ESTIMATION AND CONTHOL OK ()l'i:ir\'ri': TIMK OK lUOLAYS 



177 



The linear ('((uatious u.sod for dcN'clopiiii;' the first a])])roxiniaii<)ii 

 oijerate time equations also represcMit the behaN'ior of the three element, 

 two terminal network of Fig. 13, sjiown i'(>ferre(l to a one turn admit- 

 tance form. 'I'his exhibits the eoi'e eddy current (effect as a, I'c^sistor shunt- 

 ing an ideal inductance, rather than as an inlinite line. Whatever \'alue 

 tile shunting resistor may ha\e, it affects only the transient res])onse of 

 the network, the part with which we are now concerned. 



In what follows, it will be assumed that the transformation relations 

 have ah'eady been applied, and the (!<■ values applying to Fig. 13 are 

 effective values related to the winding tui'ns in accordance^ with (Hjua- 

 tions (30). 



For two such networks in series, the voltage division would be in- 

 dependent of time if the ratios of the shunting to series conductances 

 for each structiu-e were eciual. The method de\'eloped for similar struc- 

 tures then would apply with no error. 



Gpe-^E/G 



L, = 



r, = 



R 



f 



NI 



1 

 L, 



Fig. 13 — Equivalent linear circuit represented by time equation. 



The ratio is: 



^-OeIOc ^ ^g- 



This function has a maximum value of 1/c; that is, the shunting re- 

 sistor is at least e times larger than the series resistor. An analysis of the 

 range of core conductances and speed windings in use, shows that the 

 actual resistance ratios are somewhat greater than this and hence the 

 ratios are not quite independent of the structure. However, because the 

 maximum is broad, it reduces the actual range to about 10 per cent, 

 including all windings plus a 2 to 1 Ge change. In turn, this signifies 

 that for a suddenly applied voltage, the initial linear network voltage 

 division would differ from the final by less than 10 per cent. This error 

 decreases with time. 



The above discussion applies to linear networks such as Fig. 13. In 

 an actual magnetic structure the initial voltage division is not affected 

 by eddy currents as they have not had time to })uild up. The voltage 



