Pulses of shorter duration than the comparator propagation delay

[Fulcrum]

Hello everyone.

I am wondering if I have been working with an incorrect understanding of the propagation delay of comparators. I understand that the propagation delay is the duration of time it takes before a change on the inputs is seen on the output, that's clear enough even from the name itself.

However, will it affect how short of a pulse can be registered? Let's say we are using a comparator with a propagation delay of 20ns (and infinite rise and fall times for simplicitys sake). This comparator is then fed a pulse that exceeds the threshold voltage for exactly 1ns. What will happen?

• The comparator outputs nothing - after all, the pulse exceeded the threshold for a shorter duration than the propagation delay.
• Twenty nanoseconds after the pulse exceeded the threshold, the comparator outputs a 1ns pulse.

Thanks for any explanatory answers. I cannot seem to find much info about this online. I assume this is because the answer must be obvious.

[Ian.M]

Or:
3. Twenty nanoseconds later the output 'twitches' but doesn't transition properly.

The peak will be limited by the max. slew rate of internal circuits and the original pulse width.  (1) is also possible if the slew rate limited pulse is too short/small to take the output stage off the rails.  (2) is not possible.

[Fulcrum]

Or:
3. Twenty nanoseconds later the output 'twitches' but doesn't transition properly.

The peak will be limited by the max. slew rate of internal circuits and the original pulse width.  (1) is also possible if the slew rate limited pulse is too short/small to take the output stage off the rails.  (2) is not possible.

Thank you for the answer! So am I correct in my understanding that for a proper transition of the output signal, the input signal must be above threshold for longer than the propagation delay?

[tggzzz]

Hello everyone.

I am wondering if I have been working with an incorrect understanding of the propagation delay of comparators. I understand that the propagation delay is the duration of time it takes before a change on the inputs is seen on the output, that's clear enough even from the name itself.

However, will it affect how short of a pulse can be registered? Let's say we are using a comparator with a propagation delay of 20ns (and infinite rise and fall times for simplicitys sake). This comparator is then fed a pulse that exceeds the threshold voltage for exactly 1ns. What will happen?

• The comparator outputs nothing - after all, the pulse exceeded the threshold for a shorter duration than the propagation delay.
• Twenty nanoseconds after the pulse exceeded the threshold, the comparator outputs a 1ns pulse.

Thanks for any explanatory answers. I cannot seem to find much info about this online. I assume this is because the answer must be obvious.

The minimum pulse duration recognised is related to the comparator's input bandwidth. That is not directly related to the propagation delay, although higher bandwidth comparators will usually have shorter propagation delays. Hence (2) is probably correct, but you should always read and understand every line of the datasheet

For example, http://www.analog.com/media/en/technical-documentation/data-sheets/ADCMP580_581_582.pdf has a propagation delay of 180ps, but the minimum input pulse width is 80ps. Note that shorter pulse widths take longer to "get through" to the outputs, as do smaller amounts of input overdrive; that is "dispersion" (figures 13, 25, 26).

[alexanderbrevig]

I think 2 is a delay line. To achieve this for 1ns you'd need a > 2GHz sample rate..

[Alex Nikitin]

I think 2 is a delay line. To achieve this for 1ns you'd need a > 2GHz sample rate..

Or ~20cm of a coaxial cable per 1ns delay  .

Cheers

Alex

[Fulcrum]

The minimum pulse duration recognised is related to the comparator's input bandwidth. That is not directly related to the propagation delay, although higher bandwidth comparators will usually have shorter propagation delays. Hence (2) is probably correct, but you should always read and understand every line of the datasheet

For example, http://www.analog.com/media/en/technical-documentation/data-sheets/ADCMP580_581_582.pdf has a propagation delay of 180ps, but the minimum input pulse width is 80ps. Note that shorter pulse widths take longer to "get through" to the outputs, as do smaller amounts of input overdrive; that is "dispersion" (figures 13, 25, 26).

It's interesting how the minimum pulse can be shorter than the propagation delay (also WOW that's fast!).
The comparator I am using in my application has a propagation delay of 500ps, yet a minimum input pulse duration of 700ps.

[Ian.M]

There's no substitute for reading the actual datasheet, but I believe my statement that (2) is not possible for a pulse of 1/20 the propagation delay will be true for nearly all mass-market comparators.  I expect that *if* anything comes out it *wont* be a clean 1ns pulse 20ns later or even within 30% of those timings.

Tggzzz's option should be labelled:
4. a stretched and further delayed pulse.

[T3sl4co1l]

Realize that comparators are just amplifiers without gain compensation.  And, that amplifiers are just analog filters: they have a gain(frequency) response.

Suppose you biased the inputs, such that the output sits halfway between logic levels.  (This might be very tricky indeed if the comparator has built-in hysteresis, but let's suppose it doesn't.  Let's also suppose it's noiseless, too...)  If you apply a very small step now (perhaps several uV), the output will at first do nothing, then after some real time delay (which might be fractional ns), it begins moving.  Some time later (10s of ns up to us), the output ramps up, then settles to a new value (which is still near halfway, but different by a fraction of a volt -- if the DC open loop gain is 100dB, then 1uV input change makes 0.1V output change).

Now suppose the input is increased to a few mV.  The output would have to jump several volts, maybe a thousand volts, if it could!  But it can't, because it's constrained by the supply voltages.  Not only that, but internal nodes are also constrained, so you get slew rate limiting, a minimum propagation delay, and a minimum output rise/fall time.

Think of it this way: what you see at the output is a many-times magnification of a very small segment of rise/fall.  The comparator's open loop time constant might be microseconds, but because it's only linear over a tiny fractional-mV segment of its full input range, the output gets chopped into "1" and "0" with a very short time spent going between them.  And, because of internal propagation and slew-rate limiting, it's actually quite a bit slower than a linear magnification: if it were fully linear (up to the output clipping), the propagation delay should remain inversely proportional to input level.  But it's not, it saturates to a minimum delay, because other internal components do the same limiting function.

In a sense, you can model a real comparator as a chain of simple comparators, which aren't really comparators themselves as such, but are amplifiers with a modest linear range and an output range that saturates between "high" and "low" limits.

Given this model, you can evaluate what will happen, in your head!

For zero overshoot (i.e., the input doesn't reverse polarity at all), the output might eventually stabilize around mid-supply (i.e., the linear condition I talked about first).  But with zero input difference, it will take a very long time indeed to get there (on the order of (DC gain) / GBW seconds), so nothing really happens, not over a time span of microseconds.

For a little overshoot, some mV perhaps, and 20ns duration of that, you still won't see an output change, because that will be enough to move the first stage, maybe, but the internal voltages don't cross the linear range of the other stages.

For a large overshoot, 10s or 100s of mV, for 20ns, enough will propagate along the chain of internal stages, that you see an output.  The output itself may simply twitch, or it may cross whatever logic threshold you are using (remember that digital is a matter of definition: everything is analog, first and foremost!).  The rise/fall time of that twitch may not be very fast, because the input wasn't very strong.

For a large, sustained overshoot, like 100mV for longer than t_PLH duration, the output rises as fast as it can, because the first internal stage is driven into saturation almost immediately, which saturates the next stage, and so on.  And the output stays there, until enough input is given, in the reverse direction, to do all this again.

Any amplifier that has a constant GBW behavior (which is typical of the average op-amp and comparator) is best modeled as an integrator with saturation: you apply an input, and this causes the output to change.  The output doesn't simply move to a new, proportional voltage.  Indeed, the voltage change is very nearly proportional to the input volts*time applied.

What else looks like this?  An inductor draws current, proportional to the volt*seconds applied.  So the input of an inverting op-amp with negative feedback looks like an inductor!  And, the same stimulus (a bump of voltage for some duration) is necessary to get a comparator to respond, too!

Tim

[Fulcrum]

T3sl4co1l, that was a very well-thought explanation. Especially the comparisons of the comparator inputs to an inductor was nice.

[tggzzz]

There's no substitute for reading the actual datasheet, but I believe my statement that (2) is not possible for a pulse of 1/20 the propagation delay will be true for nearly all mass-market comparators.  I expect that *if* anything comes out it *wont* be a clean 1ns pulse 20ns later or even within 30% of those timings.

True, but since I'm not aware of any such comparator, I assumed the 1ns/20ns were plucked out of thin air for the purposes of making a clear-cut question.

There's a lot to be said for framing a question with "unrealistic" values, so the key issues aren't clouded by unimportant details. I treated the OP's question in that light.

[Ian.M]

When your thought experiment is less practical than a RFC1925 compliant pig, its unlikely to tell you much about the real world.

[alexanderbrevig]

When your thought experiment is less practical than a RFC1925 compliant pig, its unlikely to tell you much about the real world.

I don't mean this as offending to the OP but 

[tggzzz]

When your thought experiment is less practical than a RFC1925 compliant pig, its unlikely to tell you much about the real world.

And from that we can infer you probably haven't studied physics beyond an introductory level. If you had, you would understand the motivation for and value of "gedankenexperiment" a.k.a. "thought-experiment".

From https://en.wikipedia.org/wiki/Thought_experiment

A thought experiment considers some hypothesis, theory,[1] or principle for the purpose of thinking through its consequences. Given the structure of the experiment, it may or may not be possible to actually perform it, and if it can be performed, there need be no intention of any kind to actually perform the experiment in question.

The common goal of a thought experiment is to explore the potential consequences of the principle in question: "A thought experiment is a device with which one performs an intentional, structured process of intellectual deliberation in order to speculate, within a specifiable problem domain, about potential consequents (or antecedents) for a designated antecedent (or consequent)" (Yeates, 2004, p. 150).

Examples of thought experiments include Schrödinger's cat, illustrating quantum indeterminacy through the manipulation of a perfectly sealed environment and a tiny bit of radioactive substance, and Maxwell's demon, which attempts to demonstrate the ability of a hypothetical finite being to violate the 2nd law of thermodynamics.

And physicists traditionally find "spherical cows" very useful. That's the kind of thinking that lead my father to predict what could happen in catastrophic "loss of coolant accidents" in PWRs. He compared PWRs to bathtubs, and gained very useful understanding of the possible consequences - decades before Fukushima.

[Ian.M]

The O.P. postulated a comparator with 20ns delay and infinitely fast rise and fall times^*.  That particular spherical cow doesn't specify what happens to pulses shorter than 20ns. Infinitely fast transitions are not physically realisable and although the simplistic model would be an ideal comparator driving a 20ns delay line, I doubt that anyone here who's ever worked with DC coupled discrete MOSFETs or BJTs would expect that type of behaviour from a real comparator whether its an IC or built from discretes.

Some spherical cows are more useful than others e.g. if you want to calculate its far gravitational field.  However over-simplification is usually unhelpful and one frequently needs to consider a cylindrical cow or an even more complex model . . . .

* at least I ASS*U*ME that's what "(and infinite rise and fall times for simplicitys sake)" meant as if you take it literally, its impossible for the output to change over any finite timescale.

[tggzzz]

As I noted, unlike the OP, you are missing the benefit of extracting the minimum necessary points relevant to a thought experiment.

All questions can be infinitely complicated and obscured by concentrating on non-essential details. Usually that is unhelpful.

Edit: changed "on-essential" to "non-essential", sigh.

[T3sl4co1l]

A useful(?) point to draw is that reality is more subtle than most toys we play with.  Not to say it's insurmountable -- at a level more comparable to reality itself -- but you must be willing to accept more levels of refinement in your thinking.

The important factor here: a real function has no discontinuity, at any derivative.  All physical functions are class \$C^\infty\$, smooth and analytic*.

*I forget if this is the exact definition, or if I'm chaining together properties I only partially understand.

It's useful to think about simplified models like zero rise/fall time -- that allows you to implement an event-driven logic analysis (which is what XSPICE and up use for simulating pure logic functions).  But it's a nonphysical model: even just looking at the output stage, it's composed of a pair of transistors (to take the example of CMOS), which saturate softly towards each supply rail, and have capacitance (which varies as a function of voltage: a complicated effect to analyze, but with a useful result).  This causes the transition to slow down near either supply rail, resembling a smooth form like the logistic function, rather than a straight line -- let alone a vertical discontinuity.

And this is the same pattern for each stage in the circuit (a comparator is usually three stages: input diffamp, voltage gain, and some sort of output buffer), so you have a stack of several poles to begin with.  But not just poles, in the strict LTI sense (because a pole is a very simple way to model the frequency response), but each stage contributes many (perhaps infinite) derivatives, and each derivative requires a pole in the frequency response (that is, if you wish to continue expressing the frequency response as a polynomial: a function made of only poles and zeroes).

So the trick to doing any kind of analysis, is to know which approximations to apply to solve your particular problem.  A polynomial LTI model misses the delay (the output always changes instantly, however imperceptibly, in response to an input event).  But if you combine that with a threshold (i.e., measuring propagation delay between threshold crossings), you can still get a useful delay measure out of it.

Tim

[orolo]

The important factor here: a real function has no discontinuity, at any derivative.  All physical functions are class \$C^\infty\$, smooth and analytic*.

*I forget if this is the exact definition, or if I'm chaining together properties I only partially understand.

It doesn't detract a bit from your great argumentation, but since you mention it, analytical functions, \$ \mathcal{C}^\omega \$, are those that are locally coincident with their series expansion, like \$ \exp x = \sum\frac{x^n}{n!}\$. There are \$ \mathcal{C}^\infty \$ functions that aren't analytical, a typical example being:

\$ f(x) = \left\{\begin{array}{cl} 0, & x \le 0 \\ e^{-\frac{1}{x^2}}, & x > 0\\ \end{array} \right. \$

The series expansion of that function at x=0 doesn't coincide with its value in x>0 even locally. The funny thing is that these functions are very important in mathematics in order to have nice properties like compact support and good separation at the topological level. Anyway, physics is full of functions that aren't either  \$ \mathcal{C}^\infty \$ nor \$ \mathcal{C}^\omega \$, like random walks, or even things that aren't functions at all, like Dirac's delta. Physics uses whatever it needs from math in order to model reality, and there is a lot to choose from. After all, adding noise to a DC source turns a constant function into some kind of fractal curve, and that is just another model, who knows what reality really is.

[T3sl4co1l]

Ah, I should qualify that -- functions that represent real physical fields, in this case E&M (and V and I when measured at a point).

Such functions tend to simulate better in SPICE, though piecewise functions do usually manage to work anyway, and continuity is no guarantee of convergence.

Tim