408 BELL SYSTEM TECHNICAL JOURNAL 



acy required when expressed in cycles is comparable with that of audio- 

 frequency oscillators so that the percentage accuracy must be much 

 higher. 



The advantages of the heterodyne oscillator have made it desirable 

 to study its sources of error to determine whether such an oscillator 

 can be designed to have sufficient accuracy for these applications. 



Oscillators With a Single Frequency Check 

 The frequency of a heterodyne oscillator is given by the expression : 



F=f'-f, (1) 



where we will assume /' to be constant and / to be variable and less 

 than /' whence the frequency of the variable frequency oscillator is 

 lowered as the output frequency of the heterodyne oscillator is raised. 



The value of F is usually much smaller than either/' or/ and rela- 

 tively small frequency shifts in the local oscillators produced by aging 

 and temperature effects upon the elements of their resonant circuits 

 and changes in vacuum tubes and in the stray capacitances of the 

 circuits produce large relative variations in the output frequency. 

 Usually the stability required of F and the ratio f'/F are so high that 

 it is impracticable to design local oscillators of sufficient stability to 

 meet requirements. Instead, in all heterodyne oscillators an adjust- 

 ment in the form of a padding condenser in the circuit of the fixed 

 frequency oscillator is used, whereby its frequency is adjusted shortly 

 before the measurement until the oscillator reads correctly at the bot- 

 tom of its frequency range. The adjustment is made by the zero beat 

 method or by comparison with a low-frequency standard such as a 

 vibrating reed or the 60-cycle power supply. 



At the time of the adjustment the frequency of the oscillator is 



Fo=f' - fo, (2) 



where fo is the value of / at the check frequency Fo. Eliminating /' 

 between (1) and (2) we obtain 



F=Fo+(fo-f). (3) 



The frequency of the variable oscillator may be expressed as 



/= l/(27rVL(C+ O), (4) 



where Ca is the change in the variable air condenser capacitance from 

 the value it has at fo, and Co is essentially the value of the fixed con- 



