Analytic model and bilateral approximation for clocked comparator

The paper discusses a model of clocked comparators, the dynamic characteristics of which are described by differential equations. In the model as an argument is used not time, but the phase difference between two signals, thereby the law of causal relationship may not apply. The paper demonstrates an example of the analytic solution of simplified model represented by first order differential equation with variable coefficient. More refined models give higher-order differential equations, which not always need to be solved analytically. As an alternative an approximate bilateral solution of differential equations is introduced. Experimental results demonstrate the transition characteristic of clocked comparator, where decision stage is built on two bipolar transistors.