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Slew Rate Limitations

Discussion in 'Electronic Design' started by Sanjayan Vinayagamoorthy, May 15, 2004.

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  1. Hello,

    I have a couple of questions regarding slew rate limits on opamps.

    Suppose I have an opamp with a 1MHz unity gain bandwidth and a slew
    rate of 1V/us (It's a very bad opamp, just my example). I place it in
    unity gain configuration i.e.:

    --------------.
    | |
    | |
    | |\ |
    '----|-\ |
    | >-----'
    ----------|+/
    |/

    Suppose I give the input a step response from 0mV to 25mV. How do I
    know if the amplifier will slew rate limit?

    What if the amplifier had a gain of -2 (using just resistors), would
    that change whether or not it would slew? What about +2? I am just not
    sure how I would go about figuring this out.

    Any guidance is appreciated.

    Thanks,
     
  2. Phil Hobbs

    Phil Hobbs Guest

    A voltage-feedback op amp goes into slew limiting when the full bias current
    of the first stage is going into charging the compensation capacitor. This
    happens when one of the input devices turns off--typically at about
    DeltaVin=60 mV for simple bipolar amplifiers, more for FET types and
    emitter-degenerated bipolars. You can sort this out approximately from the
    unity gain frequency.

    A perfect integrator with a unity-gain frequency of f_T responds to a step
    input from 0 to V by slewing at pi*V*f_T volts per second. Thus if its
    maximum slew rate is SR, the approximate step height required to cause slew
    limiting is

    V = SR/(pi*f_T).

    A 741, with a plain bipolar input, has f_T=1.2 MHz and SR=0.5 V/us, typical,
    so that slew limiting sets in at about 66 mV.

    5e5/(pi*1.2e6) = 0.066 V

    This is a bit of an overestimate, since the degradation is gradual, so the
    amp ceases to be linear well before this.

    Cheers,

    Phil Hobbs
     
  3. John Larkin

    John Larkin Guest



    This isn't bad:

    Ignoring slew rate for a second, you can model your closed-loop opamp
    as a pure gain of G (+1, -2, +2, whatever you set it up for) followed
    by an R-C lowpass having corner frequency gbw/G, where gbw is the
    opamp open-loop gain-bandwidth, 1 MHz in your example.

    So R*C = 1/w, where w = 2*pi*gbw/G

    So poke your signal into this model, say a step of V volts. The output
    will be a step of G*V volts, which passes through the RC to produce an
    exponentially-smoothed step, a classic R-C curve. The steepest part is
    at the very beginning, where the slope is just G*V/(R*C) volts/second.

    If that slope turns out to be greater than the spec'd slew rate, it
    can't move fast enough to follow the curve, so it slew limits. Later
    on, when the curve slows down, it will again follow the exponential.

    Did I get all that right? It feels like there may be some algebraic
    simplifications in there somewhere.

    I recently had to design a precision dac-programmed slew-rate limiter
    for an NMR gradient amp, to keep the customer's signal from trying to
    push too much dI/dT into the gradient coil inductance and railing my
    amp. Turns out that the loop dynamics is non-trivial to get this to
    have clean, crisp corners and be stable over a wide slew range.

    John
     
  4. Nico Coesel

    Nico Coesel Guest

    The slew rate defines the maximum steepness of the signal. It doesn't
    depend on the bandwidth of the opamp configuration because whatever
    the bandwidth is, the slewrate is always the same.

    If you differentiate a sine wave, you'll find the maximum signal
    rise/fall occurs at zero crossings.
    You can define a sine wave by s=a * sin(2pi * f) (a=amplitude,
    f=frequency). If you differentiate this you get: s'=a*f*cos(2pi).
    Since cos(2pi)=1 the maximum steepness (=slew rate) is equal to (a*
    (1/f)) (in Volts per second). If you want an opamp to produce a signal
    of 1V (peak-peak) at 1MHz, the formula will indicate you'll need at
    least an opamp with a slew rate of 1V/us. If you want a signal of 10V
    you'll need at least 10V/us.
     
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