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OVERVIEW


Rise time is an important and fundamental parameter in all high speed circuits. Many efforts over the years have been made to reduce the rise times of generators and measuring equipment.


CALCULATION OF RISE TIME


For any Gaussian-response system, the rise time (Tr) is related to Bandwidth (BW) by the formula

Tr = 0.35 /BW.

or

  • risetime = 0.35


where BW is in GHz and risetime is in Nanosecond s

Here BW is approximated to high frequency cutoff (-3dB point) (Fh). In general BW = Fh - Fl. where Fl is the low frequency cutoff. So, if the bandwidth of an oscilloscope is 350 MHz , its 10% to 90% risetime is 1 nanosecond.


NETWORK TIME CONSTANT


For a simple one stage RC network, rise time (Tr) is related to the network time constant (tau) by a factor:

  • 2.197


This factor can be derived by using the equation

y = A(1-1/e^(t/tau))

  • A and 0.9---A (10% and 90% of stead-state value) and solving for t's where A is the steady-state value, t time and tau the time constant.

  • A and t2 be the solution for when setting the equation to 0.9---A. Subtracting the two we get:


  • ln(9)


Which is the rise time.

Rise time is therefore related to the time constant by:

  • ln(9) = tau---2.197


  • pi---F_H


  • pi---F_H = 0.349/F_H


Since the upper -3dB point is approximately equalt o the bandwidth,

Tr = 0.35/BW


FACTORS AFFECTING RISE TIME


Rise time (also risetime) values in a resistive circuit are primarily due to stray Capacitance and Inductance in the circuit. Because every Circuit has not only Resistance , but also Capacitance and Inductance , a delay in voltage and/or current at the load is apparent until the Steady State is reached. In a pure RC Circuit , the output risetime (10% to 90%) is approximately equal to 2.2 RC.


RISE TIME IN CONTROL APPLICATIONS

In control theory, it is often defined as the 10% to 90% time from a former Setpoint to new setpoint. The Quadratic approximation for normalized rise time for a 2nd-order system, Step Response , no zeros is:
: t_r = 2.230n^2-0.078n+1.12\, where n\,=damping ratio


SEE ALSO