RESISTANCES 



and the linearity so poor as for the control to be practically useless. It is 

 worth noting that at Rj^ = 0-5 R^ the form of the curve is approximately 

 parabolic, which implies that if we square the ordinates we shall get a line 

 which is substantially straight. Since the square of the ordinates is (output 

 voltage)^ and since the power delivered to a load resistance is V^IR, it appears 

 that we have here an arrangement for securing approximately linear control 

 of power. 



Case 2 requires a little care in interpretation. Since the load is matched 

 to the generator, in varying the resistance of the load with respect to that of 

 the potentiometer we are also varying the resistance of the generator. This 

 explains why Rl= 10 R^, is the lowest curve instead of the highest. It is 

 probably better to visualize the potentiometer resistance as being varied 

 with respect to the other two. The following then emerges : when the potentio- 

 meter resistance is small compared with the load {Rj^ = 10 R^) the linearity 

 of control is good but the maximum output is small. As R^, is raised the 

 maximum output rises, till at Rj^ = 0-5 R^ the linearity is still tolerable and 

 the maximum output 40 per cent of the generator e.m.f. Thereafter some- 

 thing rather surprising happens; the maximum output continues to rise 

 (asymptotically towards 50 per cent of E) but the output at other potentio- 

 meter settings collapses to a lower value than before. Once more, then, we 

 find that conditions which give low wastage of power in R^ also yield unsatis- 

 factory control characteristics. 



There is another respect in which potentiometer control is unsatisfactory. 

 It is not hard to see that as the potentiometer is varied, the resistance 'seen' 

 by the generator 'looking into' the potentiometer also varies. So does the 

 resistance seen by the load looking back into the potentiometer. Many real 

 generators and loads, such as valve power amplifiers and penwriters, only 

 work properly when driving a load of, or being driven by a generator of, a 

 certain fixed resistance. In the next section we study the attenuator, which is 

 an arrangement for controlling the transfer of power in which both generator 

 and load 'see' a constant resistance. 



The constant resistance attenuator 



In Figure 2.27 we have a generator of internal resistance r feeding a 

 'black-box' which in turn feeds a load R, equal to r. The black-box draws 

 power from the generator, passes a certain fraction on to the load and 



R(=r} 



Figure 2.27 



dissipates the rest within itself (as heat). This fraction is frequently adjustable, 

 but however large or small it is the generator must always see a resistance r 

 looking forward into the attenuator with the load connected, and the load 

 must always see a resistance R = r looking back into the attenuator with the 

 generator connected. 



16 



