We might think, at this point, that we are done, because we can simply ``replace'' each RLC type circuit element by the derived signal flow path. Consider what happens with the discretization of the following simple LC filter:
Here, is an input voltage, the output voltage, the current, and in addition, we will define to be the voltage across the inductor. We thus have the three differential equations:
The first two come from the definitions of the inductor and capacitor respectively, the third from Kirchoff's voltage law.
Discretizing these equations according to the trapezoid rule yields:
and this yields the following signal flow diagram:
Note however, the delay-free loop which prohibits this implementation from being realizable.
In other terms, connecting two explicit finite difference models has resulted in an implicit finite difference model.