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or other output device is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained within a specified error band.
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Systems with energy storage cannot respond instantaneously and will exhibit transient responses when they are subjected to inputs or disturbances.
289:{\displaystyle T_{s}=-{\frac {\ln({\text{tolerance fraction}}\times {\sqrt {1-\zeta ^{2}}})}{{\text{damping ratio}}\times {\text{natural freq}}}}}
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Settling time is the time required for an output to reach and remain within a given error band following some input stimulus.
193:{\displaystyle T_{s}=-{\frac {\ln({\text{tolerance fraction}})}{{\text{damping ratio}}\times {\text{natural freq}}}}}
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411:{\displaystyle T_{s}=-{\frac {\ln(0.02)}{\zeta \omega _{n}}}\approx {\frac {3.9}{\zeta \omega _{n}}}}
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for computing settling time, rise time, and other step response characteristics
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Modern
Control Engineering (5th Edition), Katsuhiko Ogata, p.160
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Time required for the output of an amplifier to stabilize
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Tay, Teng-Tiow; Iven
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489:Second-Order System Example
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317:{\displaystyle \zeta \ll 1}
298:Thus, if the damping ratio
122:{\displaystyle \zeta \ll 1}
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464:. Birkhäuser. p. 93.
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511:Settling Time Calculator
462:High performance control
91:The settling time for a
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494:Op Amp Settling Time
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80:Mathematical detail
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520:Categories
438:References
72:Definition
427:Rise time
397:ω
393:ζ
384:≈
372:ω
368:ζ
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345:−
309:≪
306:ζ
276:×
255:ζ
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52:amplifier
421:See also
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360:0.02
63:slew
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351:ln
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