## Download Signal Flow Analysis by J. R. Abrahams, G. P. Coverley and N. Hiller (Auth.) PDF

By J. R. Abrahams, G. P. Coverley and N. Hiller (Auth.)

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16 branch by branch and calculate the overall transmission. (l - GF), x\ = Xl (l — DC) — x2GEC = - 2 (1 - DC)(1 - GF) - x2GEG, B and therefore xo - Q ) * î = ^ [(1 - DC)(1 - GF) - GECB]. Thus the results agree whether node- or branch-preserving inversions are used, although in general the latter method will produce a flow graph where the transmission is more easily written down from inspection. OPERATIONS WITH A FLOW GRAPH 29 There are as many possible inversions of a flow graph as there are arrangements of the related algebraic equations.

16. Inversion of path 012, by splitting two nodes. through Fig. 16 branch by branch and calculate the overall transmission. (l - GF), x\ = Xl (l — DC) — x2GEC = - 2 (1 - DC)(1 - GF) - x2GEG, B and therefore xo - Q ) * î = ^ [(1 - DC)(1 - GF) - GECB]. Thus the results agree whether node- or branch-preserving inversions are used, although in general the latter method will produce a flow graph where the transmission is more easily written down from inspection. OPERATIONS WITH A FLOW GRAPH 29 There are as many possible inversions of a flow graph as there are arrangements of the related algebraic equations.

The problem of Fig. 23 emphasizes the point that the flow graphs should be chosen in the form that coincides with our knowledge of the circuit. For instance, we know that — Ï2 == *12 "T *22 and Ï31 = Ï41· I2 31 n 2l '32 FIG. 24. Flow graph for network of four quadripoles. 56 SIGNAL FLOW ANALYSIS It is therefore clear that i2 should be a sink and the other incoming currents represented by source nodes. Using this flow graph the relationship between the output voltage v3 -and either of the input voltages may be found by Mason's rule.