For a correct understanding of internal transfer functions, the difference between intrinsic and extrinsic integrators must be clear.
The signal flow graph of the filter shown in Figure 6 contains three branches designated by 1/s . These branches represent the intrinsic integrators. The extrinsic integrators each consist of one intrinsic integrator together with all the branches in the signal flow graph that are connected to its input. Consider for instance the leftmost integrator in the signal flow graph of Figure 6. Figure 7 shows both the intrinsic and the extrinsic integrator that correspond to this integrator.
The intrinsic integrators have no direct representation in the filters of Figures 3 and 5. The extrinsic integrators, however, are represented in these circuits. The output node of an intrinsic integrator is the output node of the corresponding extrinsic integrator and therefore corresponds to the output node of the appropriate physical integrator. The input nodes of the intrinsic integrators, on the other hand, do not exist in real filters. But these nodes are important in the filter design program.