# Rise and Fall Times - 2.6 English

## Zynq UltraScale+ RFSoC RF Data Converter Gen 1/2/3/DFE LogiCORE IP Product Guide (PG269)

Document ID
PG269
Release Date
2022-10-21
Version
2.6 English

In some applications where the input signal is a burst signal, or the amplitude changes dramatically, the rise/fall time of the leaky integrator needs to be evaluated. The rise time can be derived from its step response; the fall time can be derived from its response with the initial conditions. The following formulas show how to calculate the rise and fall times, respectively:

• h[n] = 1 - αn+1
• h[n] = αn+1

where:

α = 1 - 1/2λ

Considering when the output of leaky integrator achieves the 90% of final value for rise time calculation, which is around 1 dB lower than final value.

For the fall time, 1% (-40 dB) is used as which will illustrate a full-scale signal fall down to -40 dBFS, this makes the fall time is around double of rising time.

The following table shows rise/fall time for reference based on different time constants:

Table 1. Leaky Integrator Rise/Fall Time
Time Constant Rise Time (0 to 90%) Fall Time (1 to 1%) Unit
2^0 1 1 T4/T8
2^2 7 15 T4/T8
2^4 34 70 T4/T8
2^8 587 1175 T4/T8
2^12 9429 18859 T4/T8
2^14 37723 75447 T4/T8
2^16 150900 301801 T4/T8