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电子滤波器设计:Sallen-Key低通滤波器有限增益带宽误差补偿方法及其应用
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内容概要:本文档由德州仪器发布,主要讨论了由于运算放大器(op amp)有限增益带宽积(GBW)导致的Sallen-Key低通滤波器误差及其补偿方法。文中首先介绍了理想情况下的Sallen-Key低通滤波器传输函数,随后详细分析了实际运放因有限GBW而引入的频率响应误差。为解决这一问题,提出了一种新的补偿方法——通过在电容旁串联电阻(Rcomp),抵消由有限GBW引起的极点效应。最后,通过仿真与测试验证了该补偿方法的有效性,证明即使使用低成本、低GBW的运放也能达到理想的滤波效果。 适合人群:具有模拟电路基础知识的专业人士,尤其是从事滤波器设计或信号处理工作的工程师。 使用场景及目标:适用于需要设计高性能、低成本Sallen-Key低通滤波器的应用场合。具体目标包括:①理解有限GBW对滤波器性能的影响;②掌握一种有效的补偿方法来减少这种影响;③能够在实际项目中应用该方法,选择合适的元件参数,确保滤波器性能符合预期。 阅读建议:本报告不仅提供了理论分析,还包含了详细的仿真数据和实验结果。因此,在阅读时应重点关注公式推导部分以及图表展示的内容,特别是不同条件下滤波器响应曲线的变化。此外,对于具体的补偿电路设计,建议仔细研究相关方程式的计算步骤,并尝试动手搭建电路进行验证。
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SBAA237–July 2017
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Copyright © 2017, Texas Instruments Incorporated
Compensation Methodology for Error in Sallen-Key Low-Pass Filter, Caused
by Limited Gain-Bandwidth of Operational Amplifiers
Application Report
SBAA237–July 2017
Compensation Methodology for Error in Sallen-Key Low-
Pass Filter, Caused by Limited Gain-Bandwidth of
Operational Amplifiers
Vito Shen, Thomas Kuehl
ABSTRACT
Analog active filters are essential signal-processing circuits, widely used to modify the frequency spectrum
of an analog signal. The Sallen-Key (SK) filter is a widely applied topology used to realize a low-pass filter.
During the design of the SK filter, the active element is always modeled as an ideal operational amplifier
(op amp), however all real op amps have a limited gain-bandwidth (GBW) product. The limited bandwidth
of the op amp introduces errors into the amplitude and phase responses of the filter.
To diminish these errors, the normal solution is to choose an op amp with a GBW of more than 100x the
–3 dB bandwidth of the filter. Only by choosing an op amp with a high GBW, relative to the bandwidth of
the filter, can it be treated as an ideal op amp. However, the cost of a high-GBW op amp may significantly
increase the cost of the filter. For some applications, the GBW requirement can be so high that it can be
difficult to identify a suitable, cost-effective op amp.
This application report provides a tutorial description of the error analysis for the SK active low-pass filter.
Additionally, the report introduces a new compensation method to reduce the errors caused by the limited
GBW of an op amp. Simulation and test data, which demonstrate the performance achieved with this
compensation technique are presented.
Contents
1 Introduction ................................................................................................................... 2
2 Ideal Transfer Function and Error Analysis .............................................................................. 2
3 Simulation and Test Results................................................................................................ 5
4 Conclusions................................................................................................................... 8
5 References ................................................................................................................... 8
List of Figures
1 Low-Pass Sallen-Key Architecture ........................................................................................ 2
2 Modified Sallen-Key Topology Incorporating Op Amp GBW Compensation ........................................ 4
3 Schematic for 300-kHz, Sallen-Key, Low-Pass Filter ................................................................... 5
4 TINA Spice AC Simulations for Ideal Op Amp and TL081 ............................................................. 6
5 Modified Schematic for 300-kHz Sallen-Key Low-Pass Filter ......................................................... 6
6 TINA Spice AC Simulations of Sallen-Key Filter Using Ideal Op Amp, Standard TL081 Circuit and
Compensated TL081 Circuit ............................................................................................... 7
7 S21 for Modified Sallen-Key Filter Using TL081......................................................................... 7
Trademarks
FilterPro is a trademark of Texas Instruments.
WEBENCH is a registered trademark of Texas Instruments.
All other trademarks are the property of their respective owners.
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