INDUCTANCES, CAPACITANCES AND RESISTANCES 



frequency which is usually in the region of the upper end of the pass-band a 

 series resonance occurs between Q + n^C^ and (1 — k'^)Lj, which appears 

 as a g-fold increase in the input to the ideal transformer. The effect is 

 to put a 'hump' into the transmission characteristic (Figure 5.11) whose 



3\^- 



L 



magnitude depends on the shunt damping (i?^ + R^jn^ and the series- 

 damping r + Rj,. With good design the hump can be useful in extending 

 the pass-band at the upper frequency end. 



This resonance sets a limit to the voltage step-up which may be had from a 

 signal transformer; for if n is too great, Q + «^Q becomes of such a size 

 that the resonance comes down into the hoped-for pass-band. Since trans- 

 mission falls away quickly above the resonance {Graph 22) the pass-band 

 actually obtained will be seriously narrowed. 



Smoothing section 



In the language of resonant circuits, Figure 5.12 is a shunt-damped, series- 

 resonant circuit, and we may anticipate that it will have a transmission 

 characteristic similar to the series-damped case {Graph 23). In the next 



L 



^WWWM^ 



X 



I 



Figure 5.12 



chapter we shall see that when power from the a.c. mains is rectified to 

 produce a direct voltage, the output carries a superposed 'ripple'. This ripple 

 is generally undesirable, and a 'smoothing section', comprising an inductor 

 and a capacitor, is employed to filter it out. In Figure 5.12, the generator 

 represents the rectifier system, L and C are the smoothing section, and R 

 represents the resistance of the apparatus being supphed. 



From Graph 22 it is clear that the device must be operated well above the 

 resonant frequency. If co is the ripple frequency and co^ = 1/(LC)^'^, as usual, 

 then if colco^ is less than unity, no filtering is achieved whatsoever, whilst if 

 (o = a>o and the load resistance is large (Q high), far from attenuating the 

 ripple the network may magnify it ! In smoothing section design it is essential 

 to check that the L-C product is adequate. 



82 



