438 BELL SYSTEM TECHNICAL JOURNAL 



of perhaps greatest importance were to high power, long-wave radio- 

 telegraph transmitters, where the fundamental input was obtained 

 from an alternator. Other applications of the idea of harmonic pro- 

 duction by magnetic means have been made in the power and com- 

 munication fields/ 



It appears that these circuits were all developed primarily to generate 

 a single harmonic. Comparatively good efficiencies were obtained, 

 values from 60 to 90 per cent being reported for the lower harmonics. 

 The theory of frequency multiplication was investigated by a number 

 of workers, among whom may be mentioned Zenneck ^ and Guillemin.^ 

 The latter, after analysis which determined the optimum conditions for 

 the generation of any single harmonic, found experimentally that the 

 efficiency of harmonic production decreased as the order of the har- 

 monic increased. He obtained efficiencies of 10 per cent for the 9th 

 harmonic, and 3 per cent for the 13th harmonic of 60 cycles. 



Where the circuits are properly tuned and the losses low, free oscilla- 

 tions may be developed. The frequencies of these free oscillations may 

 be harmonic, or subharmonic as in the circuit described by Fallou ; ^ 

 they may be rational fractional multiples of the fundamental, or in- 

 commensurable with the fundamental, as in Heegner's circuit.^ The 

 amplitudes of these free oscillations are usually critical functions of the 

 circuit parameters and input amplitudes, and where the developed 

 frequencies are not harmonic, they are characterized by the fact that 

 the generated potentials are zero on open circuit. The theory of the 

 effect has been worked out by Hartley.^ It is presumably this effect 

 which is involved in the generation of even harmonics by means of an 

 initially unpolarized ferromagnetic core, an observation which has been 

 attributed to Osnos.^'^ 



II. Circuit Description 



The harmonic producer circuit which forms the subject of the 

 present paper differs from those mentioned in that it is designed to 

 generate simultaneously a number of harmonics at approximately the 

 same amplitude. 



Harmonics developed in circuits of this type have been used for the 

 supply of carrier currents to various multi-channel carrier telephone 

 systems, for synchronizing carriers used in radio transmitters, and for 

 frequency comparison and standardization. Only odd harmonics are 

 generated by the harmonic producer when the core of the non-linear 

 coil is unpolarized, as is the case here. To generate the required even 

 harmonics, rectification is employed. This is accomplished by means 

 of a well balanced copper oxide bridge, which provides the even har- 

 monics in a path conjugate to the path followed by the odd harmonics. 



