# Time constant for RLC circuit?

#### Sci

Joined Jan 21, 2005
8
Whats the time constant for an RLC circuit?

#### dragan733

Joined Dec 12, 2004
152
Originally posted by Sci@Feb 13 2005, 05:40 PM
Whats the time constant for an RLC circuit?
[post=5297]Quoted post[/post]​
I think that in a RLC circuit one doesn't define time constant. There has two expressions with dimensional unit: time, but that is not time constant.
T=1/((-R/2L)±SQRT((R/2L)^2-1/(LC)))

#### iamspook

Joined Aug 6, 2008
27
Time Constant for an RC circuit is tor = RC
for an LC circuit it is tor = L/R

In a RLC circuit, you have both combined to worry about. So we actually need to calculate what's
called the Q-factor. (Quality factor) which describes how resistance dampens the peak value at the resonant frequency, and the bandwidth over which oscillation is significant.

In a series RLC tuned circuit, Q = (1/R )(sqrt(L/C))
In a parallel: Q = R sqrt(C/L)

Q is called 'quality' because it is the ratio of 2 * pi *
(energy stored) / (power lost)

Pure L and C lose no energy, so it is the resistive component which
lowers Q (and makes Q finite)

If you pull a weight on a spring and let it go, then it will exponentially
decay as resistive forces absorb and dissipate energy. Since the maths
for this involves an exponential decay, you need some point which describes
when it falls to a percentage point of the original swing, otherwise theoretically,
it will be infinitesimally moving for ever. The time constant is the time it takes
to reach that point. Q factor describes it nicely.

Depending on the weight and strength of spring, this decay will either be oscillatory
or an exponential decay. There is a special value of Q which describes the
boundary between oscillatory and exponentially decaying behaviour. This is called
'critical damping' and is a desirable target for filter networks. (The calculation of
Q(crit) varies with the type of filter.