By G. Mourier

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The Current Layer Equivalent to Another Delay Structure C. Perturbation by a Dielectric D . Induced Current in a Real Conductive Layer E. The Current Layer Equivalent to Plane Waves Propagating on Two Parallel Biperiodic Structures IX. Babinet's Principle List of Symbols References 17 19 20 22 22 24 25 27 27 27 28 30 30 31 32 33 I. Fundamental Considerations about Delay Lines T h i s section is concerned with t h e s t u d y of circuits used in injection M - t y p e tubes. I t is possible t o specify t h e general shape a n d t h e char acteristic quantities of such circuits; t h e y a r e periodic in t h e direction of propagation (of period ρ a n d of transverse width I); in most t u b e s t h e circuit s t r u t c u r e can b e considered infinite.

Complementary tape structures; the magnetic field of structure I I is equal, within a constant factor, to the electric field of the structure I . position of t h e two constitutes t h e whole plane, Fig. 5) will b e shown t o be t h e same. I t is obvious t h a t in a t a p e structure, t h e electric field is in t h e plane of t h e structure in a gap and normal t o it on t h e conductor; and reciprocally for t h e magnetic field. L e t us assume t h a t Ei, Hi are t h e fields of a wave propagating along structure I ; t h e t w o sets of fields E2, H2 defined b y Ει ± J * H 2 = 0 Hi Τ E2 = 0 (76) also satisfy Maxwell's equations.

T h e field varies a t t h e t a p e edges as 112 (z — ap/2)~ . v/2 t h e origin is e ; t h e integral of Ez from ζ = —ap/2 to ap/2 m u s t be equal t o 2j sin (φ/2). T h e n , we h a v e E = 2j sin φ/2 ρ V2 _ Ρ- 2Λ0) exp φ/ 2ττζΤ 1/2 ~7Ϊ7Γ -— φ)ζ~ φ)ζ~] Yj(TT — COS L Ρ L ρ JJL r ~ p J (17) where P„(cos Θ) is a Legendre polynomial generally of nonintegral order. ηπ as shown in Fig. 3, curve (3). taw FIG. 3 . Magnitude of the space harmonics in a tape structure (pitch unity, voltage unity between adjacent conductors).