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:
“We may prepare food for our children, chauffeur them around, take them to the movies, buy them toys and ice cream, but nothing registers as deeply as a simple squeeze, cuddle, or pat on the back. There is no greater reassurance of their lovability and worth than to be affectionately touched and held.”
—Stephanie Martson (20th century)
“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)
“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)
“Could it not be that just at the moment masculinity has brought us to the brink of nuclear destruction or ecological suicide, women are beginning to rise in response to the Mother’s call to save her planet and create instead the next stage of evolution? Can our revolution mean anything else than the reversion of social and economic control to Her representatives among Womankind, and the resumption of Her worship on the face of the Earth? Do we dare demand less?”
—Jane Alpert (b. 1947)
“Everything ponderous, viscous, and solemnly clumsy, all long- winded and boring types of style are developed in profuse variety among Germans—forgive me the fact that even Goethe’s prose, in its mixture of stiffness and elegance, is no exception, being a reflection of the “good old time” to which it belongs, and a reflection of German taste at a time when there still was a “German taste”Ma rococo taste in moribus et artibus.”
—Friedrich Nietzsche (1844–1900)