. At unity gain, the Sallen-Key Q sensitivity to resistor and capacitor variations is always low. Unfortunately, however, the sensitivity of the unity-gain Sallen-Key pole-pair to op amp gain can be high. Q Sensitivity for MFB Pole-Pair %/%5.0±=QCS )(2 332 332 RKRR RKRRS QR ⋅++ ⋅−−±= (MFB complex pole-pair) 332 3 RKRR RKS QK ⋅++ ⋅±= (MFB complex pole-pair) Notice, by inspection: QRS is always less than ±0.�%/%, and Q KS is always less than �.0%/%. 0=fKS （MFB复极点对） （MFB复极点对） 通过观察可发现， QKS 则始终小于±1.0%/%。 �0 ZHCA053 FilterProTM MFB及Sallen-Key低通滤波器设计程序 http://www.ti.com.cn Sallen-Key极点对（增益=1）的Q值敏感度 SBFA001A �0 FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program Q Sensitivity for Gain = 1 Sallen-Key Pole-Pair %/%5.0±=QCS )(2 21 21 RR RRS QR + −±= (Sallen-Key complex pole-pair) So, QRS is always less than ±0.�%/%. 22 2 QSS QK ⋅<< S (Sallen-Key complex pole-pair) where: =QKQCQR SSS ,, Sensitivity of fn and Q to resistor, capacitor and gain variations (%/%) K = Op amp gain (V/V) Figure � circuit, K=R�/R� Figure � circuit, K=�.0 Figure �0 circuit K=�+R�/R� NOTE: FilterPro always selects component values so unity-gain Sallen-Key QKS will be closer to Q� than to � • Q�. However, it will allow you to design Sallen-Key pole-pairs with high sensitivities (high Qs and GAIN >> �). You must make sure that sensitivities to component variations do not make these designs impractical. A feature in the display allows you to view the f n and Q sensitivity of filter sections to resistor and capacitor variations. Using the Sensitivity Display Feature To use the Sensitivity display option, click on the sensitivity radio button in the Settings area of the screen. The schematic shows sensitivity of fn and Q to each component for each filter section. The format is Sf ; SQ. Rather than displaying the derivative with respect to component variations, the program calculates fn and Q change for a �% change in component values. This gives a more realistic sensitivity value for real-world variations. Using the Seed Resistor Setting The Seed Resistor setting allows you to scale the computer-selected resistor values to match the application. Move the cursor to the Seed Resistor field and enter your seed resistor value. The default value of �0 k Ω is suggested for most applications. When the circuit is in a power sensitive environment (battery power, solar power, etc.) the value can be increased to decrease power consumption. Some high speed op amps require lower feedback resistance, so their seed resistor value should be decreased. （Sallen-Key复极点对） 因此 QRS 始终小于±0.5%/%。 SBFA001A �0 FilterProTM MFB and Sallen-Key Low-Pass Filter Design Program Q Sensitivity for Gain = 1 Sallen-Key Pole-Pair %/%5.0±=QCS )(2 21 21 RR RRS QR + −±= (Sallen-Key complex pole-pair) So, QRS is always less than ±0.�%/%. 22 2 QSS QK ⋅<< S (Sallen-Key complex pole-pair) where: =QKQCQR SSS ,, Sensitivity of fn and Q to resistor, capacitor and gain variations (%/%) K = Op amp gain (V/V) Figure � circuit, K=R�/R� Figure � circuit, K=�.0 Figure �0 circuit K=�+R�/R� NOTE: FilterPro always selects component values so unity-gain Sallen-Key QKS will be closer to Q� than to � • Q�. However, it will allow you to design Sallen-Key pole-pairs with high sensitivities (high Qs and GAIN >> �). You must make sure that sensitivities to component variations do not make these designs impractical. A feature in the display allows you to view the f n and Q sensitivity of filter sections to resistor and capacitor variations. Using the Sensitivity Display Feature To use the Sensitivity display option, click on the sensitivity radio button in the Settings area of the screen. The schematic shows sensitivity of fn and Q to each component for each filter section. The format is Sf ; SQ. Rather than displaying the derivative with respect to component variations, the program calculates fn and Q change for a �% change in component values. This gives a more realistic sensitivity value for real-world variations. Using the Seed Resistor Setting The Seed Resistor setting allows you to scale the computer-selected resistor values to match the application. Move the cursor to the Seed Resistor field and enter your seed resistor value. The default value of �0 k Ω is suggested for most applications. When the circuit is in a power sensitive environment (battery power, solar power, etc.) the value can be increased to decrease power consumption. Some high speed op amps require lower feedback resistance, so their seed resistor value should be decreased. （Sallen-Key复极点对） SBFA001A �0 FilterProTM MFB and Sallen-Key Low-Pass Filter