April 24, 1997

Analog filters: even more essential in the digitized world

BILL SCHWEBER, TECHNICAL EDITOR

Designing filters has never been easy or fun. But the latest advances in analog ICs simplify implementation and provide required performance.

DIGITAL FILTERS ARE WONDERFUL CREATIONS. They are simultaneously predictable, malleable, precise, simulatable, flexible, consistent, and accurate. They avoid messy physical resistors, capacitors, and even inductors, and they let you make changes via a keyboard rather than with new components. They can even implement filter topologies that you cannot realize using conventional physical components.

But they have one unavoidable shortcoming. They can't answer the Nyquist criteria's need for strict bandwidth-limiting before any sampled data-signal processing--whether by an A/D converter or a DSP-based filter. You need to precede digital signal processing with an analog lowpass filter, as a mandatory line of defense against aliasing due to an input signal bandwidth that is greater than one-half the sampling rate.

There's another reason to look beyond digital low-pass filters, even in non-Nyquist situations: You may find that a digital filter is more costly in total system resources (converter, processor burden, memory, initialization, and power consumption) than is the analog implementation.

Fortunately, the complex theory of filter-design and component selection points to some effective active-filter implementations using both dedicated-filter ICs and building-block matched dual and quad high-performance op amps. Further, you can look at combinations of continuous-time-active and switched-capacitor-filter designs that let you combine simple versions of both or use higher sampling rates followed by post-sampling decimation to get the desired results.

Begin with filter basics

Engineers have been studying, analyzing, and building filters since the earliest days of electronics, and many analytical references and practical design guides are available (References 1 to 4).

The ideal antialiasing filter would be a "brick wall" with constant gain through the passband-frequency range, infinite attenuation in the stopband beyond the passband, a sharp rolloff in attenuation at the cutoff frequency boundary between passband and stopband, and other characteristics. Because you cannot build this ideal filter, you must choose among several filter types, each with its own transfer-function and performance trade-offs. (See box 1, "Ponder one of four filter-transfer functions.")

Passive filters, consisting entirely of resistors, capacitors, and inductors, use no gain elements and require no power supply. They usually generate only the thermal noise from their resistive components, and you can use them at very high frequencies because they lack the bandwidth and response limitations of active devices. They can handle large currents and voltages. However, their virtues are also their vices. Their lack of gain means that another part of the system usually has to provide that gain, and their input and output impedances are usually too low or too high, respectively, so they often need buffering. Multistage filters with characteristics that are closer to ideal are complex to design because of interaction between successive stages, and the components you need--especially inductors--can be large and expensive. Passive-component tolerances usually require you to hand-tune each filter in production.

Active filters use op amps, along with resistors and capacitors, to implement the desired filter. They don't use inductors, which is a great practical benefit. These filters provide gain and are easier to design because the cascaded stages of higher order filters function with relatively little interaction among them. Although the active devices contribute noise, you can usually meet your requirements with a sufficiently low-noise device and careful circuit layout. The primary limitation on performance results from the amplifier's finite gain-bandwidth product, so choose devices with this specification in mind.

Switched-capacitor filters are well-suited for implementation in monolithic form as complete, or nearly complete, filter functions. The clocked, sampled-data filters sample the input signal at a high rate and operate on the samples on a discrete-time basis. A clock is the primary determinant of cutoff frequency, so it is easy to vary the cutoff value. Conversely, it's easy to make the cutoff frequency accurate by using a precise clock source. Like an active filter, a switched-capacitor filter provides gain. Its major drawback is that it has higher noise--both random and clock feedthrough--than an active filter. You also need to precede it with a conventional analog filter to prevent aliasing as the switched-capacitor filter samples its analog input.

Because the clock frequency is usually 50 to 100 times the rolloff point, this aliasing occurs only for spectral components that are at 25 or 50 times the rolloff value. Even though spectral components occur in this range, these aliases may not be a problem because they often are reflected into the filter stopband, so the filter attenuates them. Still, it's good design practice to precede the switched-capacitor filter with a passive RC filter or simple active filter.

(Note that passive and active filters are sometimes called "continuous-time filters" to distinguish them from these sampled-data filters. Also, although switched-capacitor filters are discrete-time filters, they are not "digital filters," because they use analog circuit elements rather than numerical signal representation to implement the filtering.)

Once you select the filter type that meets your requirements, you have to look at actual designs that can implement it. Again, you have choices. (See box, "Four ways to realize your goals.") Although you're primarily considering lowpass filters, many of the filters also support bandpass, highpass, and allpass (phase-shift) transfer functions just by using different input points, output points, or interconnection paths.

Most aspects of filter theory are not new; most filters derive their names from classic mathematicians and scientists. However, designers have long endeavored to get close-to-theoretical performance from active filters. Although some of this challenge results from layout issues, such as grounding and bypassing, much is the result of the nonideal performance of the available op amps. The latest amplifiers, however, feature better gain-bandwidth products, lower distortion and noise, and higher input impedance. Many are available as dual and quad devices that don't compromise performance and let you build filters that take up little space for either the IC itself or the interconnecting board tracks.

An even greater assist to your design comes from software that eases filter analysis. There are two levels to such analysis. First, you need to determine the passive-component values that provide the filter response you need. Although you can calculate exact values, the challenge is to use standard, obtainable values for the resistors and capacitors; in fact, you may want to try to use values, such as 100 kV, you're already using elsewhere. You need to do some iterative analysis here, as you substitute such standard or common values for the 106.7-kV resistor that your calculations show would be best.

These programs also let you explore some other what-if dimensions: If you preset some of the passive values to common ones, what are the resulting values for the remaining passives? Or, what's the effect on theoretical performance of tolerance-based variations, especially for less precise capacitors?

For example, Burr-Brown's FilterPro program lets you configure Butterworth, Chebyshev, and Bessel filters, enter the desired performance, and then obtain the required passive values. You also force the program to choose the nearest 1% resistors, set some resistor values, enter realistic or measured capacitor values, and then plot the actual gain/phase-vs-frequency performance. Similarly, the design software for the Maxim MAX274 and MAX275 filters lets you explore before you build, and you can use it for discrete continuous-time filters that also use other parts.

If your filter needs are critical, you may have to go beyond these design programs and qualify your filter with a Spice analysis. By combining the op-amp models that nearly all vendors provide, along with more realistic models of your passive components, you can better assess the effects of tolerance, drift, parasitics, and op-amp limitations on real-world performance.

You're not limited to IC-vendor-analysis or Spicelike packages, either. Independent software-only vendors have addressed the filter problem, and you may want to look at these other packages if you do a lot of filter work or need advanced analysis. Tatum Labs, for example, offers the $498 Superfilter package for Windows-based PCs. The package lets you do design, synthesis, performance analysis, and tolerance analysis in both frequency and time domains. It supports passive, active, switched-capacitor, and even FIR and IIR DSP filters. Superfilter fits an "optimum" filter configuration to your desired requirements and determines the minimum performance parameters you need from the nonideal op amps you're considering.

Be sure to look at how you are driving the filter. You must have a low-impedance source, so you may need to include a unity or low-gain buffer stage between the signal's origin and the filter input.

Finally, look at your overall filtering strategy in the context of whatever other system resources and digital signal processing you have. Look at the trade-off between two approaches: You can bandlimit the signal and sample at its Nyquist rate using a more expensive filter and a slower A/D converter. Alternatively, you can use an inexpensive filter that rolls off well beyond the actual signal bandwidth and follow this filter with a faster A/D converter and more sample decimation. In effect, you can shift the signal processing and cost burden between the analog and the digital worlds, which may be a good trade-off if your application involves relatively low-frequency signals in the audio or sensor ranges.

In the past few years, your choice of easy-to-use filters has greatly expanded as vendors introduced switched-capacitor filter ICs. These filters require few or no external components, are available in packages as small as SO-8, and provide performance that is comparable to continuous-time filters.

There are many reasons for this interest in switched-capacitor filters. For example, ratios of capacitor values rather than absolute values determine these filters' performance, fitting in well with IC processes. These filters are also compatible with digital-IC processes, and you can integrate the filters onto a digital device. The newest designs offer much lower noise than do earlier versions, making the newer filters competitive with active filters. (A well-designed active filter, however, is still 20 to 40 dB quieter than switched-capacitor filters.) Advances in technology make switched-capacitor filters practical at 100 to 250 kHz, which means they can handle many aspects of audio, cable modem, integrated services digital network, and similar applications. Like some of the conventional active-filter topologies, switched-capacitor devices can implement bandpass, notch, and highpass transfer functions in addition to lowpass functions. Also, because of the increased use of oversampling techniques for CDs, multimedia, and related applications, users are more comfortable with this discrete-time approach than they were a few years ago.

For example, the LTC1069 family from Linear Technology comprises a series of eighth-order filters in SO-8 packages. With a 400-kHz clock, the LTC1069-1 response is flat to 0.95 of the cutoff frequency, f_CUTOFF, and drops 20 dB by 1.2f_CUTOFF; attenuation at 1.4f_CUTOFF is 52 dB. In contrast, the LTC1069-6, aiming to minimize power consumption, operates from 3 or 5V supplies and draws about 1 mA. It has a sharper rolloff at the cutoff transition area, with 42-dB attenuation at 1.27f_CUTOFF. You can choose between the approximately 3-mA-consuming LTC1069-1 and the less aggressive but lower power LTC1069-6 (Figure 1).

If you're not sure which filter transfer function will work best in your application--which is likely if you don't fully understand the dynamics of your input or haven't completed the postdigitization processing algorithms--switched-capacitor filters are a good way to painlessly forestall the decision. Because virtually all the filtering occurs within the IC, vendors can provide the various transfer functions in pin-compatible packages. Maxim's MAX290 series for cutoff frequencies from 0.1 Hz to 50 kHz has Bessel, Butterworth, and elliptic-response members (Figure 2). SNR is 70 dB (THD plus noise), and the ICs operate from a single or bipolar 5V supply. Like many of the other switched-capacitor filters, these ICs also include a free op amp, which you can use either for a front-end, wideband, antialiasing filter or for further filtering of clock noise, which is typically 6 mV p-p.

National Semiconductor offers devices such as the LMF60, a sixth-order Butterworth filter for cutoff frequencies from 0.1 Hz to 30 kHz. It uses a 350 or 3100 clock, depending on which version you select, and clock feedthrough is 10 mV p-p. You can use it with a single 4 to 14V supply or bipolar 2 to 7V supplies. Typical dynamic range is 88 dB when operating with maximum supply rails; it has two uncommitted op amps.

If your application requires low noise or a wide dynamic range, you may find that standard monolithic filters fall short and you have to use discrete op amps and passive components to build your own. It's a similar situation if your cutoff frequencies are several hundred kilohertz or higher. Be aware that filter configurations have different sensitivities to op-amp imperfections (Table 1). Therefore, you need different rules of thumb as starting guidelines when you try to select an op amp. Look at op-amp dynamic specifications, such as slew rate, bandwidth, open-loop gain, and slewing symmetry. Fortunately, these performance attributes have improved in the last few years (Reference 5). Use filter-design software to let you model the filter along with the op-amp imperfections.

Simply changing the clock controls the cutoff frequency of a switched-capacitor design. However, you may need a filter that you can program for other characteristics, such as gain or Q. Multichannel op amps and DACs are a big help here, because they save space and provide matched performance. You can build a programmable state-variable filter with a quad op amp, such as the Analog Devices AD713, with support from two dual DACs acting as digitally controlled resistors (Figure 3). This filter is adjustable for 0- to 15-kHz cutoff frequencies and 0.3 to 4.5 Q values.

DC offsets in op amps can be a problem in active filters. Unless you ac-couple the filter throughout, you may amplify the offset of the op amp and cause excessive output offset and reduce dynamic range and headroom. AC coupling is also unacceptable when you need response as low as 0 Hz or when you want to avoid the subtleties of choosing the coupling capacitor. Again, the newest op amps combine dc precision with excellent dynamic performance, so you make fewer compromises than you would have just a few years ago.

Current-feedback op amps are increasingly popular for wideband operation but are generally not useful for filters, except in Sallen-Key topologies. This situation results from the op amp's feedback loop capacitance, relatively small capacitive load drive, and noninverting operation. Unless you are doing a Sallen-Key filter, consider only voltage-feedback op amps.

The need for antialiasing filters for video signals is increasing as video goes digital. Unlike many other filters for lower frequency applications, these filters must also provide low differential gain and phase errors and low group-delay variation. Micro Linear provides the ML6420 family for continuous-time filtering of video signals. For the first product in the family, the ML6420 sixth-order filter, you can order bandwidths of 1.8, 3, 5.5, 8, or 9.3 MHz. Stopband rejection for these 5V, 16-pin SOICs is greater than 40 dB, and you can cascade the filters for sharper cutoffs (Figure 4). Gain and phase errors are below 2% and 28, respectively, and delay variation is less than 20 nsec.

Raytheon Electronics' RC6601 video filter provides user-programmable control of the cutoff frequency. Although factory-trimmed to 5.5 MHz, you can adjust the cutoff value of this active filter from 250 kHz to 10 MHz via an analog control voltage. The fifth-order elliptic filter with a phase equalizer provides a stopband rolloff of 40 dB from the nominal 5.5 MHz cutoff to 8 MHz approximating the CCIR (Consultative Committee, International Radio) 601. The differential gain and phase errors are 0.25% and 0.208, respectively, with a 20-nsec group delay variation in the passband for this bipolar 5V, 16-pin SOIC.

If you need a lowpass antialiasing filter for the audio band, even as high as several hundred kilohertz, a switched-capacitor filter offers you the lowest cost, component count, and size, along with flexibility--as long as noise, SNR, and distortion requirements are 60 to 80 dB. With a few extra design steps, you may be able to improve this figure by 10 dB (Reference 6). However, for the ultimate in filtering performance in the greater-than-100-dB range, you must use a carefully designed continuous-time filter.

You should stick with an active filter if you need to vary the filter parameters, such as Q or gain. Although you can easily change the switched-capacitor cutoff frequency by simply changing the clock, other parameters are fixed by the design. This simplicity is a big virtue. You can combine a switched-capacitor design with a simple continuous-time filter to get some of the benefits and simplicity of both, however.

Don't rule out older devices, either. Many vendors still offer ICs that are relatively old but are still viable when you judge them by the rapid obsolescence associated with digital ICs. For example, Burr-Brown's UAF42 is a 100-kHz universal active filter using state-variable design that can implement two-pole Butterworth, Bessel, or Chebyshev transfer functions. The 150-kHz MAX274 eighth-order filter and 300-kHz MAX275 fourth-order filter support the same filter and transfer functions as the Burr-Brown devices with THD better than ­89 dB. Both provide the low noise and wide dynamic range of continuous-time filters and require only external resistors for completion.

References

1. Lacanette, Kerry, "A basic introduction to filters--active, passive, and switched-capacitor," Application Note 779, National Semiconductor Corp.
2. Kester, Walt, Linear Design Seminar, Chapter 10, Analog Devices Inc, 1995.
3. Ghausi, MS, and KR Laker, Modern Filter Design: Active RC and Switched-Capacitors, Prentice Hall, 1981.
4. Lancaster, Don, Active Filter Cookbook, Synergistics Press, 1995.
5. Schweber, Bill, "Choosing an op amp: It's no longer a trying task," EDN, May 25, 1995, pg 38.
6. Garcia, Fernando, "A continuous-time monolithic filter," Audio Amateur, Issue 1, 1993.
7. Galter, Robert, and Victor Mayper, "Reducing noise in a switched-capacitor low-pass filter," Sensors, December 1996.

Acknowledgment

Thanks to Nello Sevastopulos of Linear Technology Corp for his insight and enthusiasm.

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