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.