The transient response of a square-law gate sampling oscillographic system excited by a steplike pulse having overshoot

The transient response of a square-law gates sampling oscillographic system excited by a step-like pulse with overshoot is quantitatively analyzed. The square-law gate is driven by a symmetrical hyperbolic cosine pulse of the form
B
[cosh(1)-cosh(2
t
/τ)] in the interval (-τ/2)≤
t
≤(τ/2) and zero for all other times. The response equivalent time transient function,
h
(
t
̅), and overshoot δ̅, are derived. For engineering applications it can be shown that the relationship between the system response overshoot δ̅ and the input pulse overshoot δ is δ̅≅
m
δ
³
where
m
is a constant.