MAGNETIC GENERATION OF A GROUP OF HARMONICS 449 



V. Calculated and Observed Performance 



In order to make practical use of the results given above, we need 

 some basis for deriving the assumed parameters of the non-linear coil 

 from the physical properties of the magnetic materials used in harmonic 

 producers. 



The fact that the actual magnetization curve is a loop instead of a 

 single-valued curve as assumed requires increased power input to the 

 circuit to provide for the hysteresis and eddy losses in the core. Other 

 than this, the principal remaining effect of the existence of a loop is a 

 lag in the time at which the pulses occur, an effect which is of no great 

 moment in determining the form or magnitude of the resulting pulses. 



The next point requiring consideration is the effect introduced by the 

 assumed abrupt change of slope contrasted to the smooth approach to 

 saturation actually observed. While no rigorous comparisons can be 

 drawn, the effect of the more gradual approach to saturation was ap- 

 proximated analytically by introducing an additional linear segment 

 between the permeable region and each saturated region of the B-H 

 characteristic, at a slope intermediate between the two, so as to form a 

 B-H characteristic of five segments in place of the original three. The 

 solutions for these two characteristics were found to yield negligibly 

 small differences in the amplitudes of the higher harmonics. It was 

 inferred from this result that no substantial change would be introduced 

 by a smooth approach to saturation. 



Finally, the actual B-H characteristic has a slight curvature in the 

 saturated region, while the analysis considered a small linear variation. 

 A rough approximation for the effect of this curvature, which leads to 

 fair agreement with experiment, consists in taking for L^s the average 

 of the actual slope, from its minimum value reached during the dis- 

 charge peak down to the point at which the slope is one-tenth maxi- 

 mum. To this is added the linear inductance contributed by the 

 dielectric included within the winding. 



To summarize then, the harmonic outputs obtained from the 

 analysis with the assumed B-H characteristic may be brought into line 

 with experimental observations by the introduction of quantities ob- 

 tained from actual B-H loops at appropriate frequencies and magnetiz- 

 ing forces. In these the maximum slope found on the loop is taken for 

 L20, the average slope over the saturated region is taken for Lis, and the 

 energy corresponding to the area of the real B-H loop must be added to 

 that originally supplied the harmonic generator input. 



A comparison between measured and calculated harmonic distri- 

 butions obtained with a 4-kc. fundamental input is shown in Fig. 8. In 

 this case the harmonic distributions were measured for four different 



