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BELL SYSTEM TECENICALJOVRNAL 



As an example of the determination of the reactance associated with a 

 given resistance characteristic, consider the resistance characteristic of Fig. 



7 and the straight line approximation shown in dotted form. The slopes 

 of the straight lines are determined as illustrated in Table VTII. 



Having determined the slopes of the various straight lines of the approxi- 

 mation, the reactance can be summed at any desired frequency. As an 

 illustration the reactance is summed at/ = 1.0, in Table ^X. 



The mesh computed reactance of the network of Fig. 7 is plotted in Fig. 



8 and the reactance summed for/ = 1.0 is seen to be within .01 ohm 

 of the true reactance. The reactance was summed at a considerable number 

 of frequencies and the results plotted as individual points in Fig. 8. The 

 degree of approximation to the true reactance should be similar to the 



Figr. 9 — Parallel T network. 



degree of approximation to the original resistance and this is borne out by 

 the example where the straight line approximation to the resistance char- 

 acteristic is within ± .03 ohm and the maximum departure of the reactance 

 determined from the straight line approximation is ± .025 ohm. 



As was pointed out in the attenuation example a much simpler straight 

 line approximation to the resistance characteristic would have resulted in a 

 reactance determination without too much greater error than the deter- 

 mination of the illustration. 



A word of caution is necessary in connection with the use of the straight 

 line approximation method discussed above. The true phase or reactance 

 is reliably obtained only in those cases where the problem in question is a 

 minimum phase one. In order to illustrate the failure of the method in 

 those problems in which non-minimum phase conditions exist consider the 

 parallel T network of Fig. 9. The transfer impedance Z012 defined by the 



