INDUCTANCES AND RESISTANCES 



The ideal transformer 



This is supposed to have a voltage ratio between input and output of n, 

 so that ^2 = ne^, and to be completely efficient, so that e^i^ = ^I'l and there- 

 fore /'i = ni^. If a load R be connected to the output terminals, then i^ = 

 e^lR, and it is easy to see that /^ = n^eiJR. 



Where -t; =n 

 A/, 



Figure 4.23 



Comparing this with the transformation obtained by electromagnetic induc- 

 tion, we see that /^ = n^eJR is analogous to the useful fraction of primary 

 current (NjNif E^jR where 1 : « : : A^^ : N^, and we can therefore represent 

 the electromagnetic transformer by an ideal transformer and a self inductance 

 {Figure 4.23). 



Reflection through an ideal transformer — n^E^/R is the current which would 

 flow if, instead of the ideal transformer and load resistance R, there was 



% 



I 



^ n 



"Vn^ 



(c) 



(b) 

 Figure 4.24 



merely a resistance Rjn^. It therefore appears that in Figure 4.24 a-c are 

 equivalent. The secondary winding load resistance R is said to be reflected 

 as a resistance Rjn^ across the input terminals. 



Use of ideal transformer for matching — The ability of an ideal transformer 

 to convert voltages and currents is often incidental to its ability to match a 



•/?/ 



%,2 



Figure 4.25 Figure 4.26 



generator to a load. For in Figure 4.25, if we have a generator of internal 

 resistance r, feeding a load resistance R, then R is reflected through the 

 transformer as i?/«^, and conditions for optimum power transfer are met 

 when n = {Rfr^^ {Figure 4.26). 



The real transformer 



We are now in a position to carry out a simplified analysis of the behaviour 

 of the real transformer, which is a practical component which attempts to 

 emulate the ideal transformer in transforming voltages and currents, whether 



64 



