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# Simplification of Networks

Communication networks are often complicated, and it sometimes is advantageous to reduce them to simple networks before a final solution is made. Thus, in Fig. 9 (a) suppose that it is desired to find the current IL that the generator of voltage Eg and of internal impedance Zg sends through the load impedance ZL.

 Figure 9. Diagrams indicating the steps in simplifying circuits.

The combination ZA, ZB, and Zc can be treated as a π section, and the equivalent T section can be obtained from equations 4, 5, and 6. This gives the circuit of Fig. 9(b). These new impedances are called Z1, Z2, and Z3.

The combination ZD, ZE, and ZF also can be treated as a π section, and the equivalent T section can be found from equations 4, 5, and 6, giving the circuit of Fig. 9(c) with the new impedances called Z4, Z5, and Z6.

All series impedances are then added, giving Fig. 9(d), which can readily be solved for the desired current IL through the load impedance ZL.

Last Update: 2011-05-14