LINEAR SERVO THEORY 629 



-E/3 _ —Stilt 1 



Em J MJOi + b}m) ' 



It is assumed that the amplifier includes an equaUzing network, such that 

 the over-all amplifier characteristic is 



<ji;2 



(^■)(; 



where A, oji , and 0^2 are positive real constants. The loop transmission is 

 given by the product of these two transfer factors and thus may be written 

 as 



where ojo is a positive real constant given by 



AStiit AStUt 



OJo 



1/ Rm + Rm 



The three factors in parenthesis have been so grouped that they all approach 

 unity for small values of co. Thus the low-frequency behavior of — ju/3 is 

 given by cooZ/'w. This quantity has a pole at co = 0, so that it is necessary 

 to plot the function 



-M/3(ico + e) - .^, (7.1) 



in the neighborhood of cj = 0. As co is, in succession, a small negative quan- 

 tity, zero, and a small positive quantity; the expression of (7.1) is correspond- 

 ingly a large positive imaginary, a large positive real, and a large negative 

 imaginary. Thus (7.1) traverses an infinite arc from the positive imaginary 

 axis to the negative imaginary axis as oj increases through the value zero. 

 Assuming the numerical values 



coo = 200 sec-i 



COm = 1 



COl = 10 " 



C02 = 200 " , 



equation (7) may be rewritten as 



The phase angle of — m/^ in degrees is, from (7.2), 



B = -90 - tan ' CO + tan"' ^^ - 3 tan"' ^^, (7.3) 



