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(2t/τ)] in the interval (-τ/2)≤t≤(τ/2) and zero for all other times. The response equivalent time transient function, h(t̅), 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≅mδ³ where m is a constant.