INDUCTANCES AND RESISTANCES 



and for the arrangement of Figure 4.14 



f^out 



R 



m 



R+JXl 



Vont 



in 



1 



U)+' 



1 1/2 



Clearly these are of the same form as the equations \j{{\looCRf + 1}^'^, for 

 the simple R-C high-pass filter, and \j{{ojCRf + 1}^^" for the corresponding 

 low-pass filter. That is, Figure 4.13 is a high-pass filter which turns over at 

 i?/L, and Figure 4.14 is low-pass, also turning over at co = R/L. R-L 



CO 



filters are not used in electronics, probably because inductors are more 

 expensive, less available, bulkier, and generally less satisfactory than capaci- 

 tors ; but it is important to bear in mind that they exist, because they set a 

 limitation to transformer performance, as we shall see. 



M-v kiki] 



^/v,^ 







-r^uur- 



^in 



R. 



Kout 



"tl 



I 



Figure 4.14 



A/, turns A/2turns 



Figure 4.15 



Tightly coupled mutual inductance 



If an iron core be used to guide magnetic flux so that nearly all the lines 

 of force due to current in one coil of a mutual inductance thread the turns 

 comprising the other, then the two windings are said to be 'tightly coupled'; 

 this is in contradistinction to the state of aff'airs where the coils are some 

 way apart, no core is provided, and the windings are said to be 'loose coupled'. 

 Most mutual inductances occurring in electrobiology are tightly coupled 

 (i.e. transformers), but loose coupled circuits are employed when using radio 

 frequency techniques (say, co > 10^) as in the R-F coupled stimulator. 



Suppose we have two tightly coupled windings, of self inductances L^ and 

 Lg and mutual inductance M. If winding 1 be supplied with any varying 

 current i^ {Figure 4. 15) then 



dzi 



^ ^ dt 



dk 

 dt 



and 



so 



M 

 M 



Now let the generator of i^ be disconnected, and a generator of any other 

 varying current /g be connected to winding 2, then 



d/o 



""2 - ^2 d/ 



and 



ei = M 



d/g 

 dt 



60 



