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High-Q switched-capacitor BandPass Filter?

Discussion in 'Electronic Design' started by mikem, May 6, 2004.

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  1. mikem

    mikem Guest

    Is there such a thing as a High-Q switched-capacitor BandPass Filter
    whose center frequency can be "tuned" +- 20% synchronously with its
    switching clock?

    I need something that would take in a ~45Hz periodic signal with lots of
    higher odd-order harmonics, and spit out only the fundamental minus the
    harmonics, with no or predictable phase shift. The Q needs to be high
    enough to attenuate the second and subsequent harmonics by more than 40db.

    I think that this function could also be done by just a low pass, but
    I'm worried about the phase shift that a low pass might introduce.

    Extra points if the filter could select the secon or third harmonics
    on command, relative to the same switching clock.

    The clock could be something like 32X to 256X the fundamental.

    Is a power of two for the clock preferable? (vs e.g. 50X)

  2. Are you suggesting that bandpass filters don't introduce phase shift, or are
    you suggesting that switched-capacitor filter don't introduce phase shift?
    I'm no expert, but I don't think either suggestion is correct.
  3. MikeM

    MikeM Guest

    Say that I'm clocking a 100X 45Hz switched capacitor bandpass filter at 4500Hz.
    Is not the frequency at which the magnitude is max and the phase shift is zero
    45Hz? (I plan to make the filter clock an exact integer multiple of the freq
    that I'm trying to filter....

  4. John Larkin

    John Larkin Guest

    Yes. This is easily done with an MF10/LMF100-type general-purpose
    filter chip and a few resistors... see the National app notes. The
    LMF100 is a more modern poly-gate version of the MF10, I think.
    Sounds feasible. Make sure you have a simple RC or Sallen-Key lowpass
    ahead of the filter to prevent aliasing, and another after to filter
    out clock glitches.
    Just rubber-band the clock.
    Not really. Doesn't matter much, but higher is better as regards
    aliasing. I think the MF10 bandpass design allows arbitrary clock-cf

    Note that SCFs are a bit noisy, and are *very* sensitive to noise on
    the power rails. They will cheerfully alias high-frequency noise back
    into the passband.

  5. MikeM

    MikeM Guest

    You got me on that one???

  6. Jamie

    Jamie Guest

    well i am not 100% sure what your doing how ever.
    i can tell you that i once made an inductive tuned filter
    using a secondary field to be shunted which effects the
    primary field over all effect on the reasonant point with out
    coming into direct contact with the primary signal.
    another way is if you want to deal with caps only you can
    use a diode switch current path to tailer the cap via some
    DC current.
    that would be 2 diodes back to back with current flowing in both
    or to really do it rite, take a PIC or Atmel 8051 type mirco with
    lots of memory and a ADC converter using a FFT (fast fourier
    Transform)! you will have a DSP filter.
  7. SioL

    SioL Guest

    Duct tape?

  8. Here's my understanding; as I said, I'm no filter expert, so perhaps someone
    who knows what they're talking about will correct me.

    A switched-capacitor filter is just a filter design that uses switched
    capacitors to implement the integrators that are part of an active filter
    design such as biquad or state-variable or whatever. There are two reasons
    to do that: one is that the integrator gain (and thus the filter frequency)
    is controlled by the switching frequency; the other is that it's easier to
    make precision capacitor ratios on silicon than it is to make precision
    capacitors and resistors. And for low frequencies, you don't need
    high-value components, you just lower the switching frequency.

    But either way, you've still got the same biquad or state-variable or
    whatever filter, it's just that it happens to be implemented using switched
    capacitors. You still have to decide on a filter characteristic: Bessel,
    Chebyshev, whatever. That characteristic, combined with the number of
    poles, determines the phase shift. And so far as I know, all filters have
    nonzero phase shift; they have to, because it takes finite time to determine
  9. Tim Wescott

    Tim Wescott Guest

    If you're picking out a carrier a bandpass filter will have zero phase
    error at the carrier, because the filter is "anticipating" the carrier
    as much as it is "sensing" it.
  10. I believe you are confusing group delay with steady state phase
    shift. I think the OP is generally correct that most band pass
    filters have nearly zero phase shift (or an inversion) at center band,
    and I think this also applies to switched capacitor implementations.
  11. Tom Bruhns

    Tom Bruhns Guest

    (I was first thinking of a particular type of switched-capacitor
    filter which almost does what you want: extremely narrow bandwitdh is
    easy, the phase shift is zero at the center frequency, etc...but
    unfortunately has response at harmonics too. Better suited to pick
    one signal out of a relatively narrow range of frequencies.)

    How about a linear-phase low pass filter, perhaps with some zeros to
    really knock out the harmonics? Or possibly a linear phase bandpass?
    Then you'd have a constant time delay...not a constant phase shift,
    but a phase shift which is linearly related to the frequency. You can
    make it as an analog active filter, or a digital filter. The digital
    one might be easier, especially at such a low frequency. In fact, if
    you eventually need to digitize the signal anyway, a delta-sigma ADC
    may be just the ticket: it may be able to do the filtering for you,
    if you pick the output rate correctly and pick a converter with FIR
    filters inside. Of course, if you digitize fast enough to capture the
    harmonics, then extracting them digitally should be no great problem.

    Can you tell us more about the application, like what you're needing
    to do with the filtered signal, and whether a linear-phase filter
    would do, and whether you can have a clock which is locked to the
    signal frequency? You mentioned "lots of higher odd-order harmonics."
    Is the third a problem, or only ones beyond that? Is the second for
    sure not a problem? (You also mentioned in your post that being able
    to look at second and third would be an advantage...) It makes quite
    a difference, because there's a lot bigger ratio between your highest
    fundamental and the lowest third than there is between the highest
    fundamental and the lowest second, and so forth! Is there a maximum
    permissable delay through the filter?

  12. Jerry Avins

    Jerry Avins Guest

    Tim Wescott wrote:

    A bandpass filter behaves enough like a tank circuit to draw conclusions
    from one by analogy. A tank (parallel L-C tuned) circuit looks inductive
    below resonance and capacitive above it. At resonance, it is resistive,
    hence no phase shift. I don't think that has much to do with sensing,
    anticipation, or any other activity commonly engaged in by hunters. :)

  13. Tim Wescott

    Tim Wescott Guest

    You're right, tank circuits also don't normally visit sleazy bars on
    their way home, or snap off "sound shots".

    I was trying to frame my answer in Walter's language, which was pretty
    well anchored in the time domain. In this respect a tank circuit _does_
    anticipate the carrier value, in that if you feed it a carrier that
    suddenly stops it will continue to oscillate at it's natural frequency
    (hopefully close to the carrier frequency), with the amplitude dying off
    according to the Q of the tank.
  14. Ban

    Ban Guest

    Well, if the design is done properly, a bandpass filter will be of minimum
    phase. This implies that at the center frequency the phase shift is indeed
    0°, but just a little bit up or down it will rise resp. fall to +/-n*45° n
    being the order. The effect for a pulse input is a smear in the response
    time. whereas a sine input at the resonance will have a slow reaction
    because of the rise time. You can calculate these effects by using the
    normal transmission equation. No free lunch here either.
  15. In addition to my own ignorance about filters, I was trying to cover for
    what I thought might be a confusion on the part of the OP - it wasn't clear
    from the posting how much he understood, and the confusion between
    implementation and filter characteristic made me wonder. Formally, a pure
    sine wave has no beginning and no end, so we can talk about zero
    steady-state phase shift. But some people seem to think that "zero phase
    shift" means you can hit a switch to turn on the sine wave, and have the
    sine wave instantly show up at the output of the filter (zero group delay).
    I don't think there are filters with zero group delay, but maybe I'm wrong
    about that.
  16. Max Hauser

    Max Hauser Guest

    "Walter Harley" in message news:[email protected]
    I think that's a good summary (although we did figure out how to make
    precise RC time constants also, so there is less motivation to substitute
    for them, and less design of sw-cap filters than in the past). It is still
    impractical to make very big capacitors on an IC.
    Agreed. (By the way S-C filters, being discrete-time, can be analyzed and
    designed using all the mathematics of digital filters. The usual topologies
    of "switched-capacitor" imply an IIR type of response, although specialized
    technologies have built efficient FIR analog filtering for years. MOS
    switched-cap integrator circuitry can be configured to do FIR responses too,
    if there is a need that fits the technology (which in practice is rare).

    Here's a bit of filter trivia for you. General writing on filters tends to
    say offhand that analog continuous-time filters always have infinite impulse
    response (IIR) and nonlinear phase response. The former is certainly wrong
    and long has been (specialized analog technologies implemented FIR filtering
    for radar long before digital filtering existed to speak of, and specialized
    continuous-time FIR technologies do so today in other applications). Common
    lumped RCL or active-RC analog filter implementations do give IIR responses
    having nonlinear phase. But they can be configured to approximate truly
    linear phase (or finite impulse response) as precisely as you want -- the
    same way they approach ideal lowpass or highpass (which they also cannot do
    in their native forms). It's all a matter of proper approximation
    approach -- Bessel, Thompson, elliptic, etc.

    (By the way, in careful usage "biquad" is a transfer function with quadratic
    numerator and denominator -- "biquadratic" -- like "bilinear" -- as in one
    of the common s-z domain mappings for continuous-discrete time filter
    tranformation. It is not a specific topology, although there is some
    history of using it for certain second-order topologies. I think that was
    in my "old farts' electronics quiz" on, from 1986,
    re-posted a few months ago.)

  17. Ted Wilson

    Ted Wilson Guest

    Hi Mike

    You can think of switched capacitors as simply a means of generating
    frequency-controlled resistive elements:

    Charge on a capacitor, q = C*V = I*t

    Therefore V/I = t/C and, since R = V/I

    R = t/C

    Substituting t = 1/f

    R = 1/(f*C)

    Thus, for a given C, the higher the frequency, the lower the

    A resistor, (or resistors), generated in this manner can be plugged
    into any standard circuit configuration, to provide circuit adjustment
    by means of adjusting a frequency, which of course can be generated
    and controled with digital precision.

    Personally, to implement a band-pass function, I would use a
    bridge-tee configuration, which provides very well controlled Q, (not
    to be confused with the "q" discussed above), and centre frequency for
    given component values.

    As discussed by others in the thread, the phase shift is nominally
    zero at the centre frequency.

    If you are interested, I will post more information.


    Ted Wilson
  18. John Larkin

    John Larkin Guest

    Then why doesn't somebody make a line of integrated continuous-time
    DDS lowpass filters? This is such an obvious need... and we surely
    have enough integrated SCSI terminators and white LED charge pumps to
    last forever.

  19. mikem

    mikem Guest

    The application is vibration analysis. I want to hang an accelerometer
    on the front of an direct-drive 6-cyl 4-cycle aircraft engine. The
    accelerometer output will respond (first order) to any mass inbalance
    at the propeller end of the engine (propeller is used as the engine
    flywheel). The accelerometer output will be periodic. It can be
    described as a sinosoid with harmonics.
    It is hard to lock the clock as an exact multiple of the period. See below.
    I'm guessing that there will be lots of third harmonic because three
    of the cylinders fire on each rotation of the engine. Since it is
    a two-bladed prop, and the aircraft will be tested by running it up
    to cruise RPM on the ground, there may be some second harmonic induced
    as each prop blade passes within a few inches of the ground (happens
    twice per revolution).
    The purpose of the analysis is to resolve the amplitude and phase of
    the fundamental. The phase will be relative to engine shaft position.
    The phase (+-180deg) tells you where to put a counteracting weight. The
    amplitude tells you how much weight to add.

    My idea is to sample the accelerometer at a fixed rate, at a rate such
    that several hundred samples are taken per each revolution. As the
    engine speed varies (and it will vary), there will be
    a slightly more or fewer samples per revolution on any given revolution.
    The sample number at which the new period begins is not always
    the same. (There will be a separate channel to record an index
    mark on the engine shaft).

    The time-series of samples will contain the funamental (at the
    rotational period) and harmonics. Since the period does not
    span the same number of samples for each revolution, I'm thinking
    that using an FFT to extract the amplitude and phase would not work
    very well.

    Suppose that I do this using a laptop and an PCMCIA analog data
    aquisition card. Sampling the accelerometer at a fixed-sampling rate is
    easy. Sampling the output of a photocell looking at a piece of
    reflective tape on the engine shaft on channel two of the AD is easy, too.

    After I have several revolutions worth of data aquired, I can
    analyise the data post facto; it does not have to be done in real
    time, rev by rev, although it could be if I built hardware with
    an embedded DSP.

    I have played around with some data in Excel. I have fitted a
    sine to the sampled data by creating a column of data generated
    by a sine function based on four parameters, DCoffset, Amplitude,
    Omega, and Phase. The next column I created is the square of the
    difference between each data point and the sine value.

    Using Excel's "Solver", it will diddle the four sine generation
    parameters to minimize the sum of the squares of the errors.
    Plotting the fitted sine on top of the original data shows that it
    does the expected job of threading the sine between the original
    data points.

    I haven't tried it, but I supposed that using a second pass,
    I could fit a sine at twice the freq of the fundamental through
    the collection of points minus each fundamental sine value...

    The Amplitude and Phase of the fundamental sine fitted to the original
    sampled data contain the information about the mass imbalance.

    In this context, what methods can be used to quickly find the ampitude
    and phase of a sine fitted to a series of points containing higher
    harmonics and some uncorrelated noise???

  20. Dave VanHorn

    Dave VanHorn Guest

    Would you be thinking of a boxcar averager?
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