Rise time

In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value.^[1] These values may be expressed as ratios^[2] or, equivalently, as percentages^[3] with respect to a given reference value. In analog electronics and digital electronics^{[citation needed]}, these percentages are commonly the 10% and 90% (or equivalently $0.1$ and $0.9$ ) of the output step height:^[4] however, other values are commonly used.^[5] For applications in control theory, according to Levine (1996, p. 158), rise time is defined as "the time required for the response to rise from $x%$ to $y%$ of its final value", with 0% to 100% rise time common for overdamped second order systems, 5% to 95% for critically damped and 10% to 90% for underdamped ones.^[6] According to Orwiler (1969, p. 22), the term "rise time" applies to either positive or negative step response, even if a displayed negative excursion is popularly termed fall time.^[7]

^ "rise time", Federal Standard 1037C, August 7, 1996
^ See for example (Cherry & Hooper 1968, p.6 and p.306), (Millman & Taub 1965, p. 44) and (Nise 2011, p. 167).
^ See for example Levine (1996, p. 158), (Ogata 2010, p. 170) and (Valley & Wallman 1948, p. 72).
^ See for example (Cherry & Hooper 1968, p. 6 and p. 306), (Millman & Taub 1965, p. 44) and (Valley & Wallman 1948, p. 72).
^ For example Valley & Wallman (1948, p. 72, footnote 1) state that "For some applications it is desirable to measure rise time between the 5 and 95 per cent points or the 1 and 99 per cent points.".
^ Precisely, Levine (1996, p. 158) states: "The rise time is the time required for the response to rise from x% to y% of its final value. For overdamped second order systems, the 0% to 100% rise time is normally used, and for underdamped systems (...) the 10% to 90% rise time is commonly used". However, this statement is incorrect since the 0%–100% rise time for an overdamped 2nd order control system is infinite, similarly to the one of an RC network: this statement is repeated also in the second edition of the book (Levine 2011, p. 9-3 (313)).
^ Again according to Orwiler (1969, p. 22).

[Std1037C-1] "rise time", Federal Standard 1037C, August 7, 1996

[10-90-2] See for example (Cherry & Hooper 1968, p.6 and p.306), (Millman & Taub 1965, p. 44) and (Nise 2011, p. 167).

[3] See for example Levine (1996, p. 158), (Ogata 2010, p. 170) and (Valley & Wallman 1948, p. 72).

[4] See for example (Cherry & Hooper 1968, p. 6 and p. 306), (Millman & Taub 1965, p. 44) and (Valley & Wallman 1948, p. 72).

[5] For example Valley & Wallman (1948, p. 72, footnote 1) state that "For some applications it is desirable to measure rise time between the 5 and 95 per cent points or the 1 and 99 per cent points.".

[risedef-6] Precisely, Levine (1996, p. 158) states: "The rise time is the time required for the response to rise from x% to y% of its final value. For overdamped second order systems, the 0% to 100% rise time is normally used, and for underdamped systems (...) the 10% to 90% rise time is commonly used". However, this statement is incorrect since the 0%–100% rise time for an overdamped 2nd order control system is infinite, similarly to the one of an RC network: this statement is repeated also in the second edition of the book (Levine 2011, p. 9-3 (313)).

[7] Again according to Orwiler (1969, p. 22).

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