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LC Time Constant=?

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LAN_403

Signification

Sun Mar 13 2016, 01:17AM

Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367

I know an LC circuit often is an oscillatory one, but from time-to-time, I run into the phrase: "LC TIME CONSTANT". Can anyone shed some light on this? In laser flashlamp circuits (I realize this is not a perfect LC circuit) the time constant is 3sqrt(LC). I have seen others written as PI*sqrt(LC) and just plain sqrt(LC).

My main use is for LC or LCR circuits in which I am just concerned with the first cycle, half cycle, or quarter cycle (not oscillations). As to be used, perhaps, in the mathematics of coilguns, large tuned flashlamp circuits, quarter-shrinker, can-crusher, maybe railguns...that type of thing--a timing phrase for firing during, at most, the first sine cycle of the shot.

DerAlbi

Sun Mar 13 2016, 02:16AM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

but from time-to-time, I run into the phrase: "LC TIME CONSTANT"

Thx for sharing sources and examples in which cases such definitions are used. It makes answering much easier and it assures that we all talk about the same thing. Good that you finally learned it. There were times you wouldnt even consider posting links or quotes..

people who use the term...
a) ...are idiots.
b) ...making a youtube tutorial about what they just learned on youtube from soneone who learned stuff on youtube.
c) ...realized that sqrt(Farad*Henry)=seconds.. therefore they concluded that it must be a time constant equal to Henry/Ohm or Farad*Ohm. Neglecting that 'time constants' make only sense in solutions of first order differential equations while second order differential equations usually yield 'frequency' and 'damping factor'.
d) ...just dont know better and mean the resonant frequency defining it by the cycle duration, which has some meaning in one-shot circuits with e.g. SCRs. But in terms of technical communication its just wrong.. well because its the 'cycle duration' or 'period' or an arbitary fraction or multiple of it. so name it as what it is.. Also the asigned letter is different: while a time constant is designated by greek 'tau' the cycle duration is written as 'T'=1/f.
e) ...actually want to define the exponential decay (envelope) of the oscillation. This is then some reference to the damping factor or 1/bandwidth of the LCR-circuit

Yes that list is sorted by 'justifiability' of using the term. e) is kind of correct while a) should just shut up

A time period of 3*sqrt(LC) or pi*sqrt(LC) correspondents to the duration T/2 or "one half cycle" - favoring (d).

Patrick

Sun Mar 13 2016, 02:48AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

DerAlbi wrote ...

b) ...making a youtube tutorial about what they just learned on youtube from soneone who learned stuff on youtube.

Funny.

I cant tell you how many times ive run into this with PID tutorials that are crap.

Signification

Sun Mar 13 2016, 09:41AM

Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367

Albi: I assumed the 4hv group would, for the most part, have a good idea of what I was looking for--I sure they have heard of "LC time constant". There were thus no specific examples--not what I was looking for--even if I could find them.

For one thing here, I was thinking about associating the occurrence of the current peak, Ip, of a critically damped LCR (WRT coilgun construction), the waveform's "Time Constant" I will have to check, but I believe that equation was simply ... Tc = sqrt(LC). While it wouldn't make much sense to assign an LC time constant for a constant amplitude sine wave i.e. I(t)=A*sin(t), this is not the case where only the first quarter cycle only is significant--in which case it makes much sense to assign it's time constant as (pi/2)sqrt(LC)...Barry's coilgun site

I believe this is a place to learn, as well as teach--whether you do or not--I do not remember if it was "learning" or "teaching" that you called 4hv the wrong place to look. I will be back with more information related to the coilgun.

Please, I am just trying to ask a 'general advice' question in the post!

I was going somewhere with this!!...I just wanted a few personal opinions first...or whatever came up

BTW, thanks for your input.

Blackcurrant

Sun Mar 13 2016, 12:14PM

Registered Member #2989 Joined: Sun Jul 11 2010, 12:01AM
Location: UK
Posts: 94

I think your looking for critically damped response

Time constant only applies to RL RC type circuits, and you could always use a circuit simulator now.

DerAlbi

Sun Mar 13 2016, 12:21PM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

Well, i googled for "LC time constant" before posting to make out any credible source where such formulation would occur. While there are some hits, specially when you search for ' "lc time constant" pdf' you cant find any reference to its actual meaning.
Time constants are purely reserved for exponential functions. It allways describes how long it takes to something reaching 63.2% of some steady state value. In LCR-Circuits there is no such thing ("steady state") nor would such a threshold be a good description for engineer-to-engineer communication because every voltage (or current) level can be passed through twice at least most of the time. So are there 2 time constants then? Or how many? Or is it only existing during the part of the step response graph where the function uniquely defined? Naaah. Thats no tech-talk. Its pseudo science. Good enough for (a) and (b) however.

What you see in a critical damped LCR-circuit as time constant is what i describe in (e) in my initial post.
Every LCR-circuit has got an envelope with exponential decay which you could draw around it.
This comes from solving the 2nd order diff. equation for the LCR-circuit which can have imaginary roots (oscillation), only one root (ciritcal damping) or 2 roots.
The general oscillation equation is allways described as:

exp(-L/(2R) * t) * SomeFunction(t). (The bold part is the envelope)
In case of oscillation the "SomeFunction(t)" = Amplitude*sin(2*pi*f_res * t). In case of critical damping "SomeFunction(t)" = SomeConstant + t*AnotherConstant. There is no sin()-function involved since trigonomic funtions only arise from imaginary roots...

The time constant of that envelope being L/(2R) has nothing to do with sqrt(L*C) but is inherently the only thing you could call "time constant" in a RLC-circuit.

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