RESISTANCE AND CAPACITANCE IN SERIES 



At this point the reader may accuse me of doing precisely what I have 

 warned against; namely, of converting voltage ratios into decibels with 

 insufficient reference to the resistances across which the voltages appear. 

 He may further ask, what is the point of considering the behaviour of net- 

 works to which no useful load is attached ? The answer is that the filters in 

 Figures 3.29 and 3.31 are frequently used to feed a valve, which constitutes a 

 load, but a load whose resistance is substantially infinite, and which therefore 

 does not influence the operation of the filters. If the load resistance is 

 infinite in all cases, we can convert voltage ratios into decibels without 

 hesitation. 



As an exercise, the reader may care to consider what happens when the 

 simple R-C high- and low-pass filters are fed from a real generator and work 

 into a load which is not of infinite resistance. 



R-C filters comprising cascaded sections 



Suppose Fin is the sum of two alternating voltages of frequency co^ and Wg, 

 and that we wish to filter out as much as possible of the contribution of the 

 generator working at 0)3, the higher frequency. We use, of course, a low-pass 

 filter {Figure 3.32). If m^ and oj^, are close together, the dilTerence in the 



Frequency^ 



IS (O 



WWW 



Frequency (r,^ 

 is a; 2 



f 



Voui 



Figure 3.32 



__L 



Attenuation received 

 with wide spacing 



Attenuation received 

 with narrow spacing 



a»] 0*2 



Figure 3.33 



attenuations received by the two frequencies is clearly less than if they are 

 widely separated {Figure 3.33). It often happens that the discrimination 

 offered by a single R-C section is insufficient, and the question arises as to 

 how to obtain more. 



In electronics, if the output of one device is fed to the input of a similar 

 device, the devices are said to be 'in cascade'. If two sections of R-C filtering 

 are connected in cascade, the best that one can hope for is that the attenuation 

 obtained from the pair of sections will be twice that obtainable from one 

 {Graph 11). In fact this is not possible, owing to the nature of the loading 

 placed upon the first section by the second. 



39 



