Investigation Into Formation of Rise Time and Fall Time of Nanosecond Rectangular Pulses With S Curve

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Abstract
The $S$ curve, with an analytical expression of $y(t) = Y$ /[ $1+ A$ exp(−kt)], has a slow-fast-saturation growth tendency, where $Y,A$ , and $k$ are constants. The formation mechanism of the rise time and the fall time of nanosecond rectangular pulses is investigated in perspective of the $S$ curve. It is found thattherise time of a nanosecond pulse is not cliffy but takes on the $S$ -curve feature, which is due to the electron avalanche in the switch-on process. In addition, the fall time of a nanosecond pulse is also not cliffy too but appears like an inverted $S$ -curve, which is due to the pulse reflection and the closure of the switch. A theoretical formula for the nanosecond rectangular pulses is presented and the output pulses of a Tesla-type generator and an LTD-type generator are reconstructed by referring to the theoretical formula. In the end, the formation mechanism of nanosecond rectangular pulses is discussed from the viewpoint of the self-feedback process.
Funding Information
  • National Natural Science Foundation of China (12175182)