1318 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



"I = e^""' - 1. (2) 



the oscillator this would be : 



[numerical increment in cur- 

 rent or voltage per cycle 



The subscript on Q is used to denote the condition where R is negative. 

 The equation is obtained from the following relationships. 



wqL L 1/21 mL 



^ R R/m 1/2/L/^/coo 



_ Energy stored in resonant circuit 

 Rate of change of energy stored 



Since R = -^ , a negative R, { — R) = ~ n' ^ 

 Q Ml 



R -(-«) -(-2ir/oI.) 



(3) 



g-2L/o (from equation 1) = e 2^>"o = e ^^^foQO = gQi . (4) 



/^ = peak value of current flowing in resonant circuit. 



The relationship of energy stored to rate of change of energy stored 

 is a convenient relationship for computing the value of Qi in this partic- 

 ular case. 



The ability of a transistor to satisfy the requirements of the resonant 

 circuit for sustaining oscillation as well as building oscillation will be 

 discussed later. 



Energy which is large in comparison to the power taken by the load 

 is stored in the tuned circuit in order to minimize: 



(a) The effect on oscillator frequency of small changes in load current 

 phase angle with trunks of different types, connected. 



(b) The effect on oscillator frequency of different values of inductance 

 in the output windings of the associated oscillator circuit. 



(c) The effect of surges on the transistor that are transmitted over the 

 connected trunk to the oscillator. 



(d) The harmonics produced by the method of supplying power to 

 the tuned circuit. This includes the use of an incorrect feedback adjust- 

 ment. 



The Q for the transformers varied from 60 to 85. The stored energy 

 was then 60 to 85 times the energy dissipated per radian at the oscilla- 

 ing frequency for the particular transformer. By adjustment of the ratio 

 of the turns between windings 1-2 and 1-3 a dissipation in the tuned 

 circuits of from 6 to 10 milliwatts was obtained. 



In the six-frequency supply three different coil designs are used. One 

 design is used for the two lower frequencies, a second for the two inter- 



