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BELL SYSTEM TECHNICAL JOURNAL 



1 



network. When the values of the inductances and capacitances are 

 unrestricted the coupling network will, in general, have three pass- 

 bands, each pass-band being characterized by a purely imaginary value 



Fig. 4 — Colpitis oscillator with plate circuit stabilization. 



of the image transfer constant 6 corresponding to a phase shift without 

 attenuation. The phase shift is zero at zero frequency, increases by 90 

 degrees in each pass-band, and remains constant at 90, 180, 270 degrees 

 in the successive attenuation bands. From the expression for tanh Q 

 in equation (7) it follows that the image phase shift of the reactive 

 network will be zero or an even multiple of 90 degrees at the zeros of D 

 and D\\, 22 and will be an odd multiple of 90 degrees at the zeros of Dn 

 and Dii- The general phase shift characteristic of the feedback net- 

 work in Fig. 4 is shown in Fig. 5. The critical frequencies /s and /4 



,« 360 



270 



uj 180 - 



O 

 z 

 < 



... 90 U 





fa 



FREQUENCY 



U 



Fig. 5 — Phase constant characteristic of the feedback network in an incompletely 

 stabilized Colpitts oscillator. 



marking the edges of the second attenuation band correspond to the 

 zeros of D and Dn, 22- Frequencies /2 and/5 are the zeros of Da and/i 

 is the single zero of Dn. The pass-bands are indicated by the heavy 

 lines on the frequency scale. An examination of the image impedances 

 of the network will show that in the second attenuation band they are 

 reactances of like sign and are of opposite sign in the first attenuation 

 band. 



