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 pain was too great. He begged me for the simple mercy of death. And I could do nothing else but help him leave a world that had become a sleepless, tortured nightmare to him.”
—Robert D. Andrews, and Nick Grindé. Dr. John Garth (Boris Karloff)
“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)
““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)
“Thou gav’st me life, but mortal; for that one
Favour I’ll make full satisfaction:
For my life mortal, rise from out thy hearse,
And take a life immortal from my verse.”
—Robert Herrick (1591–1674)
“For me, it’s enough! They’ve been here long enough—maybe too long. It’s a funny thing, though. All these years Fred was too busy to have much time for the kids, now he’s the one who’s depressed because they’re leaving. He’s really having trouble letting go. He wants to gather them around and keep them right here in this house.”
—Anonymous Parent. As quoted in Women of a Certain Age, by Lillian B. Rubin, ch. 2 (1979)