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:
“His character as one of the fathers of the English language would alone make his works important, even those which have little poetical merit. He was as simple as Wordsworth in preferring his homely but vigorous Saxon tongue, when it was neglected by the court, and had not yet attained to the dignity of a literature, and rendered a similar service to his country to that which Dante rendered to Italy.”
—Henry David Thoreau (1817–1862)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
““To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.”
“And yours,” said the P.B.”
—Samuel Beckett (1906–1989)
“... the French know that you must not succeed you must rise from the ashes and how could you rise from the ashes if there were no ashes, but the Germans never think of ashes and so when there are ashes there is no rising, not at all and every day and in every way this is clearer and clearer.”
—Gertrude Stein (1874–1946)
“The inmost in due time becomes the outmost.”
—Ralph Waldo Emerson (1803–1882)