RESISTANCES 



Clearly this modification makes no difference to the currents flowing in 

 the various branches of the circuit ; but it gives the arrangement an additional 

 axis of symmetry which is sometimes useful. 



By applying the star-delta transformation to the T attenuator, we can 

 write down the equations for the resistances in the pi form {Figure 2.30). 

 They are : 



^M = ^2 + ^1 + ~^ 

 ^iV = ^1 + ^1 + ji 



Substituting the expressions found for R^ and R^ in terms of d and r yields 



1 + 



Rm — f 

 R^ = r 



1 -02 



16 



A variant, related to the pi network in the same way as the H attenuator 

 is to the T, is the box or O attenuator {Figure 2.31). This is another balanced 



R(=r) 2 >Rm <R' <R(=r) 



\/2Rn 

 Figure 2.30 Figure 2.31 



form, in which R^ is split into two halves and one placed in each horizontal 

 limb. 



Varying the attenuation — An attenuator for which d can be varied is a 

 useful piece of apparatus, and we consider now how this can be done. In 

 principle d can be varied either smoothly — continuous control — or in discrete 

 steps. At first sight continuous control would seem to be more satisfactory, 

 since Q can be set to any desired value; we consider it first. 



Continuous control of attenuation — Clearly, to reduce Q we have — in the T 

 attenuator, for example — to make the i^^'s larger and i?2 smaller. We could 

 just have three calibrated variable resistances, separately adjustable, and 

 secure any desired value of Q by working out from the equations already 

 derived the necessary values of R^ and R^, and setting them on the resistances. 

 Such an arrangement has the merit of flexibility in that the attenuator so 

 formed can be used over a range of generator (and load) resistances. However 

 it would be rather clumsy in use, as to alter the Q value 3 knobs would require 

 adjustment. The question then arises whether all three resistances can be 

 operated from the same shaft, that is, whether they can be 'ganged'. The 

 answer is that theoretically they can, but that if they are the resulting attenua- 

 tor will have to be restricted to work between generators and loads of a 



18 



