GENERAL CIRCUIT CONSIDERATIONS 



227 



field. We then wish to relate the peak field strength to the stored energy in 

 comparing various circuits. 



Let us first consider a helically conducting sheet of radius a. The upper 

 curve of Fig. 5.3 shows {F^/ff^Py^iv/cyi^ vs. j8a. In obtaining this curve it 

 was assumed that v <$C c, so that 7 can be taken as equal to /3. The field E 

 is the longitudinal field at the surface of the helically conducting cylinder. 

 Figure 5.3 can be obtained from Fig. 3.4 by multiplying F{ya) by {Io(ya)Y'^ 

 to give a curve valid for the field at r = a. 



The helix has a very small circumferential electric field which represents 

 "useless" stored energy. The lower curve of Fig. 5.3 is based on the stored 

 electric energy of an axially symmetrical sinusoidal field impressed at the 

 radius a.f This field has no circumferential component but is otherwise the 



5 6 7 8 9 to 



(3a 



Fig. 5.3 — The impedance parameter (Er/p-P)^'^ compared for a helically conducting 

 sheet (A) and a forced sinusoidal lield (B) with a group velocity equal to the phase ve- 

 locity. The helix has a higher impedance because the phase velocity is higher than the 

 Kioup velocit}' by a radio showni to the j power by curve C. 



same as the electric field of the helix (again assuming r <<C c). We can imagine 

 such a field propagating because of an inductive sheet at the radius a, 

 which provides stored magnetic energy enough to make the electric and 

 magnetic energies equal. The quantity plotted vs. I3a is {Er/fS^Py^ (v/cY^^ 



The forced sinusoidal field is not the field of some particular circuit for 

 which a certain group velocity Vg corresponds to a given phase velocity i'. 

 Hence, the factor (vg/vY'^ is included in the ordinate, so that the curve will 

 be the same no matter what group velocity is assumed. For the helically 

 conducting sheet, a definite group velocity goes with a given phase velocity. 

 In Fig. 5.3, the ordinate of the curve for the helically conducting sheet 

 does not contain the factor (vg/vy^. If, for instance, we assume Vg = v 



t See Appendix III. 



