Slew rate, bandwidth and settling time

Question

I have a system which has to be as fast as possible. The system has to sense a current across a shunt.

My first idea as I have no experience on this subject would be to take a "current sense amplifier" integrated circuit. It seems to me careful as the system was designed by engineers and it is probably optimised.

Nevertheless when I took a look on the datasheets, the bandwidth (f3dB) is generally about 1 MHz, which is pretty high from my point of view. Nevertheless, the slew rate and the settling time are far lower.

When I compared it to an op-amp (OPA810) with a high bandwidth (GBWP = 70 MHz,) the current sense amplifier seems to be very slow. The slew rate may be 134 V/µs.

I have some trouble to understand why there is so much difference and how slew rate/settling time depends on the GBW.

The GBWP is 70 MHz but depending on the feedback the closep loop bandwidth (f3dB) may be of 1 MHz. In that case (which would be similar to the current sense amplifier,) would the slew rate be so different from the one of the current sense amplifier? I mean if the GBW is 1 MHz, why would the slew rate be so different between ywo devices with the same GBW?

Answer 1

These parameters are related, but not strongly.

Slew rate is determined by internal structures of the op-amp; classically, gain and bias of the input stage (I'm not sure if this is different for more complicated / non-classical (so to speak) designs). Generally, input transconductance and slew rate trade off, hence the low rate of µA741 (BJT, 0.5V/µs) versus the high rate of TL071 (JFET, 20V/µs), for parts of comparable age (~70s) and supply consumption (1-2mA).

Performance is generally proportional to power consumption, by the way. Also note these are unity-gain-stable op-amps; less compensation can be used, netting a higher slew rate and bandwidth, but then it won't be stable down to a certain gain.

Slew rate is a large-signal parameter: some part of the design is distorting (entered saturation), and the circuit is literally working as hard as it can to return to a stable condition. Usually this is overdriving the input stage, i.e. the input differential voltage is 100s mV (maybe ~V for JFET types).

Bandwidth is a small-signal parameter, meaning all parts of the amp are working in the linear range, responding by small incremental changes.

Settling is also a small-signal parameter, but whereas bandwidth is concerned with the frequency (a sinusoid), settling follows a step change. Settling generally wavers above and below the final level, crossing a few times -- it is indicative of subtle peaks and valleys in the frequency response of the amp, and the circuit it's embedded in. We could also measure these peaks and valleys with sine waves, but the amplitude change is extremely small, and such a measurement isn't all that useful, whereas step response is more useful.

Some parts can have unexpectedly long settling, despite high bandwidth. Usually this arises from a pole-zero cancellation in the internal architecture; higher-performance types, using feed-forward or slew-boosting techniques, may do this. (Mind, I'm not accusing any particular class or type here; read this purely as speculation over a potential underlying mechanism.)

Pole-zero cancellation is where we have a drop in frequency response (a pole is a frequency where low-pass action begins), and we can apply a zero (a high-pass filter action) to mostly cancel it out. Well, even with best design practices, those two frequencies may not perfectly overlap, and so there's some "hook" in the step response -- which is to say, it doesn't settle perfectly until those time constants have passed. So that determines the timing. And how much (amplitude error, which is to say, settling %) depends on how closely matched the pole-zero pair is (i.e. if they're off by 0.1% in frequency, the settling to higher % may be fast, but below 0.1% it will take at least this long).

So, all that considered:

• The LT1999 has 2MHz BW and 3V/µs slew, 2.5µs settling to 0.5%.
• The OPA810 has 133MHz BW, 134V/µs slew*, and 100ns settling to 0.1%.
• If LT1999 were as fast as OPA810, it would have 133MHz BW, 200V/µs slew, and 37ns settling to 0.5%. (Maybe ~100ns to 0.1%, but again, it's not reasonable to infer lower settling thresholds, because there can be minute "hook" in the response that doesn't settle until much later).

(Settling can't be any faster than the exponential decay of the step response, but it can be slower due to "hook" effects. The OPA810, settling to 0.001% = 10ppm(!) in 565ns, suggests it's very close to a pure exponential decay, free of "hook".)

*Two figures are given, for two different step sizes. Interestingly, it's slower at the higher amplitude, suggesting perhaps the absence of "slew boosting" techniques, or that feedforward has occurred (notice G = +2, so input capacitance may be feeding part of the step directly to the output); or just straight up weird things, who knows. Also interesting they only measure it positive-going (-2 to 2V output); in general, slew rate can vary with direction, and there's probably a figure later in the datasheet illustrating this. It's a pretty fast amp, in any case!

Note that, while LT1999 is fixed-gain and ~2MHz BW, its gain-bandwidth (GBW) is considerable: the -10 and -20 (gain) versions have GBW = 20MHz, and the -50 has 60MHz! This makes the OPA810 look a bit poorer in relative terms -- but keep in mind, it is handicapped by design, being unity-gain stable. In fact, this is most likely exactly what they're varying in the LT1999: because gain (feedback resistors) and compensation are set by manufacture, they can use largely the same (overall) design, with only minor changes (resistors and capacitors) to support this range of gain, while giving consistent performance across the series.

Answer 2

The slew rate is a large-signal characteristic of the op-amp, while the GBWP is an small-signal one.

The slew rate expression comes from: $$ \frac{d[V_p\sin(2\pi ft)]}{dt} = 2\pi f V_p \cos(\omega t) $$

Therefore, if you know your max. voltage peak \$V_p\$, you can then find out what is the maximum frequency you can operate at (i.e. your large-signal bandwidth) without suffering from slew-rate distortion: $$ f_{max} = \frac{SR}{2\pi V_p} $$

You can understand this intuitively by realizing that your amplifier has to make more effort to pull your output signal up or down the bigger the amplitude peak is.

There could be many reasons why the slew-rate is different from one op-amp to the other. Two I can think of:

• "Miller" Capacitance in the 2nd stage. Normally used to frequency compensate the op-amp. At higher frequencies, this capacitor has a very low impedance, this loading the stage containing it as well as a the preceding stage.

• Maximum bias current capability of the output stage. If it's a class-A output, then the slew rate might be limited by the current source of the stage (I think in one direction only).

Answer 3

I have a system which has to be as fast as possible.

That's a very general requirement. You could build a discrete current sense amplifier using 50GHz transistors and it would nicely amplify GHz currents, but is that what you want? As fast as possible is very fast nowadays.

The bandwidth (f3dB) is generally about 1 MHz, which is pretty high from my point of view. Nevertheless, the slew rate and the settling time are far lower.

How can they be "far lower", since they are different quantities in incompatible units? Apples and oranges: comparing the two is not possible without knowing the maximum amplitude of a maximum frequency signal of interest.

For a system with a maximum frequency of interest \$f_{\rm max}\$, the slew rate \$S\!R\$ only limits the signal amplitude. Namely, the peak amplitude $$V_p\le{S\!R\over2\pi f_{\rm max}}.$$

Answer 4

.. I have a system which has to be as fast as possible.
why the slew rate would be so different between 2 devices with the same GBW ?

In this case of measurement part, the most important is the "settling" time at 0.01 % or less,
depending of the resolution of the ADC used.

For SR determination, one can use this "setup". Just use a "high" enough frequency at input.

Here is a test (SR=0.5 V/us for LM741) with 10 Vpp output (what should be), 30 kHz, Gain = +5.

Answer 5

Perhaps some background information regarding the SLEW RATE are helpful?

• Slew rate is defined for an opamp with negative feedback only (for reference purposes often with 100% feedback, that means: Unity closed-loop gain)

• For measurement/simulation purposes, the input step must be large enough to fully overdrive the first stage (saturation) without consideration of the feedback effect.

• Therefore, when this input step is applied, the first stage will go into saturation within the first µ-seconds (because - due to delay properties of real amplifiers - feedback is not yet active).

• That means: This stage works like a current source and can charge the Miller-capacitance (compensation capacitance) of the next stage. This effect gives the quasi-linear slope that can be observed and causes the triangle-distortion.

• The amplifier will come back to linear operation as soon as the feedback signal is effective and brings the first stage back to "normal" operation.