User:Mets501/Sandbox

The input signal is first split into two halves; the first is attenuated to a fraction $f$ of its original amplitude $A$ and the second is inverted and delayed by a time $t_{d}$, where both $f$ and $t_{d}$ are configurable depending on the application. When these two pulses are then added together, the zero crossing is always at a specific time, the time at which the CFD output pulse begins.

As an example, assume that the input pulse is a linear ramp, $V=At$. This is split into two pulses, $V_{1}=fAt$ and $V_{2}=-A(t-t_{d})$. Solving for the zero crossing time $t$ of the sum of these two pulses ($V_{1}+V_{2}$) gives

$0=fAt-A(t-t_{d})$

$t={\frac {t_{d}}{1-f}}$

which is independent of the pulse amplitude.