INDUCTANCES, CAPACITANCES AND RESISTANCES 



if the circuit is critically series-damped by series resistance R = 2(L/C)^'-, it 

 will also be critically damped by a shunt resistance 



L U^V'^ 



Conclusions 



R' 



'Kl 



Generator 



Series L-C-R 



Parallel L-C-R 



Constant-voltage 

 alternator — E 



Constant-current 

 alternator — / 



Constant direct voltage 



Constant direct current 



At resonance, current rises 

 to max. £■//?. Voltage 

 magnification of Q times 

 available across reactive 

 elements 



At resonance, terminal 

 voltage falls to min. /Z, 

 according to Graph 23 



Varies from vigorous ring- 

 ing to sluggisH follow-up, 

 depending on damping 



Trivial 



At resonance, generator 

 current falls to min. 



EV{LICR) 



At resonance, terminal 

 voltage rises to maximum 

 IZp according to Graph 24. 

 Current magnification of 

 Q times in circuit 



Trivial 



Varies from vigorous ring- 

 ing to sluggish follow-up, 

 depending on damping 



Critical series damping, R = 2{LjCyi~. Critical shunt damping, R = ^(LlCyi^. 

 Critical damping corresponds to Q = 1/2. 



The reader may care to satisfy himself that the cases marked 'trivial' 

 are in fact so. The circuit responses are the sum of responses found for more 

 elementary circuits in previous chapters. 



Effect of a series resonance upon the performance of signal transformers 



In deriving the equivalent circuit for the signal transformer we have 

 neglected the effects of the self-capacitance of the two windings. 



Rp*r 



n-K^)Lp 



'Rl*Rs 





^out 



i+n 



2c2 



Figure 5.10 



Let the effect of the distributed secondary capacitances be represented by a 

 capacitor C^, connected across the secondary winding, and let the distributed 

 primary capacitances be represented by Q across the primary winding. 

 Then Q is reflected across to the primary side as n^C^ {Figure 5.10). At a 



81 



