HIGH ACCURACY HETERODYNE OSCILLATORS 



409 



denser, usually a good mica unit. L is the inductance of the resonant 

 circuit. 



Combining (3) and (4) we get 



F = Fo+ \I{2tv4LCo) - l/(27rVL(C + CJ). 



(5) 



The accuracy of the oscillator will depend on the variations in the 

 values of Fo, L, Co and Ca and is independent of the constants of the 

 fixed frequency oscillator. 



By giving increments AFo, ACo, ACa and AL to the constants Fo, 

 Co, Ca and L we obtain after simplifying the expressions 



^Ffo = AT^o, 



^Co 



AFco = 



2C 



fo 



1-1 + 





Fo F 

 1 + — — - 



^ fo fo 



Fo 



Fo_l 



fo f 



1 - 



AL 

 " 2L 



^ fo fo 



{F - Fo), 



(6) 

 (7) 



(8) 



(9) 



giving the corresponding frequency errors AF where /o = l/{2TyLCg) 

 is the variable oscillator frequency at the check frequency Fo. 



A variation in Fo will produce an error constant over the whole 

 frequency range. On Fig. 1 the other errors are found plotted in 

 parametric form. To find the error AF corresponding to a frequency 

 F the ordinate y corresponding to the value oi x = {F — Fo)/ifo) 

 should be found. Then 



AFca = yCafoACa/Ca] 



AFco = ycoACo/Co] 



AFl = yifoAL/L. 



It is found that Fo can be neglected in all practical cases. The ratio 

 of the ordinate to the abscissa gives the percentage error in frequency 

 caused by a one per cent variation in the element involved. 



An examination of the curves shows that they differ only slightly 

 from straight lines which can be interpreted as meaning that the errors 

 are fairly independent of the choice of fo. This constant should be 

 chosen therefore sufficiently low to require infrequent adjustment at 

 the low-frequency end of the scale. For low values of /<, such that 

 X > .3 difficulties in shaping of the air condenser plates and in designing 

 the modulator filter begin to appear. If the errors in an ordinary type 

 of oscillator due to capacitance and inductance variations were plotted 

 on the same set of coordinates the curves would coincide with the line 



