850 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1953 



Ri is the symmetry determining resistor and is in parallel with the 

 input terminals of the shaping network in order to limit the maximum 

 value of the series impedance. The equation of symmetry may be ex- 

 pressed as 



R is the image impedance of the shaping network. The thermistor has 

 this value at its normal setting. 



Ro is the impedance of the circuit in which the regulator is inserted, 

 in this case, 75 ohms. 



p is the reflection factor between the network impedance, 72, and the 

 thermistor impedance, Rt and is given by 



r is the image transfer constant of the shaping network and may be 

 expressed as 



r = (T + ixi^. (17) 



Returning to expression (13) for the insertion gain, if the series expan- 

 sion of the arc tangent is used and the higher order terms discarded, 

 the insertion transfer constant becomes 



e = a^ + Ke'^" cos 2i/^ + iKe~^ sin 2^, (18) 



or the insertion loss may be expressed 



a = aff + Ke~^ cos 2^ nepers, (19) 



This approximation is valid for design purposes if the regulation range 

 is not too large or the accuracy required too great. For example, omis- 

 sion of the cubed term in the repeater temperature design produced a 

 maximum error of 0.014 db and in the tube aging design, 0.007 db. 



From the above expression it is seen that both real and imaginary 

 parts of the image transfer constant for the shaping network enter 

 into the insertion loss expression, and thus the relationship between 

 the desired insertion loss and the shaping network makes the design 

 process difficult. At this stage in the design considerable art and in- 

 genuity is required in order to continue the design efficiently. The ap- 



