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:
“When I think of God, when I think of him as existent, and when I believe him to be existent, my idea of him neither increases nor diminishes. But as it is certain there is a great difference betwixt the simple conception of the existence of an object, and the belief of it, and as this difference lies not in the parts or composition of the idea which we conceive; it follows, that it must lie in the manner in which we conceive it.”
—David Hume (1711–1776)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
““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)
“[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)
“A man in love is like a clipped coupon—it’s time to cash in.”
—Mae West (1892–1980)