REAL GENERATORS 



and the output voltage 



R^ + R^ + r 



In a potentiometer R^ + R2 is constant. Let it equal Rp, then the output 

 voltage is 



E . Ri^ . R2 



R^iRp - i?2 + r) + Rl(R„ + r) 



Remembering that shaft rotation is proportional to R^, let us plot the output 

 voltage as a function of R2, for various Rj^ for 3 types of generator : /• large 



R\ + Ri* r 



0: 



f'^^\R^+R2^r) 



u. 



Figure 2.26 



(constant-current type generator), r = i?^ (generator matched to load), and 

 r small (constant-voltage type generator). 



(1) For the constant-current case, the equation reduces to 



output voltage 

 (2) For the matched case, 

 output voltage 



E RlRj 

 r Rl + Rz 



= E 



R%Rl 



(i?2 + RlXR, + Rl) 



Rr^ 



(3) For the constant-voltage case. 



R.R 



output voltage = E-—- ' (^ 



These are plotted in Graphs 2, 3 and 4. 



In case 3, potentiometer fed from constant-voltage type generator, we see 

 that the relationship between volts output and shaft rotation is nearly linear 

 when R^= 10 Rp, and is moderately satisfactory when Rj^ = Rp. When 

 i?^ = 0-1 Rp, which is the best condition of the three in-so-far as the least 

 power is wasted in the potentiometer, the control is downright bad; half 

 the output voltage is controlled in 9/lOths of the shaft travel, and the other 

 half in 1/lOth. 



In case 1 , potentiometer fed from constant-current type generator, linearity 

 is again optimum when i?^ = 10 Rp, and the maximum output voltage 

 available is 90 per cent of that obtainable when Rj^ is infinite, i.e. E(Rp)lr. 

 At Rj^ = Rp the linearity has deteriorated and the maximum output is down 

 to 50 per cent. At Rj^ ^O-l Rp the maximum output is below 10 per cent 



15 



