Can physical or other real world systems have negative time constants? Doesn't negative time constant mean the output of the system is ahead than the input provided? If I am missing some basic concepts, please feel free to remind me of them.
I would say time constant is like frequency . we use negative frequency in the sense of direction only ie eg a rotating vector is clockwise or anticlockwise but its speed of
rotation is just rad/ sec. In the case of time constant the minus sign would indicate
the variable magnitude decreasing with time and with plus sign an unstable
system with variable magnitude increasing with time. The time constant itself
tells how long the system takes to react.eg in a Vdc L-R circuit the(zero init condn
and passive parameters)
current is I= V/R( 1- e^ (- R/L*t ) ) here the current takes L/R seconds to reach
say .67 of ss value , one can interpret this as L takes time to establish ss flux..
One could i suppose think of making + R/L by either R being negative
or L as negative . This would not be normal and definitely unusual .sometimes neg R can be seen as a generator (active device) . so we can imagine current building up without final ss a some what impractical case..hope it helps..
Cheers
If we agree that (in electronics) time is running in positive direction only it seems to be logical that time constants can be positive only. Time constants are a measure (an indication) how fast a physical quantity changes its value (up or down).
Thus, even in case of an expression like exp(-RC) the time constant T=RC is to be considerd as positive. The minus sign makes the quantity to decrease with time - that´s all.
As Mr Ramesh said, a negative time constant can result from negative values of R, L or C. I agree with that and would like to add that negative resistance values happen in cases were nonlinear devices are present in a circuit. In practice, there are several devices capable of showing operation conditions with negative resistances, a well known example is the Unijunction transistor (UJT). The negative resistance condition is unstable as the device is not capable of providing energy to sustain it, therefore it jumps to the closest and less energetic operational condition. Other nonlinear devices perform in similar ways. Hopefully this comment will help to go further. Cheers.
call me just narsim .. you are right .good point... we have this in many nonlinear
systems with limit cycles..eg oscillations in motor drives..etc
Cheers
First of all it is defined only for a LTI first order system. And, by definition, it is the amount of time required for the output to reach 63.2% of the steady state value. From this itself it is clear that it is defined for a stable system.
A negative time constant is meaningless for the reasons that : 1) Time can't be negative, 2) If at all we take it negative, analytically we get an unstable system (exponent will diverge) for which there is no physical relevance of a time constant.
Well, as long we are talking about self-impedance, a response on the excitation occurring at the same point, I suppose a time constant is positive, unless negative resistance etc. exists. However, when talking about a transfer-impedance, excitation at some point and response at a distant point, a time constant can be negative. In the Fourier world, at some frequencies the excitation and the response can be in opposite phase due to the runtime between the two points.
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