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I want to measure distance by electromagnetic wave travel time.

Capacitor charging voltage on time dependency is well-known:

\$V_{capacitor} = V_{source}(1-e^{\dfrac{-t}{RC}}) \$

Equation above is often used to get voltage from given time.

But, we can use this equation to get time from given voltage.

Theoretically, if we know source voltage, loop resistance and capacitance, if we measure voltage at capacitor, we can get time.

My question, is how high the precision of the measurement can be? Can the accuracy be about picoseconds?

If we have a loop with 5V source, 1 Ohm resistance, and 1 nF capacitor, every 3 picosecond (upto 3RC), the voltage on capacitor will increase on about 14 mV, which is pretty easy to measure.

Then, we off the source voltage or even not, i.e. asynchronously use connected voltmeter chip, as I understand it is called “Analog to Digital Converter”, get current voltage on capacitor and pass data somewhere to microcontroller.

Should it work?

Circuit fantasist
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Stdugnd4ikbd
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4 Answers4

15

Yes, this is a well-established method of measuring with resolution in the picoseconds without requiring impossibly high clock frequencies. You switch a current source to a capacitor.

The generic term is TAC (time to amplitude converter). Here is an overview of the circuitry.

enter image description here

Of course you would use a simple clock in the hundreds of MHz or higher and a counter to get "close" (nanoseconds) for a long interval and use the TAC to get down to picoseconds.

Spehro Pefhany
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  • As for Your last statement, this is what exactly what I was thinking of! Use counter or something else for nanoseconds resolution (1 meter) and some more precise method, like this — for picoseconds (1 millimeter). I already bought some resistors and capacitors and will make experiments with Raspberry Pi Pico, that actually has Analog to Digital converter with about 1 mV resolution – Stdugnd4ikbd Jul 28 '23 at 16:16
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    I've come across it in the context of time-of-flight flow meters etc. – Mark Morgan Lloyd Jul 28 '23 at 19:30
  • Somewhat related design: Nutt Time Interval Digitizer. – d3jones Jul 29 '23 at 01:11
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Within some very wide tolerances, yes it will work. Capacitors have initial tolerances, measured in %, some types are affected by DC voltage - they change their value based on the applied voltage. All types are sensitive to temperature and drift. Resistors also have tolerances and are affected by temperature and drift. ADC introduce their own set of errors. When you add up all these sources of errors, you end with a method that has around 10% potential error. That's not a good measurement method, and there are better alternatives.

Update: Since the OP posted the actual requirements, there are time of flight ICs that do exactly that - measure a distance to an object using the speed of light.

Lior Bilia
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  • I found page on Wikipedia, where it seems (didn't read quite will yet) states, that such method has 1 - 10 ps resolution. https://en.wikipedia.org/wiki/Time-to-digital_converter#Ramp_interpolator – Stdugnd4ikbd Jul 28 '23 at 11:41
  • Also, which are better alternatives? – Stdugnd4ikbd Jul 28 '23 at 11:41
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    @Stdugnd4ikbd a resolution says nothing about the error, right. your measurement "5ps" could still be 10% off. Just as the fact that my ruler having mm-pitch lines doesn't mean that over its length of 50cm, it's any more accurate than a ruler that only has cm-pitch lines. (also, tell us if you're consider building something that measures time in picoseconds. None of the answerers here presumed you were into cryogenically operated custom IC design) – Marcus Müller Jul 28 '23 at 11:45
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    Alternatives: look at what a crazy class of devices called "clock" does to measure time ;) There's many ways to do that :) That's rather well-documented on Wikipedia. – Marcus Müller Jul 28 '23 at 11:47
  • Mathematical equation with ideal parts have infinite resolution and absolute accuracy. We are dealing with the real world, where parts are not ideal and ADCs are required to translate analog voltages into useful data. – Lior Bilia Jul 28 '23 at 11:56
  • Unfortunately, the best-accuracy counters, time-to-digital converters and similar components I found, has tens of picosecond – Stdugnd4ikbd Jul 28 '23 at 12:14
  • This seems to be an XY problem, what exactly are you trying to measure? – Lior Bilia Jul 28 '23 at 12:22
  • @LiorBilia distance by electromagnetic wave travel time – Stdugnd4ikbd Jul 28 '23 at 16:11
  • As for Your update, every TOF solution, that I found had laser, so it measures the time between laser beam being emitted, bounced and received. I am not interested in such functionality, I only need measurement functionality, without lasers. – Stdugnd4ikbd Jul 28 '23 at 20:07
  • @Stdugnd4ikbd uff. You should have mentioned what you were trying to build in your question! Seriously, that's hard. I'd call it "impossible" if you can't design a chip (which costs hundreds of thousands of Euros to produce). You will have to buy someone else's Time-of-Flight sensor. (to make a comparison: what you're asking in the question is like "I want to drill a hole in a somewhat round stone to make 'wheel'. Should it work?", and then, colloquially, after many tips from experts, you mention that you want to build a formula 1 racing car with that wheel. – Marcus Müller Jul 28 '23 at 20:50
  • @Stdugnd4ikbd AFAIK it can be measured indirectly using wave interference. if you can generate a wave with 100s of ps inverse-frequency, then subtract the reflected wave from the outgoing wave, the amplitude of the subtraction should let you infer how far the wave traveled, less than one wavelength (use something different to measure the number of wavelengths). I don't mean the light wave itself, but you can modulate another wave onto the light wave. Getting it accurate is probably difficult. – user253751 Jul 28 '23 at 21:45
  • @user253751 any solution with reflection of the wave is not acceptable – Stdugnd4ikbd Jul 29 '23 at 06:17
  • @MarcusMüller, I think this is not a case. First, the analogy, You provided is wrong, because, instead of “drilling a hole”, the subject I was asking about is self-sufficient — there are scientific articles on this topic, out of any other context. Second, as mentioned, I already know about “Time to Digital converters”, “Time of Flight converters”, counters and similar stuff (although “Amplitude to Time converter” is what I didn’t know about) – Stdugnd4ikbd Jul 29 '23 at 06:26
  • @MarcusMüller, oh and I actually mentioned in the original post what I need it for, so, I do not understand at all, what are You writing about – Stdugnd4ikbd Jul 29 '23 at 06:52
  • @Stdugnd4ikbd I am assuming you are sending the wave at some object and measuring the reflection you get back. If that's not the situation, then adapt what I said to your situation – user253751 Jul 29 '23 at 10:50
  • @MarcusMüller, oh, no, it was actually added by You, I thought it was me, bringing back my last comment – Stdugnd4ikbd Jul 30 '23 at 08:47
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To get a linear voltage change over time, you need to charge the capacitor from a current source and not a voltage source. Then Q = I.T = V.C and the time is simply T = V.C/I.

Circuit fantasist
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    This is an excellent comment. But it's not an answer to the question ("My question, is how high the precision of the measurement can be? Can the accuracy be about picoseconds?") I'm ignoring the later edit that introduces a second question - but this doesn't answer that question, either. – JBH Jul 30 '23 at 05:02
  • @JBH, Thanks for the responce. I agree that this is not exactly an answer to the OP's question which is about an exponential timing setup but rather a description of the correct (linear) timing setup. Of course, I could turn it into a comment if you insist. The Spehro's response gives a possible linear implementation. – Circuit fantasist Jul 30 '23 at 06:55
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    Spehro's response answers the original question by presenting a known circuit solution that meets the OP's precision expectations. My concern here is that you're only commenting on the equation the OP is using but not indicating whether or not that will get the OP the precision they're looking for. – JBH Jul 30 '23 at 07:06
  • @JBH, but the Spehro' circuit is an implementation of what I have described - a *constant-current source charging a capacitor*. It meets the OP's precision expectations because it is linear. It does not need any calculations as the RC nonlinear circuit; the voltage directly represents the time. This is the well-known principle widely used in integrating digital voltmeters (ADC), timers, clocks... I just have shown the principle; Spehro has shown its circuit implementation – Circuit fantasist Jul 30 '23 at 10:53
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    I apologize, but you're asking me to believe your answer is legitimate because someone else did all the work. Nothing about the equation relates to precision. It's just an equation. Judging only from equations, both are legitimate, both could be used to achieve the OP's goal... based on implementation. He provided it. You didn't. (\*Shrug\*) – JBH Jul 30 '23 at 18:03
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    Can You please describe more? I do not really know what is the difference between current and voltage source (though, I remember, we studied it). Assume, that it is just a voltage source with closed loop with some resistance. – Stdugnd4ikbd Jul 30 '23 at 19:18
  • @Stdugnd4ikbd, I wonder how to put it briefly here... Well, when you charge a capacitor from a constant voltage source Vin through a resistor R, the voltage drop Vc across the capacitor increases exponentially because it is subtracted from the input voltage and the current decreases - I = (Vin - Vc)/R < Vin/R. To keep the current constant, you can simultaneously increase the input voltage with Vc; then I = (Vin - Vc + Vc)/R = Vin/R. Thus you have created a constant current source. See more in a [related answer of mine](https://electronics.stackexchange.com/a/547742/61398). – Circuit fantasist Jul 30 '23 at 21:34
1

You can use capacitors to measure time, as long as you don't need much precision.

You will just need a high precision capacitor and resistor.

For the resistor, it's quite easy to get a 0.1% resistor for no more than a few $ (you might even find some still more accurate). The best I've ever seen had a 1% tolerance.

So the best you can hope for is 1-2% accuracy. Maybe down to 0.5% or so with calibration. Maybe to 0.1% with calibration + controlled temperature.

For the capacitor, they tend to be far less precise. For a random capacitor, you might be as bad as -50%,+100% tolerance.

But if you need anything more precise than 5%, I would strongly advise you to use some dedicated IC (or timers and interupts on a microcontroller) instead of using a capacitor

Sandro
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  • All capacitors I found, have 1-5% tolerance, at least manufacturer states that – Stdugnd4ikbd Jul 29 '23 at 09:21
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    @Stdugnd4ikbd [0.1% tolerance caps exist](https://www.yageo.com/en/Product/Index/rchip/thick_film_precision). I know of no cap with such a tight tolerance that isn't a surface-mount cap. – JBH Jul 30 '23 at 05:10