Rise Time - Simple Examples of Calculation of Rise Time

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.

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