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While I'm aware that a component can never "fully" charge or discharge to 100%, one textbook I'm using (Practical Electronics - 6th Edition, Sinclair, Dunton) says that we can assume a component has reached roughly its full practical potential after 4 time constants. Another source (allaboutcircuits.com) says that it takes 5 time constants for a component to reach its potential.

I understand that 4 time constants equal roughly 98% of capacity and 5 time constants equal roughly 99% due to 63% of value being added every time constant, but one is telling me to assume component has completed charge after 4, another tells me 5. This makes it confusing when calculating time for component to reach its capacity (difference of 25%).

Which is right?

Tim Crossey
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    Your books are just plain wrong if they claim something settles in a fixed number of time constants without any further qualification. For example, if the output of the R-C is going into a Schmitt trigger input with 20/80% thresholds (like a lot of PIC inputs), then only 1.6 time constants gets you to the guaranteed correct logic level. – Olin Lathrop Apr 10 '13 at 12:32

5 Answers5

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The correct answer to this question would have to be: Neither, the set point is insufficiently specified.

To elaborate:

  • Let us say the component in question is a capacitor, to be charged / discharged.
  • As this charging / discharging process approaches limit asymptotically, clearly there is no finite time to completion, as the question rightly notes.
  • Thus, to specify sufficient condition for "reaching practical potential", an acceptable variance from the asymptotic value must be specified.
  • This may typically be specified as a percentage, say "within 1% of supply voltage"
  • Depending on the percentage specified, the number of time constants to fulfillment would be calculated, as the question already mentions.

Thus, both textbooks are correct, with the caveat that neither mentions acceptable percentage (or the question has not reported this).

Anindo Ghosh
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Like many "rules of thumb" in engineering, it's just a rough guideline, and the correct answer depends ultimately on you and your specifications.

We know that in theory the voltage will never reach the full potential, so how many time constants we deem suitable depends on the circuit. For example, if we have a simple event triggered at 50% charge, or a relaxation oscillator that swings between 1/3 and 2/3 of the applied voltage (such as the 555 timer IC), then 1 or 2 time constants may be fine for our purposes.

For a high precision ADC sample and hold circuit, we may want to wait much longer, say > 8 time constants. So how long depends entirely upon the application.

For most purposes, above 99% (or ~5 time constants) will do, but remember it's always your call with this type of thing, not the books.

Oli Glaser
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  • Thanks. It would have been handy if one book hadn't explicitly said 4."Question: In the circuit, how long does the voltage at the output take to die away? Answer: With C=o.o1uf and R=15k, T=150us. 4x150=600. tc=6ms." – Tim Crossey Apr 10 '13 at 07:37
  • @TimCrossey - I agree, if the book stated that with no further elaboration then it's misleading. – Oli Glaser Apr 10 '13 at 09:15
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    +1 despite mentioning the 555 timer. – Olin Lathrop Apr 10 '13 at 12:28
  • Both state outright that it is a specific number. I guess it's to make it easier to get used to calculating the times. Hopefully in more advanced chapters it will explain that this it what they've done, otherwise I don't have much respect for the books and have to find another. Any suggestions (I'm pretty new to electronics, but when I apply myself I seem to understand it pretty quickly)? – Tim Crossey Apr 11 '13 at 01:58
  • @TimCrossey - there are quite a few good books out there, rather than list any here I'll direct you to [this question](http://electronics.stackexchange.com/questions/616/basic-electronics-book) which has many good suggestions. – Oli Glaser Apr 11 '13 at 04:39
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It entirely depends on the application, and whether you consider a 2% error or a 1% error "negligible" in that application.

Dave Tweed
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If you were creating a circuit in which a delay is based on an RC time, you would not choose the "on" voltage to be the maximum voltage, but something less. If a capacitor C is charging to 5V through some resistor R then it theoretically never quite reaches 5V. However, it reaches, say, 4.4V in a finite time that can be calculated exactly (within the tolerances of all the parts, like R and C, the voltage regulation, and so on).

The closer you choose the high threshold to 5V, the flatter the charging curve gets at that threshold, and the harder it is to establish the time accurately.

Kaz
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Imagine you worked on a machine in a factory making 2 inch nails to sell in hardware stores. If you took every nail you made for one day and measured how long each one was you'd find that most (probably more than 95%) were between 1.9 inches and 2.1 inches and the rest were out of specification and got recycled.

The decision to recycle 5% is based on quality control but that decision could easily have been at the 2 inch +/- 0.05 inches limit where only 90% of nails produced in a day could be shipped.

It's all about quality and what is good enough for your requirements.

Andy aka
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