Now let 



INDUCTANCES, CAPACITANCES AND RESISTANCES 



1 



CO. 



(LC) 

 JQ 



1/2 



CO, 



Zj, = M^L 



a> 



J+Q 



CO coj 



At co/cOg = 1, this is approximately equal to co^LQ if Q is large. Putting cOg 

 back in terms of L and C, and Q back in terms of L, C, and R, we see that 

 MJMg = 1, Zj, = Ll(CR), as before. 

 Further, we have 



\Z-p\ = ^oL 



co^ 



.CO 



+ Q' 



i + e 





1/2 



cOqL is a constant of the circuit. The impedance function for a parallel reso- 

 nant circuit is plotted in the form \Zj\jcOgL as a function of frequency, for 

 various Q, in Graph 25. 



Shunt damping 



We often need to control the damping of a resonant circuit, and this is 

 conveniently achieved by varying the amount of resistance present. Hitherto 

 we have considered the damping resistance as being in series with the induc- 

 tance, because this condition must obtain with real components, being the 

 resistance of the inductor winding. However, if the damping on a given 

 resonant circuit is insufficient we can get more by connecting additional 

 resistance in series with the inductor, or by connecting resistance across it 



(b) 



Figure 5.9 



(or across the capacitance). When a resistance is connected across one of 

 the reactive elements the circuit is said to be 'shunt damped'; thus the 

 circuits of Figure 5.9 are equivalent. The amount of shunt damping required 

 is suggested by the fact that a parallel resonant, series-damped circuit con- 

 taining resistance R behaves as a resistance R' = LfCR {Figure 5.9a). Thus, 



80 



