INDUCTANCES AND RESISTANCES 



direct or alternating, without loss of power. Real transformers are used in 

 three ways. 



Power transformer — Works on alternating current of a definite frequency 

 and at a definite voltage from the mains, and steps the voltage up and down 

 as required by other parts of the apparatus. Prime consideration, efficiency. 



Pulse transformer — This handles a waveform such as Figure 4.27, and 



Voltage 



Voltage 



Figure 4.27 



Figure 4.28 



might be used, for example, to match the output of a stimulator to a prepara- 

 tion. Prime considerations, efficiency and absence of distortion. 



Audiofrequency transformer — This deals with a 'signal', some complicated 

 waveform such as Figure 4.28, which might be an E.C.G., E.E.G. or heart 

 sound. A signal of this kind is composed of the sum of a number of pure 

 sinusoidal waves of fluctuating frequency and amplitude, and the requirement 

 of the transformer is that it should treat all the frequencies alike; thus 

 prime consideration, absence of distortion. 



At this point it may be objected that the pulse in Figure 4.27 is also a signal, 

 and that therefore a pulse transformer and a signal transformer are the same 

 thing. In fact this is perfectly true, but the analyses for the two types are 

 quite different because the questions one is likely to ask about their per- 

 formances are different. We apply transient analysis to the pulse transformer, 

 and steady-state analysis to the signal transformer. 



In a real transformer we have two windings L^ and L^ linked by an iron 

 core. The windings have resistances R^ and i?, because they are made of 

 real wire and it cannot be avoided. The coupling is made as tight as it can 

 possibly be made, yielding a k value usually better than 0-9. We represent 



{\-k^)Lp a 



Figure 4.29 



this State of affairs by splitting L^ into two parts, k^Lj, whose flux completely 

 links with Lg, and (1 — k^)Lp whose flux fails to Hnk with L^. (1 — k^)Lj, is 

 called the 'leakage inductance' and k^L^ the 'primary inductance'. For a good 

 transformer/:^ is sufficiently near one for it to be permissible to call the primary 

 inductance Lj,. The arrangement feeds a load Rj^ and is fed by a generator 

 of unspecified type having internal resistance r. This gives us Figure 4.29. 



There ought to be a further resistance to represent losses occurring in the 

 iron — hysteresis and eddy-current loss — but we cannot go too deeply into 

 transform.er theory here. 



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