Time Constant systems have many uses.  One important - but not immediately obvious - use is to filter signals.

        A filter is a device that removes something from something else.  Examples include fuel filters that remove small dirt particles from the stream of gasoline that fuels your car.  Electrical filters remove electrical noise (often produced by lightning, arcing of motor commutators, arcing in switches, etc.) from electrical signals.

        Time constant systems can often be used as electrical filters.  The important aspect of the behavior of a time constant system is that it does not respond instantaneously to a sudden change of input.  Here is the response of a time constant system to a step change of input (from one level to another level).  In this case it takes close to ten seconds before the output reaches a steady state value.

        We can take advantage of this behavior to build an electrical filter.  We need an electrical time-constant system, however.  The simplest such circuit is the R-C (Resistor-Capacitor) circuit shown below.

In this circuit, v_in(t) is some input signal source, and the output voltage, v_out(t), is a filtered version of the input signal.  The circuit satisfies the same differential equation satisfied by most simple time-constant systems.

        In this situation, the parameters are:

• t = the Time Constant
• For the electrical circuit above, the time constant is the product of electrical resistance, R, and the electrical capacitance, C.  In other words, t = R*C
• Note the amazing similarity of these constants to those found in the thermal time-constant system we used as an example in another page.
• G = the System Gain
• This system has G = 1, so we really don't need to have G in there at all.

• If the input is constant, then the output should asymptotically approach the input.
• In a thermal time-constant system, the temperature of the system asymptotically approaches the ambient temperature.  If there is a heat input, then the system temperature asymptotically approaches a steady state.
• If there is a short pulse added to the input, the system will not respond much because the pulse is too short and doesn't give the system enough time to respond.

        There's one last point.  If you really want to understand how these things filter, you are going to need to know more about how to represent signals.  You need that so that you can apply your mathematical skills to analysis of these circuits.

• Signals
• Representation of Sinusoidal Signals
• Parameters of Sinusoidal Signals
• Fourier Series Representations