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 underdamped second order systems, 5% to 95% for critically damped and 10% to 90% for overdamped 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]

  1. ^ "rise time", Federal Standard 1037C, August 7, 1996
  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.".
  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).