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

Abstract

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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> [cosh(1)-cosh(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> /τ)] in the interval (-τ/2)≤ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> ≤(τ/2) and zero for all other times. The response equivalent time transient function, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> ̅), 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≅ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> δ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> is a constant.