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BELL SYSTEM TECHNICAL JOURNAL 



stituted paraffin-type, carbon chain dielectrics no difference, greater than 

 experimental error, exists between the 22.5 and 10 cm. measurements. 



Acknowledgement 



The measurements by means of the double-detection set were made by 

 my co-worker, Mr. W. E. Eckner, whose valuable assistance I am glad to 

 acknowledge. To Mr. C. F. Mattke, also of the Bell Laboratories, I am 

 indebted for assistance in getting my crude original apparatus into its final 

 finished form. 



APPENDIX 



The typical ultra high-frequency transmission line can be represented as 

 in Fig. 3 



(Eo.io) (Ex.ix) (Ei,Ii) 



Fig. 3 — Equivalent circuit of transmission line 



and the equations describing it are 



Z^ cosh ^ DZ ^l - X) ^ \/ 

 £x = Fo 



Z^ cosh ^DZ (^ - x) + 4/^ sinh ■\/ DZ {I - x) 



Fo 



(Zo + Z^) cosh ^DZ I + (^oZ^i/l + J^A sinh VdZ I 



cosh ^m. {I - x) -\r ^lA/^ sinh ^DZ {t - x) 

 (Zo + Zi) cosh ^/dZ I + f ZoZ^i/| + |/| j sinh ^DZ i 



X ~7~ — 



£. /z ^^ "^ ^/\ ^^^ ^^^ ^^ ~ ^^ 



J^- -f Z( tanh ^DZ {t - x) 



Ep — Zpli 



(1) 



£0 = Fo — ZqIo , -c</ — ^fJ^f 



The line constants are Z — R-\- iwL, the series impedance per unit length, 

 and D — G -i- iwC, the shunt admittance per unit length. From these we 



have: surge impedance = A/ j^ = So , propagation constant = \^DZ. 



