Signal Chain Basics #43: Active Filters

(Editor's note : go to for a complete, linked list of all previous installments of the Signal Chain Basics series.)

Analog signals are frequently filtered to band-limit noise or prevent aliasing in data acquisition systems, or to select a certain range of frequencies out of a wideband signal so that only those frequencies of interest can be operated upon. At frequencies above a few MHz, these filters usually consist of passive components, such as inductors (L), resistors (R), and capacitors (C); these are often referred to as LCR filters.

At lower frequencies, larger inductor values require physically large and often expensive inductors. This is where active filters, which combine an operational amplifier (op amp) with some resistors and capacitors, become attractive. Active filters can provide an LCR-like performance at low frequencies, and much has been written on the multitude of design options possible with these filters. Since this is a “basics” article, we’ll examine the basic concepts here to get you started with an active filter design.

Any n-th order filter may be realized by cascading the required number of first- and second-order filter stages. The transfer function of a single low-pass stage is:

The ai and bi coefficients determine the placement of poles and zeros for that stage. For a first-order stage, the b coefficient is always zero.

Each active filter stage is then comprised of one or more op amps and associated resistors (R) and capacitors (C). Without the use of op amps and feedback, imaginary poles could only be developed with the use of inductors and capacitors. The active filter stage gyrates the equivalent function of the inductors in the circuits, replacing them.

The two most commonly applied active filter topologies (Figure 1 ) are the Sallen-Key, which is a non-inverting, voltage-controlled, voltage-source (VCVS) topology; and the infinite-gain, multiple-feedback topology (MFB). The latter is an inverting topology in which the output polarity is inverted relative to the input.

Figure 1. The Sallen-Key and MFB active filter topologies.
(Click on image to enlarge)

Determining the coefficients of each stage’s transfer function, and the component values needed, can be a tedious exercise of looking up coefficients in tables and performing several mathematical transformations to get to component values. Fortunately, many design tools exist to assist the designer. Texas Instruments, for example, offers the free FilterPro software to assist designing low pass, high pass, and bandpass filters, as well as some other specialized filter types.

Variations in component values from the ideal values calculated will limit the accuracy of the filter response. Because the requirements for accuracy track the filter order, these errors appear more noticeable for higher order filters. For example, when resistor values are allowed to move from the ideal to the closest 1% value, the overall gain of a sixth-order bandpass filter can drop by nearly 6 dB!

Keep in mind that capacitor values are seldom right on value, either. Therefore, for high-order filters such as sixth-order and up, plan on using 0.1% resistors and the lowest tolerance capacitors that costs and circuit performance dictate.

Another source of error that is often overlooked is selecting op amps having too low gain-bandwidth (GBW) to support the filter function. Limited gain-bandwidth may affect the filter’s cutoff frequency, gain, response curve shape, phase and transient behavior. A good rule of thumb is to select an op amp with a GBW at least one hundred times the product of the stage’s natural frequency (fn ) and Q. Some tools, such as FilterPro, will recommend the GBW needed for the op amps used in each stage.

Join us next month when we will talk about methods for saving power in home audio applications.


· Kugelstadt, T., “Active Filter Design Techniques”, Chapter 16 of Op Amps for Everyone , 2009, Elsevier Inc.

· Huelsman, L.P., Allen, P.E., Introduction to the Theory and Design of Active Filters , 1980, McGraw-Hill.

About the author

Rick Downs is signal chain applications manager for Texas Instruments’ Analog eLab, which provides analog design tools online. Over the past 25 years, Rick has held various positions in applications and marketing of analog semiconductors focused on audio, data acquisition, digital temperature sensors and battery management products. Rick received his BSEE from the University of Arizona, and holds four patents. He has authored several articles and application notes on analog topics, and prepared and delivered several seminars on data acquisition. You can send your questions to Rick at .

1 comment on “Signal Chain Basics #43: Active Filters

  1. jsdoifjweljd
    August 17, 2015

    1. Change your marketing strategy. Any agent who wishes to stay relevant and in business must change his or her marketing strategy. In the past, it had been all about the listings and how many bedrooms a home had; these days that style of advertising just isn't going to cut it. The majority of individuals don't want to be the focus advertising, therefore advertisements should focus on lifestyle, and all marketing should feel authentic and organic.

    2. Customize your services. The world continues to evolve a rapid pace. We've gone from Web 1.0 to almost Web 3.0, better known as the Internet. We need to focus on delivering a customized experience. How does this work in real estate? Focus on the now. Make sure each of your clients is getting serviced on their schedule, not yours. Your customers want everything to be about them, and anything you send them should be tailored specifically to their interests and needs. Personalize their experience from beginning to end and offer additional services. Don't limit your services to just the transaction; provide them with concierge-style services.

    3. Establish a brand. Creating a brand is an absolute must when it comes to real estate, and doing it well is what separates outstanding agents from the mediocre agents. Clients need to feel that they can trust you with their home — a solid brand will do just that. Your brand should speak volumes about your services, knowledge and ability for success. Be consistent; otherwise your clients will not recognize you.

    4. Become an industry leader. Sound simple? It is. All it requires is time. It's probably the last thing you want to hear especially during the season. However, it is crucial to establish yourself as an industry expert. When you are quoted in the news, and you provide a wealth of content online, you become a greater asset to your client. Did you know that 80 percent of people prefer content to advertisement? That's a big number. Your target audience is looking for content, and they want to know that you are the go-to expert.

    5. Offer a wealth of knowledge. Perhaps the most significant piece of the puzzle is offering your audience local knowledge. Your extensive knowledge on the real estate industry and the lifestyle available in the area are critical. Your audience is looking at you as their guide not only for their home, but also for the area. They rely on you to give them insight into everything there is to know about the area where they are focusing their search, especially if you live there. Whatever you are doing now, stop. Take a step back and evaluate your marketing. Is it working? Are your clients looking for something different? What are you doing to make yourself indispensable? The world is quickly changing, and if you aren't prepared to adapt and evolve, you'll get left behind and your competition will get ahead.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.