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tions are that Vg is in phase with and equal to y.Vg (note that /x is considered 

 negative). Like Koga, Boella assumes the current 1 2 small compared to /i , 

 hence the voltage drop across Zi is approximately Zi/i . The angle this 

 makes with Vg is determined by the value of Zi and the internal plate 

 impedance Rp . Any change in either of these requires a change in the 

 angles \p and yp' in order that Vg shall be in phase with nVg . This means 

 that the frequency must vary to produce this change in \j/ and 1/''. Because 

 of the rapid change in the reactance and resistance of the crystal with 

 frequency, these requirements are met with very little change in frequency, 

 which accounts for the high degree of frequency stability obtained with 

 crystals. This is described more in detail in a later section. 



G-C 



G-P 



-Z.I 



Z.I, 



-Z1I1 



Z,Ii 



Fig. 12.20 — Vector diagrams of currents and voltages in the oscillator circuit Figure 

 12.11 with crystal connected grid to cathode (A) and grid to plate (B) 



12.31 Change in Frequency with Decrement of Crystal 



It has been found that for the crystal connected from grid to cathode 

 there is a maximum theoretical frequency at which the circuit can be made 

 to oscillate by reducing the plate circuit impedance. This also corresponds 

 to the minimum frequency which can be obtained with the crystal connected 

 between grid and plate. This was called the limiting frequency /o . It is 

 interesting to note that/o is determined by the intersection of the reactance 

 curve of the crystal plotted as a function of frequency and the reactance 

 curve of the capacitance in series with the crystal. This series capacitance 

 is the grid-plate capacitance for one case and the grid-cathode capacitance 

 for the other. As illustrated in the curves Figure 12.21, the limiting fre- 

 quency /o increases as the decrement of the crystal increases. 



The difference between the true frequency of oscillations and/o increases 



