Filter Design in Thirty Seconds

Application Report SLOA093 December 2001 Filter Design in Thirty Seconds Bruce Carter High Performance Analog ABSTRACT Need a filter fast? No theory, very little math just working filter designs, and in a hurry? This is the right document. Contents 1 Introduction...2 2 Low Pass Filter...4 3 High Pass Filter...5 4 Narrow (Single Frequency) Band Pass Filter...6 5 Wide Band Pass Filter...7 6 Notch (Single Frequency Rejection) Filter...8 7 Band Reject Filter...9 Appendix A Standard Resistor and Capacitor Values...12 Appendix B Filter Notes (for the More Technically Minded)...13 Figures Figure 1. Low Pass Filter...2 Figure 2. High Pass Filter...2 Figure 3. Narrow (Single Frequency) Band Pass...3 Figure 4. Wide Band Pass...3 Figure 5. Notch Filter Single Frequency Rejection...3 Figure 6. Band Reject Filter...4 Figure 7. Low Pass Filter for ± Supplies...4 Figure 8. Low Pass Filter for a Single Supply...4 Figure 9. High Pass Filter for ± Supplies...5 Figure 10. High Pass Filter for a Single Supply...5 Figure 11. Narrow Band Pass Filter for ± Supplies...6 Figure 12. Narrow Band Pass Filter for a Single Supply...6 Figure 13. Wide Band Pass Filter for ± Supplies...7 Figure 14. Wide Band Pass Filter for a Single Supply...7 Figure 15. Narrow Band Pass Filter for ± Supplies...8 Figure 16. Narrow Band Pass Filter for a Single Supply...9 Figure 17. Band Reject Filter for ± Supplies...10 Figure 18. Band Reject Filter for a Single Supply...10 1

1 Introduction This document is intended for designers that do not have the time to check filter theory in old college textbooks and try to translate transfer equations into something that can be put into production. This is like looking at the back of the textbook for the answer. Speaking of the back of the book Appendix B contains a brief introduction to the filter circuits given here, and the limitations of this quickie approach to design. To design a filter, four things must be known in advance: The power supplies available: positive / negative or only positive (single supply) The frequencies that need to be passed, and those that need to be rejected. A transition frequency, the point at which the filter starts to work or a center frequency around which the filter is symmetrical. An initial capacitor value pick one somewhere from 100 pf for high frequencies to 0.1 µf for low frequencies. If the resulting resistor values are too large or too small, pick another capacitor value. Ready? Let s design the filter. Pick the filter type from one of the following 6 options that represents the frequencies to be passed (shaded area): Figure 1. Low Pass Filter Go to Section 2 Figure 2. High Pass Filter Go to Section 3 2 Filter Design in Thirty Seconds

Figure 3. Narrow (Single Frequency) Band Pass Go to Section 4 Figure 4. Wide Band Pass Go to Section 5 Figure 5. Notch Filter Single Frequency Rejection Filter Design in Thirty Seconds 3

Figure 6. Band Reject Filter 2 Low Pass Filter Supply Supply Figure 7. Low Pass Filter for ± Supplies Supply Supply R3 Cin R4 Cout Figure 8. Low Pass Filter for a Single Supply Design Procedure: Pick : Calculate = * 2: 4 Filter Design in Thirty Seconds

Calculate and = Appendix A). 2 1 2 * π * * Frequency SLOA093 : (pick a standard value from For the single supply case only: Calculate Cin = Cout = 100 to 1000 times (not critical): DONE 3 High Pass Filter Supply Supply Figure 9. High Pass Filter for ± Supplies Supply Cout Supply / 2 Design Procedure: Pick = : Figure 10. High Pass Filter for a Single Supply Calculate : Appendix A). 1 : (pick a standard value from 2 * π * * Frequency Filter Design in Thirty Seconds 5

Calculate : Appendix A). 2 1 : (pick a standard value from 2 * π * * Frequency For the single supply case only: Calculate Cout = 100 to 1000 times (not critical): DONE 4 Narrow (Single Frequency) Band Pass Filter NOTE: These circuits include a gain of 10 (20 db) at the center frequency. Supply R3 R4 Supply Figure 11. Narrow Band Pass Filter for ± Supplies Supply Cin R3 R4 Cout Supply / 2 Design Procedure: Figure 12. Narrow Band Pass Filter for a Single Supply Pick = : 6 Filter Design in Thirty Seconds

Calculate = R4: Appendix A). 1 : (pick a standard value from 2 * π * * Frequency Calculate R3 = 19 * Calculate = 19 For the single supply case only: Calculate Cin = Cout = 100 to 1000 times (not critical): DONE 5 Wide Band Pass Filter NOTE: The start and ending frequencies of the band should be at least five times different. Supply Supply Supply Supply Figure 13. Wide Band Pass Filter for ± Supplies Supply Supply Cout Supply / 2 Design Procedure: Figure 14. Wide Band Pass Filter for a Single Supply Go to Section 3, and design a high pass filter for the low end of the band. Filter Design in Thirty Seconds 7

Go to Section 2, and design a low pass filter for the high end of the band. For the single supply case only: Calculate Cin = Cout = 100 to 1000 times in the low pass filter section (not critical): DONE 6 Notch (Single Frequency Rejection) Filter Supply R3 Supply Supply R4 R5 Supply R6 Figure 15. Narrow Band Pass Filter for ± Supplies 8 Filter Design in Thirty Seconds

Supply Cin Cout R3 Supply R4 Supply / 2 R5 R6 Figure 16. Narrow Band Pass Filter for a Single Supply Design Procedure: Pick = : Calculate R3 = R4: Appendix A). 1 : (pick a standard value from 2 * π * * Frequency Calculate = = 20 * R3 For the single supply case only: Calculate Cin = Cout = 100 to 1000 times (not critical): 7 Band Reject Filter DONE NOTE: The start and ending frequencies of the band to be rejected should be at least fifty times different. Filter Design in Thirty Seconds 9

Supply Supply Supply Supply Supply Supply Figure 17. Band Reject Filter for ± Supplies Supply Cin Supply Supply Cout Supply / 2 Supply / 2 Figure 18. Band Reject Filter for a Single Supply 10 Filter Design in Thirty Seconds

Design Procedure: Go to Section 3, and design a high pass filter for the low end of the upper band. Go to Section 2, and design a low pass filter for the high end of the lower band. For the single supply case only: Calculate Cin = Cout = 100 to 1000 times in the low pass filter section (not critical): DONE Filter Design in Thirty Seconds 11

Appendix A Standard Resistor and Capacitor Values E12 Resistor / Capacitor Values 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, and 8.2; multiplied by the decade value. E24 Resistor / Capacitor Values 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, and 9.1; multiplied by the decade value. E96 Resistor Values 1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, 2.37, 2.43, 2.49, 2.55, 2.61, 2.67, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, 3.16, 3,24, 3.32, 3.40, 3,48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, 4.22, 4,32, 4.42, 4,53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76; multiplied by the decade value. 12 Filter Design in Thirty Seconds

Low Pass Filter Appendix B Filter Notes (for the More Technically Minded) The filter selected is a unity gain SallenKey filter, with a Butterworth response characteristic. Numerous articles and books describe this topology. High Pass Filter The filter selected is a unity gain SallenKey filter, with a Butterworth response characteristic. Numerous articles and books describe this topology. Narrow Band Pass Filter The filter selected is a modified Deliyannis filter. The Q is set at 10, which also locks the gain at 10, as the two are related by the expression: R3 R4 2 = Q = Gain A higher Q was not selected, because the op amp gain bandwidth product can be easily reached, even with a gain of 20 db. At least 40 db of headroom should be allowed above the center frequency peak. The op amp slew rate should also be sufficient to allow the waveform at the center frequency to swing to the amplitude required. Wide Band Pass Filter This is nothing more than cascaded SallenKey high pass and low pass filters. The high pass comes first, so energy from it that stretches to infinite frequency will be low passed. Notch Filter This is the Fliege Filter topology, set to a Q of 10. The Q can be adjusted independently from the center frequency by changing and. Q is related to the center frequency set resistor by the following: R 1 = = 2 * Q * R3 The Fliege filter topology has a fixed gain of 1. The only real possibility of a problem is the common mode range of the bottom amplifier in the single supply case. Band Reject Filter This is nothing more than summed SallenKey high pass and low pass filters. They cannot be cascaded, because their responses do not overlap as in the wide band pass filter case. Filter Design in Thirty Seconds 13

IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications, enhancements, improvements, and other changes to its products and services at any time and to discontinue any product or service without notice. Customers should obtain the latest relevant information before placing orders and should verify that such information is current and complete. All products are sold subject to TI s terms and conditions of sale supplied at the time of order acknowledgment. TI warrants performance of its hardware products to the specifications applicable at the time of sale in accordance with TI s standard warranty. Testing and other quality control techniques are used to the extent TI deems necessary to support this warranty. Except where mandated by government requirements, testing of all parameters of each product is not necessarily performed. TI assumes no liability for applications assistance or customer product design. Customers are responsible for their products and applications using TI components. To minimize the risks associated with customer products and applications, customers should provide adequate design and operating safeguards. TI does not warrant or represent that any license, either express or implied, is granted under any TI patent right, copyright, mask work right, or other TI intellectual property right relating to any combination, machine, or process in which TI products or services are used. Information published by TI regarding third party products or services does not constitute a license from TI to use such products or services or a warranty or endorsement thereof. Use of such information may require a license from a third party under the patents or other intellectual property of the third party, or a license from TI under the patents or other intellectual property of TI. Reproduction of information in TI data books or data sheets is permissible only if reproduction is without alteration and is accompanied by all associated warranties, conditions, limitations, and notices. Reproduction of this information with alteration is an unfair and deceptive business practice. TI is not responsible or liable for such altered documentation. Resale of TI products or services with statements different from or beyond the parameters stated by TI for that product or service voids all express and any implied warranties for the associated TI product or service and is an unfair and deceptive business practice. TI is not responsible or liable for any such statements. Mailing Address: Texas Instruments Post Office Box 655303 Dallas, Texas 75265 Copyright 2001, Texas Instruments Incorporated

易迪拓培训 专注于微波 射频 天线设计人才的培养网址 :http://www.edatop.com 射频和天线设计培训课程推荐 易迪拓培训 (www.edatop.com) 由数名来自于研发第一线的资深工程师发起成立, 致力并专注于微波 射频 天线设计研发人才的培养 ; 我们于 2006 年整合合并微波 EDA 网 (www.mweda.com), 现已发展成为国内最大的微波射频和天线设计人才培养基地, 成功推出多套微波射频以及天线设计经典培训课程和 ADS HFSS 等专业软件使用培训课程, 广受客户好评 ; 并先后与人民邮电出版社 电子工业出版社合作出版了多本专业图书, 帮助数万名工程师提升了专业技术能力 客户遍布中兴通讯 研通高频 埃威航电 国人通信等多家国内知名公司, 以及台湾工业技术研究院 永业科技 全一电子等多家台湾地区企业 易迪拓培训课程列表 :http://www.edatop.com/peixun/rfe/129.html 射频工程师养成培训课程套装该套装精选了射频专业基础培训课程 射频仿真设计培训课程和射频电路测量培训课程三个类别共 30 门视频培训课程和 3 本图书教材 ; 旨在引领学员全面学习一个射频工程师需要熟悉 理解和掌握的专业知识和研发设计能力 通过套装的学习, 能够让学员完全达到和胜任一个合格的射频工程师的要求 课程网址 :http://www.edatop.com/peixun/rfe/110.html ADS 学习培训课程套装该套装是迄今国内最全面 最权威的 ADS 培训教程, 共包含 10 门 ADS 学习培训课程 课程是由具有多年 ADS 使用经验的微波射频与通信系统设计领域资深专家讲解, 并多结合设计实例, 由浅入深 详细而又全面地讲解了 ADS 在微波射频电路设计 通信系统设计和电磁仿真设计方面的内容 能让您在最短的时间内学会使用 ADS, 迅速提升个人技术能力, 把 ADS 真正应用到实际研发工作中去, 成为 ADS 设计专家... 课程网址 : http://www.edatop.com/peixun/ads/13.html HFSS 学习培训课程套装该套课程套装包含了本站全部 HFSS 培训课程, 是迄今国内最全面 最专业的 HFSS 培训教程套装, 可以帮助您从零开始, 全面深入学习 HFSS 的各项功能和在多个方面的工程应用 购买套装, 更可超值赠送 3 个月免费学习答疑, 随时解答您学习过程中遇到的棘手问题, 让您的 HFSS 学习更加轻松顺畅 课程网址 :http://www.edatop.com/peixun/hfss/11.html `

易迪拓培训 专注于微波 射频 天线设计人才的培养网址 :http://www.edatop.com CST 学习培训课程套装该培训套装由易迪拓培训联合微波 EDA 网共同推出, 是最全面 系统 专业的 CST 微波工作室培训课程套装, 所有课程都由经验丰富的专家授课, 视频教学, 可以帮助您从零开始, 全面系统地学习 CST 微波工作的各项功能及其在微波射频 天线设计等领域的设计应用 且购买该套装, 还可超值赠送 3 个月免费学习答疑 课程网址 :http://www.edatop.com/peixun/cst/24.html HFSS 天线设计培训课程套装套装包含 6 门视频课程和 1 本图书, 课程从基础讲起, 内容由浅入深, 理论介绍和实际操作讲解相结合, 全面系统的讲解了 HFSS 天线设计的全过程 是国内最全面 最专业的 HFSS 天线设计课程, 可以帮助您快速学习掌握如何使用 HFSS 设计天线, 让天线设计不再难 课程网址 :http://www.edatop.com/peixun/hfss/122.html 13.56MHz NFC/RFID 线圈天线设计培训课程套装套装包含 4 门视频培训课程, 培训将 13.56MHz 线圈天线设计原理和仿真设计实践相结合, 全面系统地讲解了 13.56MHz 线圈天线的工作原理 设计方法 设计考量以及使用 HFSS 和 CST 仿真分析线圈天线的具体操作, 同时还介绍了 13.56MHz 线圈天线匹配电路的设计和调试 通过该套课程的学习, 可以帮助您快速学习掌握 13.56MHz 线圈天线及其匹配电路的原理 设计和调试 详情浏览 :http://www.edatop.com/peixun/antenna/116.html 我们的课程优势 : 成立于 2004 年,10 多年丰富的行业经验, 一直致力并专注于微波射频和天线设计工程师的培养, 更了解该行业对人才的要求 经验丰富的一线资深工程师讲授, 结合实际工程案例, 直观 实用 易学 联系我们 : 易迪拓培训官网 :http://www.edatop.com 微波 EDA 网 :http://www.mweda.com 官方淘宝店 :http://shop36920890.taobao.com 专注于微波 射频 天线设计人才的培养易迪拓培训官方网址 :http://www.edatop.com 淘宝网店 :http://shop36920890.taobao.com