MAGNETIC GENERATION OF A GROUP OF HARMONICS 443 



the harmonic output corresponding are but little affected by change of 

 input amplitude. With a linear amplifier the harmonic output current 

 would vary roughly as the four-tenths power of the input current. 



Another application involving higher frequencies has been made to 

 the generation of the so-called "group" carriers used in conjunction 

 with a coaxial conductor.^^ There odd harmonics of 24 kc. from the 

 9th to the 45th are used. The circuit differs from Fig. 1 in that the 

 copper oxide bridge is omitted, and the non-linear coil is provided with 

 two windings to facilitate impedance matching. The performance of 

 an experimental model is similar to that of the generator described 

 above. A notion of the physical size and construction of the non- 

 linear coils used may be had from the photographs of Fig. 5. 



In both applications the required harmonics are generated at ampli- 

 tudes high enough to avoid the necessity for amplification. 



III. Theory of Operation 



The analysis of operation of the harmonic generating circuit de- 

 scribed above meets with difficulties, since a high degree of non-linearity 

 is involved in working the coil well into its saturated region. 



To avoid these difficulties, an expedient is adopted by which the 

 hysteresis loop is replaced by a single-valued characteristic made up of 

 connected linear segments ^ as shown in Fig. th. It is then possible to 

 formulate a set of linear differential equations with constant coefficients, 

 one for each linear segment. The solutions are readily arrived at and 

 may be pieced together by imposing appropriate conditions at the 

 junctions, so that a solution for the whole characteristic is thereby 

 obtained. From this solution the wave form of current or voltage 

 associated with any circuit element may be calculated. Resolution of 

 the wave form into components may then be accomplished by an 

 independent Fourier analysis. 



The assumed B-H characteristic of Fig. 66 is made up of but three 

 segments. While it is manifestly a naive representation of a hysteresis 

 loop, it will be shown by comparison with experiment that the main 

 performance features of harmonic generators may be reproduced by 

 this crude model. 



It will be noted on Fig. db that the differential permeability of the 

 assumed non-linear core, a quantity proportional to dB/dH, takes on 

 one of two values, determined by the absolute value of the magnetizing 

 force. These are designated by n in the permeable region and ;u« in the 

 saturated region. The corresponding inductances are L20 and Lit, -^20 

 being many times greater than Lis. The values of current through the 

 coil at which the differential inductance changes are designated ± Iq, 



