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From this lecture notes, the open circuit time constant approximation:

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How to prove the yellow part? The lecture note mentioned Richard Adler at MIT did prove this but I could not able to find his proof and also don't have access to that.

Basically I want to know why when you calculate time constant for a capacitor you should open-circuit all other capacitors not shorting all other capacitors?
I know this is zero value time constant so C = 0 means that you open circuit capacitors but that doesn't really explain the root cause why each time constant in the transfer function is equal to "open circuit" time constant.

jsotola
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emnha
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    Good question and it led me to find [this](https://chic.caltech.edu/wp-content/uploads/2014/02/Final-Paper.pdf), which is publicly available. I need to source the earlier papers but MIT maintains a site dedicated to Alder and it is almost certainly there. I think the date will be between about 1961 and 1963, thereabouts. – jonk May 11 '22 at 01:30
  • [Here's](http://circuits.ece.ntua.gr/documents/conferences/Introducing%20Senior%20Undergraduate%20Students%20to%20the%20Open-Circuit%20Time-Constant%20Method%20for%20Circuit%20Analysis.pdf) another example to consider. Both this and the one above reference the same paper/book by Adler, dated 1965. (I've just ordered myself an original 1965 edition to read.) – jonk May 11 '22 at 04:14
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    @jonk thanks, that looks interesting to read. I see I should use limit concept to prove that. – emnha May 11 '22 at 07:13
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    I want to thank you for the question, itself. It is exposing me to something interesting. I'm sure that some people will think it only of minor importance. But I'm no super-genius and sometimes small things may seem very important to my small brain. Anyway, I'll learn a few things from this. And I appreciate what you've brought to me. :) – jonk May 11 '22 at 07:35
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    Glad to hear that. The video below is of the same author with the article you sent probably helps too. https://youtu.be/I9A9BeGJsEM – emnha May 11 '22 at 07:53
  • These are the first steps to the fast analytical circuits techniques or FACTs promoted by Dr. Middlebrook. However, it is important to specify that summing the time constants and considering that the frequency response is dominated by the term \$b_1\$ only works for a very low \$Q\$ circuit only and it is important to underline this. Anyway, this is a pity that the authors do not push one step farther in which the higher-order terms are computed also by determining time constants in different configurations. – Verbal Kint Jun 13 '22 at 18:59

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