Settling Time


Settling time is the time required for an op amp to respond to an input voltage step, enter and stay within specified error range of the final value. It’s important in applications that drive an a/d converter, digitizing rapidly changing inputs. But let’s look beyond the definition and focus on the character of settling waveforms.

Last week’s blog on slew rate showed how an op amp transitions from a slewing ramp to a small-signal settling portion of the waveform, figure 1. As the gain is increased, you can see the slower closure to final value. This is due to reduced closed loop bandwidth in higher gain.

This example op amp is tuned to have virtually 90° phase margin in G=1. Notice that there is no overshoot, even in unity gain. Its virtually perfect first-order response serves as a benchmark for comparison but you are unlikely to find an op amp with such generous phase margin in G=1.

The response in figure 2 is more realistic (maybe a bit pessimistic). These waveforms are produced by the same op amp but with approximately 35° phase margin at G=1. (The ideal op amp responses are also shown for comparison.) Its small signal overshoot is approximately 32% in G=1. It appears to be this less overshoot with the 1V step shown because only the small-signal portion of the response produces this overshoot behavior. A larger input step would have the same magnitude overshoot but look proportionally even smaller. This is why you should always check overshoot and stability with small input voltage steps.

Figure 3 shows an expanded view of the G=1 small-signal response. Note that the settling of the final humps to a final steady value appear to require two complete up/down cycles. The wiggles continue, smaller and smaller—beyond the resolution of this graph. An additional cycle or two might be required to settle to high accuracy.

When we visualize this final settling behavior, we often tend to imagine a compressed time scale in the final over/undershoots, as if the natural frequency of this ringing is shifting upward with each hump. But every cycle of settling requires the same time. Excessive ringing can be costly—a good reason to select a reasonably well-behaved op amp.

The true settling time to high accuracy, 16-bits or greater often includes other factors. Behaviors produced by fancier phase compensation techniques and thermal effects can add to the settling time. The amplifier can also be perturbed by glitches from input switching of an a/d converter. Optimizing all this can be tricky business—a good future topic. Still, it’s important to visualize the primary effects at work—slew rate combined with a second-order system response.

Thanks for reading and comments are welcome below.

Bruce       email:  thesignal@list.ti.com

   60+ other interesting The Signal topics.

  • Hi Bruce,

    Can you show us how you modelled that 35° in your circuit?

    regards,

    hugo

  • Hugo--  I hastily prepared a design note to show how I simulated the two op amps as I cannot attach schematics in this comment. I thought others might be interested in the liberties I took in creation of the graphs in this blog. The link is below. --  Regards, Bruce.

    e2e.ti.com/.../2446.an-op-amp-with-35-degrees-phase-margin.aspx

  • Thanks for the link and the modelling info

    regards,

    hugo

  • Bruce,

    This is a very good article. Thank you for covering this topic. Is the settling time for an amplifier different if you have the amplifier in a positive gain (i.e. +1V/V) versus a negative gain (- 2V/V)?

  • Bonnie—There would be quite a dramatic difference in settling behavior between gain of G=+1 and G=-3 as the noise gain is 1 versus 4, respectively. The final settling would be considerably slower due to reduction in closed-loop bandwidth.

    I believe you may have intended to compare G=+2 and G=-1 because they have equal noise gains of 2. For a given output step size, these two gains will have similar settling behavior through the transition to small signals. In spite of the equal noise gains, there can be significant differences in behavior with a real op amp. The G=+2 case applies a changing common-mode signal to the op amp that can reveal different behaviors in the input stage. In comparison, the common-mode voltage of the inverting amplifier is unchanged before the step and after settling. This effect is on my list of possible topics but I’ll probably leave it to my successors. — Bruce

  • Bruce,

    I'm glad you mention what can be a significant difference between inverting and non-inverting amplifiers...the presence of a changing common mode voltage at the inputs which can potentially use a significant portion of the CM range.  While the non-inverting configuration has the advantage of a higher input impedance, it is not without a cost.

    "...leave it to my successors" -- are you retiring?

    Tim