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Integration Choices: Analog Filters vs. Digital Filters

In the wonderful world of integrated circuits, filters play a key role in many important functions within a system design. There are many types of filter architectures from which to choose, but one of the myriad of decisions which a designer must work through is the choice of using an analog vs. digital filter.

Let's explore some of the pros and cons of different filter types. Below are some excerpts from several experts on filter design. These comments only touch on a small sampling of the characteristics from which to choose. This discussion will hopefully stir some educational and experiential comments from you, the analog field of experts.

Walt Kester/ADI [2]
Walt Kester from Analog Devices has this to say about the need for analog filter techniques:

Even in highly oversampled sampled data systems, an analog antialiasing filter is still required ahead of the ADC and a reconstruction (anti-imaging) filter after the DAC. Finally, as signal frequencies increase sufficiently, they surpass the capabilities of available ADCs, and digital filtering then becomes impossible. Active analog filtering is not possible at extremely high frequencies because of op amp bandwidth and distortion limitations, and filtering requirements must then be met using purely passive components.

Walt also talks about digital and analog filtering pros and cons. That information is summarized in Table 1.

Table 1

Digital vs. analog filter comparison (Image courtesy of Walt Kester, Analog Devices)

Digital vs. analog filter comparison (Image courtesy of Walt Kester, Analog Devices)

One comparison example of an analog vs. digital filter
Let's look at a low-pass filter at 1 kHz. Steven W. Smith observes the following[4] analog vs. digital filter comparisons: Flatness
Typically, an analog filter flatness is governed by the accuracy of the discrete resistors and capacitors used. Residue ripple of 1 percent is not unexpected. The flatness of digital filters is primarily limited by round-off error, making them hundreds of times flatter than their analog counterparts. Frequency response
A digital filter will usually have better rolloff and stopband attenuation. Step response
A digital filter's step response has linear phase; i.e., symmetry between the lower and upper parts of the step waveform. The analog filter has nonlinear phase and is not symmetrical in the lower and upper parts of the step waveform. Overshoot
The analog filter typically has more overshoot on one side of the step, but the digital filter also has overshoot evenly on both sides of the step — but if added together, in total, the overshoot can be close to the analog filter in overall total peak voltage level. Where analog filters shine
Steven W. Smith says, “There are times that an analog filter must be used; for example, as an anti-alias filter in front of an ADC. Analog filters should be used since analog has better speed : digital is slow; analog is fast. For example, a personal computer can only filter data at about 10,000 samples per second, using FFT convolution. Even simple op amps can operate at 100kHz to 1MHz, 10 to 100 times as fast as the digital system.” Switched capacitor filters
Enter the modern switched-capacitor architecture, which uses both digital and analog functions to achieve compactness and tunability.

VLSI circuits use MOS transistors and pico-farad range MOS capacitors (CMOS technology gives an added feature of lowering the power in the IC). So audio and instrumentation applications are hindered due to limited ability of the R and C component values and their accuracy. Designers have overcome these problems by replacing resistors with MOS switches that are rapidly turned on and off and MOS capacitors. Time constants are given as capacitance ratios and capacitors can be matched really well in silicon and will track each other accurately with temperature[1] . See Figure 1.

Figure 1

The basic switched-capacitor network consists of two NMOSFETs driven by an alternating and non-overlapping clock. (Image courtesy of Technology Interface[1])

The basic switched-capacitor network consists of two NMOSFETs driven by an alternating and non-overlapping clock.
(Image courtesy of Technology Interface[1] )

Switched capacitor filters have the added features of tenability by simply changing the frequency of the clock pulses that drive the circuit. Footprints are reduced since modern IC packages are small and can support many filtering functions in a single monolithic chip.

Now, high value resistors can be created in a small area on silicon. For example, a 1MΩ resistor can be created by switching a 10pF capacitor at a 100kHz rate.

The switched-capacitor biquadratic filter [1]
This type of filter, in a conventional design, is usually architected with a lossy inverting integrator, a lossless inverting integrator, and a unity gain inverting amplifier and uses three op amps.

By using a switched-capacitor technology architecture, we can do this with only two op amps. One for the lossy inverting integration function and the other op amp for the lossless inverting integration. See Figure 2.

Figure 2

The biquadratic bandpass and highpass filter is created by a switched capacitor network. (Image courtesy of Technology Interface[1])

The biquadratic bandpass and highpass filter is created by a switched capacitor network.
(Image courtesy of Technology Interface[1] )

The switched-capacitor biquad filter has far improved capacitance ratios as compared with a conventional filter architecture.

Integrated filters and signal processing [4]
Professor Paul Hasler states the following: Basic directions for integrated circuit filters

  • Continuous or Discrete: Time and/or Amplitude
  • High level specifications of filters
  • Obtaining a filter function (H(s) or H(z))
  • Implementing the filter function into basic blocks (first and second-order filter sections, integrators, delays, etc.)

Essentially, digital filters are binary-valued and analog filters can be continuous or multi-valued using a sampled data or continuous time architectures.

Where do we draw the boundary between analog and digital?
To get a sense of where we can put the boundary between filtering via analog techniques and digital techniques, see Figure 3.

Figure 3

Where do we separate the digital from the analog? (Image courtesy Prof. Paul Hasler[3])

Where do we separate the digital from the analog?
(Image courtesy Prof. Paul Hasler[3] )

Analog filters tend to have low SNR and digital has high SNR, but at what cost? It's not so straightforward. See Figure 4.

Figure 4

Analog vs. digital filter power and area costs. (Image courtesy Professor Paul Hasler) 
For a larger image, click here.

Analog vs. digital filter power and area costs.
(Image courtesy Professor Paul Hasler)
For a larger image, click here.

National Instruments weighs in
National Instruments comments on Digital vs. Analog filters in this way:

An analog filter has an analog signal at both its input x(t) and its output y(t) . Both x(t) and y(t) are functions of a continuous variable t and can have an infinite number of values. Analog filter design requires advanced mathematical knowledge and an understanding of the processes involved in the system affecting the filter.

Because of modern sampling and digital signal processing tools, you can replace analog filters with digital filters in applications that require flexibility and programmability, such as audio, telecommunications, geophysics, and medical monitoring applications.

Digital filters have the following advantages compared to analog filters:

  • Digital filters are software programmable, which makes them easy to build and test.
  • Digital filters require only the arithmetic operations of addition, subtraction, and multiplication.
  • Digital filters do not drift with temperature or humidity or require precision components.
  • Digital filters have a superior performance-to-cost ratio.
  • Digital filters do not suffer from manufacturing variations or aging.

Stanford University's “two cents”
Here's what a Stanford University Center for Computer Research in Music and Acoustics (CCRMA) has to say about digital vs. analog filters:

For our purposes, an analog filter is any filter which operates on continuous-time signals. In other respects, they are just like digital filters. In particular, linear, time-invariant (LTI) analog filters can be characterized by their (continuous) impulse response h(t), where t is time in seconds. Instead of a difference equation, analog filters may be described by a differential equation. Instead of using the z transform to compute the transfer function, we use the Laplace transform (introduced in Appendix D). Every aspect of the theory of digital filters has its counterpart in that of analog filters. In fact, one can think of analog filters as simply the limiting case of digital filters as the sampling-rate is allowed to go to infinity.

In the real world, analog filters are often electrical models, or “analogues”, of mechanical systems working in continuous time. If the physical system is LTI (e.g., consisting of elastic springs and masses which are constant over time), an LTI analog filter can be used to model it. Before the widespread use of digital computers, physical systems were simulated on so-called “analog computers.'' An analog computer was much like an analog synthesizer providing modular building-blocks (such as “integrators'') that could be patched together to build models of dynamic systems.

I hope to have stirred your creative juices. So please let us know of your experiences with filters of both types and examples that you may have had in some of your designs.

Reference

  1. The Technology Interface
  2. Walt Kester, “Digital Filters” ADI
  3. Signal Processing Design of Integrated Analog and Digital Filters, Prof. Paul Hasler
  4. The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D.

21 comments on “Integration Choices: Analog Filters vs. Digital Filters

  1. kendallcp
    July 15, 2013

    Steve, there's so much to comment on here!  Looks like I just found my next blog post topic  (-8b

  2. Steve Taranovich
    July 15, 2013

    Hello Kendall,

    I was sure that this blog would squeeze the creative juices from your brain onto the website! When I think of filters, your name always comes up first in my mind!

  3. Davidled
    July 15, 2013

    I am wondering which one will be most effective way either analogy filter or digital filter.  Analogy filter may be used before A/D.  After A/D, any digital filtering process can be done in DSP processor.  For example, to design low pass filter, LF356 with a few R and C might be used. I do not think that extra digital low pass filter portion may be added in the DSP chips, unless the precious digital filter manipulation is required based DSP book, Oppenheim.

  4. Steve Taranovich
    July 15, 2013

    Hello DaeJ,

    Usually a simple RC filter at the ADC input will help prevent aliasing (Remember the Nyquist rule) and improved dynamic range and further filtering can be achieved by using a good digital filter after the ADC if needed. Maxim has a really good tutorial that gives a great overview of anti-alias filter before the ADC at http://www.maximintegrated.com/app-notes/index.mvp/id/928

     

  5. Netcrawl
    July 15, 2013

    That was great! interesting topic, I'm still on digital filter, because of digital processing tools, we can now replace analog filters with digital filters in applications that require programmability and flexibility, digital filters also have a superior performance to cost ratio.

     

     

  6. JeffL_#2
    July 17, 2013

    1. That switched cap biquad is interesting, would that only be usedul for design inside an SoC or would it be practical to do with discretes? Are there tools written just for this topology or is this just a “special case” of a digital filter in inverse-z? Does it simulate well in SPICE or is another tool necessary?

    2. Does anyone have experience with how well one can extend the frequency range of active filters by using current mode op amps, and which filter topologies are most suitable?

  7. kendallcp
    July 17, 2013

    Hi JeffL_2 – 

    (1) Variations of that generic switched cap biquad turn up widely.  A suitable textbook, old but still relevant, is Gregorian & Temes.  The topology appears in the first generation Cypress PSoC devices too!  And I've recently been working on updating the synthesis approach to make it more accessible to people primarily trained on digitally-implemented sampled data filters.  You can build such ciruits with discrete components if you really want.  LTC used to do (perhaps still do) a dedicated low charge injection switch pack for dabbling with switched-cap circuitry.  If tuneability is the key requirement, they are a viable choice (also consider duty-cycling your filter resistors, or cummutating multiple RC networks to make an N-path filter).

    For simulation just of the time and frequency response, it's easy to extract the z-domain function and then use your favourite plotting method for that.  Accurately predicting the signal handling parameters such as noise is *really* hard, though (and frankly, if signal path quality is your priority, these may be the wrong choice for you).

    (2) Good question about current mode amplifiers because of course some filter topologies will 'ask' their amplifiers to do something that CFAs don't like.  If you can get acceptable performance and stability from your CFA in non-inverting mode, try straight Sallen & Key lowpass.  Highpass S&K filters will need you to throw some gain away in the feedback path.  Single section bandpass filters, let me think about that.

    As a rule of thumb, though, you may lose as much as you gain with CFAs.  If linearity (for instance, high performance ADC front end) is important, you may be disappointed with many CFAs.  It might be better to use the best VFA you can fit into your application (for cost, current) and carefully choose a topology that doesn't magnify the amplifier's issues too much.  The noise gain seen by an amplifier in a filter circuit may be way different (higher!) than the forward signal gain, degrading noise and linearity.

  8. JeffL_#2
    July 17, 2013

    Hi Kendall,

    Your comment about switched-cap not having the best signal path quality reinforces my concerns, I've been reading that in some generation of delta-sigma A/Ds it was common to use a switched-cap to anti-alias. I don't know if that topology was also used in the highly oversampled audio A/Ds, I guess you don't need a very steep cutoff since your rejection only needs to hit the desired S/N ratio by the ACTUAL sampling rate but then as you say the overall S/N of the filter isn't that great to begin with. Or maybe if (as I suspect) the bulk of that noise is of rather high frequency they suxxeed in “getting away” just putting up with it in the converter, then suck it down in a multistage CIC at the output, but this is mostly conjecture since I never actually worked in that business. I'm just trying to understand if there's some structured way to figure out by analysis if some designs could be expected to work better than others. I still wonder, maybe these converters are kind of like sausage, enjoy the results as long as you don't get too concerned about what went into them!…

  9. kendallcp
    July 17, 2013

    >> maybe these converters are kind of like sausage, enjoy the results as long as you don't get too concerned about what went into them!

    Actually we filter and converter designers are like chefs, or sometimes it feels that way.  We put a huge amount of effort and the finest ingredients into creating the very best signal processing we can, only to find, metaphorically, that the guy who orders it just shovels it down while talking to his buddy about the football game, without being at all bothered by the quality and elegance we struggled to get onto the plate…

    To get real, it's important to note that if you're designing to hit a specific performance target, it's perfectly OK to use switched cap circuitry and that it can be the best choice.  This ties right back into the 'good enough' theme of analog integration.  It's economically unnecessary to make a circuit better than it needs to be, even though it might feel philosophically essential to us engineers to make it as good as it can be.

  10. JeffL_#2
    July 17, 2013

    Maybe you're wondering why I seem a bit skeptical about the “integrity” of some of these converter designs. Well I've been reading technical papers written by a number of the designers, and in many cases they've offered explanations that (at least on the surface) don't appear to make sense. In one case an author APPEARED to suggest that he found it necessary to ADD a certain amount of pseudorandom noise as a source of “dither” in order to INCREASE (no this is not a typo) the signal-to-noise ratio of the overall system! Now I understand that this “dither” of course need not occupy the same spectrum as the output signal, but on its face the statement was – let's say not terribly reassuring? Furthter investigation disclosed that the S/N ratio he was concerned about was actually the ratio of “desired” output to the level of “spurious tones”, the exact frequency and amplitude of which varied markedly between individual units. In such a case it would seem that there is a certain “non-deterministic” character to this particular system that might suggest that its performance might not be as “uniformly predictable” as some others might be. Does this make sense or do you really think I'm reading a concern into this that it doesn't really deserve? Do you understand at least why I'd like to understand the design process a little better if it helps me make a better converter selection?

  11. kendallcp
    July 18, 2013

    You touch on a deeply interesting topic, much more in the domain of converter designs than filters.  There's no doubt that “a bit of noise can help' – but of course it does depend what you are trying to optimize.  Converter gurus please jump in, but I don't think adding any form of uncorrelated [you hope] dither can actually reduce the error noise *power*.  But it can spread out what might otherwise be a very tonal limit cycle that existis for a sonically pertinent length of time, and might poke up off the noise floor enough to raise a bin level alarmingly.  Just like using spread spectrum to spread some leaking RF over several FFT bins to make it 'look smaller', you spread out the idle patterns of a delsig modulator to make them less audible.

    Gold standard for the analysis of the effects and their remediation in design is I think the ESS stuff, it's certaily the most thought-through approach that I've seen.

    Like the character Juiliet in 'The Cinema Show' by Genesis, who applies perfume 'concealing to appeal'. there's a sense that adding noise that would generally be unwanted can actually suppress a greater evil.

    Using the noise from an analog filter as the dither source for a subsequent sampling or modulating converter does however strike me as a depserate justification for circuit noise.  Too many factors are insufficiently predictable, and variable in manufacture.  And the whole thing is horrendously unsimulatable.  If you need some form of additional signal to break up the behaviour of a circuit in the time domain, you should know the signal in the time domain.  Circuit noise is only known statistically, so you can only ever make statistical predictions about its action.

    PCs these days are so powerful that in principle you can set up a model of any given modulator, and just run a cascade of interpolation, modulation and decimation to actually listen to what your converter will do on that source material.  So, it's not predictable, but it's certainly evaluatable, if you believe that listening to a music file is more revealing than staring at a spectrum analyzer or scope.  I don't want to be drawn on that in this forum!

  12. Steve Taranovich
    July 18, 2013

    I will shortly be following up this blog with details about integrating filters into designs and ICs

  13. PCR
    July 22, 2013

    Steve thanks for the article You have presented It in a way that can be identified very well.

  14. PCR
    July 22, 2013

    DaeJ I think that digital filters is the best selection cause that high accuracy and easiness to do the design. 

  15. Brad_Albing
    July 22, 2013

    @KCP – an excellent discussion – thanks! And thanks for the reference to Genesis. Not often we see that around here.

  16. rnquan
    July 23, 2013

    Hi Steve,

    Thanks for the informative article on analog and digital filters. If one is willing to pay the price, one can get phase linear analog brick wall low pass filters. Soshin is one company that makes video filters for video processing such as input filters for ADCs/DACs, and also in the past for the FM video modulators and demodulators in analog video recorders. Usually, the tolerances were very tight within 0.05 dB in the passband and within a couple of nanoseconds on the group delay.

    The general configuration would be a Cauer Chebychev low pass filter followed by all pass phase equalizers. Ampex had used this type of configuration for example in their VR1200 video tape recorder back in 1967.

    Also, “naturally” linear phase filters such as Bessel filters have been around for many years and can be easily inplemented in active and passive topologies. And when I was at Ampex, the chief filter designer there designed a linear phase brick wall active filter with the phase equalizer rolled in.

    And if you look at the pulse or square wave response of the older analog scopes, you will notice a symmetry in the “take off” the “leveling off” of the waveform…that is an “S” shape, which denotes phase linearity. A simple RC low pass filter, which is not phase linear, will have an abrupt “take off” followed by a smoother “leveling off” on a square wave signal.

    For those HiFi buffs, Marantz had designed phase linear LC 10.7 MHz IF filters for some of their FM tuners (e.g., Marantz 10B and Model 125) in the 1960s and 1970s.

    Also for those who are interested in phase equalizers and filters in general, I can highly recommend “Electronic Filter Design Handbook”, by Arthur B. Williams, a terrific book.

    Thanks.

    Ron

    23 July 2013

  17. Steve Taranovich
    July 23, 2013

    Thanks for the information and the references Ron—especially the audio ones—sounds like a good future blog piece. I know that my colleague, Kendall Castor-Perry will definitely want to comment on your discussion too—he's a resident filter guru and former Burr-Brown colleague

  18. rnquan
    July 23, 2013

    Thanks Steve. I followed up with some checking. It turns out the Ampex AVR-3 (circa 1976) video tape recorder had a 7 pole Cauer Chebychev LPF with three zeros followed by a three section phase equalizer. The Ampex VR1200 (circa 1967) had an all pole 10 pole LPF with also a three section phase equalizer.

    Thanks.

    Ron

    23 July 2013

  19. Steve Taranovich
    July 23, 2013

    Cauer did some really great things for electrical engineering, besides having the elliptical filter named for him, he worked in the area of analysis and synthesis of electrical filters and was a pioneer in the field of network synthesis (I remember that course well in engineering school—taught by Sidney Shamus—one of my best NYU professors back in 1968)

  20. kendallcp
    July 26, 2013

    Ah, those were the days.  Important, though, to distinguish between filters that are linear phase as a consequence of their magnitude response – e.g. Bessel lowpass filters – and filters that are linear phase because you added on some stuff to a filter that started out non-linear-phase – again, because of its amplitude response.

    The Hilbert transform will immediately tell you that if you make a minimum phase filter with a passband that approximates a lowpass brick wall, you'll get a characteristically non-linear phase response.  That can be brought mostly into line by adding an allpass phase equalizer.

    Both of these pieces implement well with classical LC or LC-derived filter techniques, the ladder variants translating best to solid state realizations.

    These days, doing a full set of system-level simulations can reveal ways to cut down somewhat on the filter requirements, or at least loosen the tolerance/margin requirements  One takeaway from a life of filter design is that filters are often too tightly specified because people are conservative and don't want to take the chance that their system performance will be degraded.

    One of the highest-volume programmable filter products I designed had very tight phase and gain error requirements, tighter than seemed reasonable for the application.  When I queried this, it turned out that the system designers had just spread the total error budget evenly across the blocks in the whole system, rather than in a way that comprehended the cost and difficulty of achieving them at each stage.  So their filter probably cost them twice what a looser spec device would have done.  I wasn't grumbling, but…

  21. SunitaT
    July 29, 2013

    In analog filters i/p n o/p are continuous time signal and in digital filters i/p n o/p r discrete time signal. Implementation of analog filters is carried out using passive and active components while digital filters are implemented on a digital or microcomputer using DSP integrated ckts.3 basic element such as adder, multiplier and delay elements are used in digital filters.

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