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.

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