Driving SAR ADCs #7: Distortion caused by large Rfilt

00:09:06
https://www.youtube.com/watch?v=g1Q-ozhTmSI

Summary

TLDRThe video addresses distortion in electronic circuits caused by large resistor values interacting with nonlinear capacitance. It highlights how higher resistor values can exacerbate distortion, especially at elevated frequencies, and discusses the balance between selecting appropriate resistor values for optimal circuit performance and ensuring adequate driver capability. The video emphasizes that while slowing down the sample rate can mitigate certain types of errors, it does not help with distortion stemming from resistor size. Designers are encouraged to understand the implications of resistor selection in relation to circuit distortion, particularly in the context of analogue-to-digital converters (ADCs).

Takeaways

  • 🎯 Distortion often stems from large resistor values and nonlinear capacitance.
  • 📉 Slower sample rates help with certain errors but not all distortion.
  • 🔍 Resistor values should typically be between 10-30 ohms for optimal performance.
  • 📈 Distortion worsens at higher frequencies with larger resistors.
  • ⚖️ There's a balance between driver needs and distortion levels in circuit design.
  • 💡 A resistor's size impacts the voltage drop and thus the distortion mechanism.
  • 🌀 Nonlinear capacitance causes changes in voltage that contribute to distortion.
  • 🔄 Identify distortion sources by adjusting resistor values if issues arise.
  • 📊 Understanding the distortion curve is critical in selecting resistor values.
  • 🤔 If distortion is unexpected, consider lowering the resistor value as a potential fix.

Timeline

  • 00:00:00 - 00:09:06

    In this video, Mahaffey, an applications engineer at Analog Devices, discusses distortion caused by large resistor values in circuits. He explains the concept of kickback error, which can lead to DC and AC errors if not settled during the acquisition cycle. While this can be mitigated by reducing the sample rate, the video focuses on a separate, non-related distortion stemming from large resistors interacting with nonlinear capacitance. Mahaffey elaborates on how the varying capacitance under different voltage conditions leads to distortion, emphasizing that larger resistors exacerbate this issue. A mathematical analysis shows that the distortion is characterized by a voltage drop across the resistor due to the nonlinear capacitor. He warns of choosing resistors larger than recommended values (10 to 30 ohms), as this could lead to dominant distortion effects, especially at higher frequencies. The key takeaway is that if one experiences unexpected distortion in their system that doesn't improve with sample rate adjustments, reconsidering the resistor value may help remedy the issue.

Mind Map

Video Q&A

  • What causes distortion related to resistors in circuits?

    Distortion in circuits is caused by large resistor values interacting with nonlinear capacitance, leading to variations in voltage that contribute to AC errors.

  • How can you mitigate distortion caused by resistors?

    One way to reduce distortion is by selecting smaller resistor values, especially if distortion worsens at higher frequencies.

  • Does slowing down the sample rate improve all forms of distortion?

    No, slowing the sample rate primarily helps with kickback-related errors, not the distortion caused by large resistor values.

  • What resistor values are typically recommended?

    Recommended resistor values usually range between 10 and 30 ohms.

  • Why is it problematic to use a very large resistor?

    Using a very large resistor can worsen distortion and may affect the performance of ADCs by increasing distortion noise.

  • How does frequency impact distortion related to resistors?

    As frequency increases, distortion caused by larger resistors typically worsens, resulting in a drop in performance.

  • What is the relationship between driver and resistor selection?

    While a larger resistor value may be better for driver performance, it can lead to increased distortion in ADC.

  • What happens if you select a resistor value outside the recommended range?

    Choosing a resistor value much larger than recommended can cause distortion to become the dominant error mechanism in the circuit.

  • What is the significance of nonlinear capacitance?

    Nonlinear capacitance causes the variable portion of capacitance to change based on voltage, contributing to distortion.

  • How can distortion be observed in circuit performance?

    Distortion can be visualized using semi-log plots, which show distortion metrics relative to frequency.

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Subtitles
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  • 00:00:03
    hi I'm an Mahaffey and I'm an
  • 00:00:06
    applications engineer working on web
  • 00:00:08
    tools here at analog devices and in this
  • 00:00:10
    video I'm going to talk about distortion
  • 00:00:12
    that's caused by this resistor getting
  • 00:00:15
    too large and just to to introduce this
  • 00:00:19
    topic and and segue from our previous
  • 00:00:22
    videos so which I've spent a lot of time
  • 00:00:24
    talking about this kickback and so we've
  • 00:00:28
    got this kickback that you you might
  • 00:00:31
    have an amount of this kickback that
  • 00:00:35
    doesn't settle by the end of the
  • 00:00:37
    acquisition cycle and this non-settling
  • 00:00:40
    can lead to DC and AC errors so an AC
  • 00:00:44
    errors would be things like THD or
  • 00:00:47
    distortion and noise and this kickback
  • 00:00:52
    related error if you're troubleshooting
  • 00:00:55
    on the bench is something that can be
  • 00:00:57
    resolved or at least improved by slowing
  • 00:01:01
    your sample rate down and making this
  • 00:01:03
    acquisition cycle longer so you can see
  • 00:01:06
    here that basically this error term can
  • 00:01:11
    can get lesser as you increase this
  • 00:01:15
    acquisition cycle so that's just
  • 00:01:17
    something to understand as we get into
  • 00:01:19
    this topic but but actually what we're
  • 00:01:21
    going to talk about has nothing to do
  • 00:01:23
    with this so as I'm talking about this
  • 00:01:26
    keep in mind that this kickback related
  • 00:01:28
    error is entirely unrelated so we're
  • 00:01:31
    going to talk about an error that is
  • 00:01:34
    caused by this resistor value getting
  • 00:01:36
    large and it's it's not at all you can't
  • 00:01:41
    improve it by slowing down the sample
  • 00:01:42
    rate and it's not at all dependent on
  • 00:01:44
    kickback so what happens is this
  • 00:01:50
    resistor it actually interacts with this
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    capacitance and specifically it's the
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    capacitance it's the portion of this
  • 00:01:57
    capacitor that is it varies with the
  • 00:02:02
    voltage across it so we've got a
  • 00:02:06
    capacitance that's that's fixed most of
  • 00:02:10
    the the value of this capacitance is
  • 00:02:12
    fixed but there is
  • 00:02:13
    a small amount of this capacitance that
  • 00:02:15
    will vary as this voltage changes and
  • 00:02:19
    the variation is nonlinear
  • 00:02:21
    so it's this nonlinear variation that
  • 00:02:24
    contributes to this distortion which is
  • 00:02:27
    not a long linear AC error and so it
  • 00:02:30
    helps to understand why why is it that
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    larger values of this resistor
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    contribute to the distortion or at least
  • 00:02:39
    it's helpful to me so just to put some
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    math around the problem we can look at
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    this this just the circuit just the
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    portion of this circuit that's related
  • 00:02:50
    to this nonlinear capacitance so if we
  • 00:02:54
    look at the voltage coming in to the NEC
  • 00:02:57
    arena from the driver and it's going
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    through this resistor and then through
  • 00:03:04
    this nonlinear capacitance and so what
  • 00:03:12
    we want to know is well first of all
  • 00:03:15
    it'll help to know what the current is
  • 00:03:17
    so what's the current going through this
  • 00:03:19
    capacitance and to determine that what's
  • 00:03:22
    helpful to know is that the frequencies
  • 00:03:25
    that we're interested in here are
  • 00:03:27
    relatively low compared to the value of
  • 00:03:30
    this capacitor so this capacitance is is
  • 00:03:32
    very small this variable part of the
  • 00:03:34
    capacitor that's very small so the
  • 00:03:36
    impedance of this capacitor is very
  • 00:03:38
    large so there's there's not going to be
  • 00:03:40
    much of a voltage drop across this
  • 00:03:42
    resistor so we can assume that the
  • 00:03:44
    voltage across this capacitance is
  • 00:03:48
    essentially this input voltage we can
  • 00:03:52
    approximate it to be that so this
  • 00:03:55
    current that goes through this
  • 00:03:58
    capacitance
  • 00:03:59
    it's just that input voltage times the
  • 00:04:06
    conductance all right and then what we
  • 00:04:11
    want to know to determine you know to
  • 00:04:15
    quantify the distortion is what's the
  • 00:04:19
    voltage drop across this resistance due
  • 00:04:22
    to this nonlinear capacitor because it's
  • 00:04:24
    this voltage drop which is change
  • 00:04:26
    a nonlinear fashion that's contributing
  • 00:04:29
    to the error so we're trying to drive a
  • 00:04:31
    voltage to this ADC but we're actually
  • 00:04:33
    losing a variable part of that voltage
  • 00:04:38
    before it gets there and so this is our
  • 00:04:41
    distortion mechanism this is it's this
  • 00:04:44
    voltage change and so what we want to
  • 00:04:46
    know is what is the voltage that's
  • 00:04:54
    nonlinear and so that's just the current
  • 00:05:00
    what's going through this RC times or in
  • 00:05:04
    astir so this current times this
  • 00:05:15
    resistor and so what we have so and we
  • 00:05:24
    this is essentially what our distortion
  • 00:05:26
    is coming from so what we've got if we
  • 00:05:30
    just visualize this
  • 00:05:32
    so for cross frequency we've got this
  • 00:05:37
    voltage we're going to think of it as a
  • 00:05:42
    distortion term and let's do this as a
  • 00:05:44
    semi-log plot so we've got DB and we've
  • 00:05:47
    got log scale and so we can see that
  • 00:05:51
    this equation is just going to be a 20
  • 00:05:55
    DB per decade line it's gonna this
  • 00:06:01
    distortion is going to get worse as
  • 00:06:03
    frequency goes up we can see that here
  • 00:06:07
    so as our frequency gets higher this is
  • 00:06:09
    going to get worse
  • 00:06:11
    and as our resistor gets bigger that's
  • 00:06:14
    going to get worse but for a given
  • 00:06:15
    resistor value let's say we've got a
  • 00:06:18
    curve like this for a resistor and as
  • 00:06:22
    long as this curve falls below
  • 00:06:29
    you know what the specified distortion
  • 00:06:32
    parameter is for the ADC so the ADC is
  • 00:06:35
    going to have a distortion that's just
  • 00:06:38
    inherent at 80s
  • 00:06:39
    that is in the datasheet and so as long
  • 00:06:42
    as you've sized your resistor so that
  • 00:06:45
    this curve is falling below there's a
  • 00:06:49
    store Shin mechanisms elsewhere in the
  • 00:06:50
    circuit then this isn't going to to be a
  • 00:06:53
    problem for your circuit but what you
  • 00:06:56
    need to worry about is if you start if
  • 00:07:00
    you select a resistor so let's say
  • 00:07:02
    instead of the recommended resistor and
  • 00:07:05
    the recommended resistors in these cases
  • 00:07:07
    they're in the datasheet and they're
  • 00:07:08
    usually somewhere between between 10 and
  • 00:07:11
    30 ohms and so let's say you you pick
  • 00:07:14
    something that was you know you sized
  • 00:07:16
    this to be 300 ohms instead then this
  • 00:07:18
    curve is going to to climb up and you
  • 00:07:21
    might get to a point where for the
  • 00:07:23
    frequency that you're interested in this
  • 00:07:25
    starts to become the dominant distortion
  • 00:07:28
    mechanism so you'll need to rethink this
  • 00:07:30
    selection and again you know this curve
  • 00:07:32
    will just continue to increase as that
  • 00:07:37
    resistors larger so on the one hand you
  • 00:07:40
    don't want to make this resistor too
  • 00:07:42
    large especially if you're looking at
  • 00:07:44
    higher frequencies where it'll start to
  • 00:07:45
    really climb up on the other hand your
  • 00:07:49
    driver this driver is going to be a lot
  • 00:07:51
    happier if this resistor value is large
  • 00:07:53
    so if you're there's a there's lots of
  • 00:07:57
    drivers that aren't going to be able to
  • 00:07:58
    drive if you put 10 ohms here or even 20
  • 00:08:03
    ohms but then there's some ATC's that
  • 00:08:07
    are gonna have increased distortion if
  • 00:08:09
    you go as high as 30 or 40 or 50 so so
  • 00:08:12
    this is this is the point where you're
  • 00:08:14
    sort of between a rock and a hard place
  • 00:08:15
    and it helps to to understand how the
  • 00:08:19
    drivers working in the ATC is working
  • 00:08:21
    and to understand that this is the curve
  • 00:08:23
    that's moving on you as you change this
  • 00:08:28
    resistor value again this is a
  • 00:08:31
    distortion that will not change it will
  • 00:08:34
    not budge as you lower the sample rate
  • 00:08:37
    and as that acquisition cycle gets
  • 00:08:39
    larger there are other sources of error
  • 00:08:42
    and distortion that will improve but
  • 00:08:46
    this is not one of them so if you're
  • 00:08:47
    seeing distortion in your system that is
  • 00:08:50
    worse than you expected
  • 00:08:52
    and it's not moving as you slow down the
  • 00:08:55
    sample rate you could try lowering this
  • 00:08:58
    resistor and see if that helps so that's
  • 00:09:01
    just just one thing to think about as
  • 00:09:03
    you're designing a circuit
Tags
  • distortion
  • resistor value
  • nonlinear capacitance
  • sample rate
  • AC errors
  • ADC
  • circuit design
  • analog devices
  • frequency impact
  • current measurement