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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?

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4 Answers 4

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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.

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  • \$\begingroup\$ 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 \$\endgroup\$
    – Stdugnd4ikbd
    Commented Jul 28, 2023 at 16:16
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    \$\begingroup\$ I've come across it in the context of time-of-flight flow meters etc. \$\endgroup\$
    – Mark Morgan Lloyd
    Commented Jul 28, 2023 at 19:30
  • \$\begingroup\$ Somewhat related design: Nutt Time Interval Digitizer. \$\endgroup\$
    – d3jones
    Commented Jul 29, 2023 at 1:11
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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.

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  • \$\begingroup\$ I found page on Wikipedia, where it seems (didn't read quite will yet) states, that such method has 1 - 10 ps resolution. en.wikipedia.org/wiki/… \$\endgroup\$
    – Stdugnd4ikbd
    Commented Jul 28, 2023 at 11:41
  • \$\begingroup\$ Also, which are better alternatives? \$\endgroup\$
    – Stdugnd4ikbd
    Commented Jul 28, 2023 at 11:41
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    \$\begingroup\$ @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) \$\endgroup\$
    – Marcus Müller
    Commented Jul 28, 2023 at 11:45
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    \$\begingroup\$ 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. \$\endgroup\$
    – Marcus Müller
    Commented Jul 28, 2023 at 11:47
  • \$\begingroup\$ 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. \$\endgroup\$
    – Lior Bilia
    Commented Jul 28, 2023 at 11:56
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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.

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    \$\begingroup\$ 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. \$\endgroup\$
    – JBH
    Commented Jul 30, 2023 at 5:02
  • \$\begingroup\$ @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. \$\endgroup\$
    – Circuit fantasist
    Commented Jul 30, 2023 at 6:55
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    \$\begingroup\$ 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. \$\endgroup\$
    – JBH
    Commented Jul 30, 2023 at 7:06
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    \$\begingroup\$ 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*) \$\endgroup\$
    – JBH
    Commented Jul 30, 2023 at 18:03
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    \$\begingroup\$ 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. \$\endgroup\$
    – Stdugnd4ikbd
    Commented Jul 30, 2023 at 19:18
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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

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  • \$\begingroup\$ All capacitors I found, have 1-5% tolerance, at least manufacturer states that \$\endgroup\$
    – Stdugnd4ikbd
    Commented Jul 29, 2023 at 9:21
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    \$\begingroup\$ @Stdugnd4ikbd 0.1% tolerance caps exist. I know of no cap with such a tight tolerance that isn't a surface-mount cap. \$\endgroup\$
    – JBH
    Commented Jul 30, 2023 at 5:10

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