REAL GENERATORS 



particular resistance. It is spoken of as, for example, a '600 ohms attenuator'. 

 The restriction is not as serious as might at first appear, for there are certain, 

 rather few, values of load and generator resistance which are either con- 

 ventional or which occur naturally in applications where attenuators are 

 used. The important ones are 80, 15 and 600 ohms; 15 ohms is the conven- 

 tional resistance for high quality loudspeakers, 80 ohms is the apparent 

 resistance of a dipole aerial, and 600 ohms is important in telephone engi- 

 neering. 



Having fixed a 'characteristic resistance' for our attenuator we can now 

 work out the range of resistance values required for a given range of d, and 

 it is here that we meet a serious practical difficulty. If 6 has to go down to 

 zero the series resistance ought to increase smoothly to infinity : if d has to 

 reach unity the shunt resistance ought to increase smoothly to infinity. 

 Neither can be achieved exactly or even approximated to very easily, and for 

 this reason wide-range (i.e. < < 1) constant resistance attenuators are 

 never found. Many electronic instruments appear to possess them, but in 

 fact they contain what might be called 'bogus attenuators', i.e. a potentio- 

 meter feeding a valve. 



Suppose we restrict the attenuation range required to 0-9 < < 1, i.e. 

 the maximum amount of attenuation our device can produce is small. This 

 is a reasonable thing to do, since greater amounts of loss can be introduced 

 by following our continuously variable control by a stepped one, so that 

 the former is a 'fine' control and the latter a 'coarse'. Then the resistance 

 values required for the T configuration are plotted in Graph 5. R^ behaves 

 in a manageable manner, but R2 goes off to infinity, as expected. Suppose 

 we leave R2 out altogether; then our attenuator reverts to a simple variable 

 series resistance in which R^ and R^' can be combined (Figure 2.32) into a 



Rs, ^ 

 — o AfVC^ o 



Ri=r) 



-o- 



Figure 2.32 



single resistance Ry. When Ry ==0, 0=1, and the matching is exact. 

 When Ry = l/9th of r, = 0-9, and the resistance seen by the generator and 

 the load is 1 1 per cent high. For many purposes this would not represent a 

 serious degree of mismatch. 



In conclusion, then, the wide-range continuously variable attenuator is 

 impossible to make. The narrow-range attenuator, however, useful in con- 

 junction with stepped attenuators as a 'fine' control, whilst still not exactly 

 realizable in practice, can be approximated to with sufficient accuracy by a 

 simple variable resistance. The degree of mismatch produced is determined 

 by the amount of fine control required. 



The stepped attenuator — For wide-range variation of d we employ the 

 stepped attenuator in which fixed resistances are controlled by ganged 



19 



