Simple Examples of Calculation of Rise Time
The aim of this section is the calculation of rise time of step response for some simple systems: all notations and assumptions required for the following analysis are listed here.
- is the rise time of the analyzed system, measured in seconds.
- is the low frequency cutoff (-3 dB point) of the analyzed system, measured in hertz.
- is high frequency cutoff (-3 dB point) of the analyzed system, measured in hertz.
- is the impulse response of the analyzed system in the time domain.
- is the frequency response of the analyzed system in the frequency domain.
- The bandwidth is defined as
- and since the low frequency cutoff is usually several decades lower than the high frequency cutoff ,
- All systems analyzed here have a frequency response which extends to 0 (low-pass systems), thus
- exactly.
- All systems analyzed are thought as electrical networks and all the signals are thought as voltages for the sake of simplicity: the input is a step function of volts.
Read more about this topic: Rise Time
Famous quotes containing the words simple, examples, calculation, rise and/or time:
“This is my letter to the World
That never wrote to Me—
The simple News that Nature told—
With tender Majesty.”
—Emily Dickinson (1830–1886)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“Common sense is the measure of the possible; it is composed of experience and prevision; it is calculation appled to life.”
—Henri-Frédéric Amiel (1821–1881)
“[T]hose wholemeal breads ... look hand-thrown, like studio pottery, and are fine if you have all your teeth. But if not, then not. Perhaps the rise ... of the ... factory-made loaf, which may easily be mumbled to a pap betweeen gums, reflects the sorry state of the nation’s dental health.”
—Angela Carter (1940–1992)
“I left the woods for as good a reason as I went there. Perhaps it seemed to me that I had several more lives to live, and could not spare any more time for that one.”
—Henry David Thoreau (1817–1862)