Time constant
The time constant T describes a characteristic variable of a dynamic system. A complex dynamic system may be characterized by n time constant Ti. Dimension of the time constant is second.
The time constant is generally the time period t = T1 / e, which requires an exponentially sinking process to 1 / e sink (about 36.8% ) of its initial value. An exponentially increasing process is growing in this period to about 63.2 % of the final value.
This time constant is not confused with the half-life T1/2zu indicating a period of time for a drop to 50% and corresponds to about 69.3 % of the time constant.
Examples of exponential running processes are the removal of a contaminant in water, the cooling of a hot water cylinder, the radioactive decay of elements and electrical circuitry to charge the capacitors or the current through a coil through a resistor.
Time constants in communication engineering and Electrical Engineering
The time constant T = 1 / p of an element is the characteristic parameter in Laplace transformation. Time constants (symbol: , Greek: tau) are used in communications engineering to describe the frequency response of filters and transmission paths, for example, in the equalization at the tape, the radio stations, with the record ( Emphasis with pre-emphasis and de-emphasis ), and in motion in the digital technology. In electrical engineering, they characterize the time courses of the voltage rise during charging of capacitors or the current rise in coil through a resistor.
Capacitor
The charging of capacitors at a constant voltage across a resistor connected in series with the capacitor and the discharge of capacitors through a resistor are exponential running processes. The time constant of series circuit of capacitor and resistor is the product of the resistance R and the capacitance C.
The rise of the voltage takes place in the charge on the capacitor after
Approximate values for the voltage of the capacitor with respect to the DC voltage:
After t = 5 · τ is the capacitor to the (1 - e -5) charged -fold ( approximately 99.3 % ) of the voltage. If there are no particularly high accuracy requirements, considering the charging order as completed.
Further approximations are:
Coil
The increase in the current in a series circuit of a coil L, with its inductance and the resistance R at a constant voltage, and the decay of the current is an exponential running processes. The time constant of the series connection of inductance and resistance is the ratio of the inductance and the resistance:
The rise of the current is carried out by:
τ is the time after which the current through the inductor reaches about 63.2% of Endstromes. 5 · τ after the current has reached approximately 99.3% of its final value, is usually considered so that the switch- complete.