HYPER-FREQUENCY TRANSMISSION 313 



pass wave-filter. The exact value of the critical frequency depends, as 

 shown later, on the type of wave transmitted; roughly speaking, 

 however, the internal diameter must be approximately equal to one- 

 half a wave-length in the internal dielectric medium at the lowest 



critical frequency. (The exact formula is diameter > ^ — times the 



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wave-length.) Since we are interested in freely transmitted waves it is 

 evident at once that for a cylinder of practicable dimensions the 

 frequencies employed must be relatively enormous. For this reason it 

 may be appropriately said that the hollow conducting cylinder is 

 applicable to the transmission of hyper -frequency waves alone. 



The types of waves which can exist inside the cylinder are broadly 

 classifiable as £-waves and JY-waves.^ By the term JS-wave is to be 

 understood a wave in which the axial component of the magnetic force 

 is everywhere absent; correspondingly in the iJ-wave the axial com- 

 ponent of the electric force is everywhere absent. In the £-waves the 

 surface currents in the cylinder are entirely parallel to the axis thereof. 

 On the other hand, in the iJ- waves the currents may have both trans- 

 verse and axial components; that is, circulatory components around the 

 periphery of the cylinder in planes normal to its axis as well as com- 

 ponents parallel thereto. 



In each class of wave there may exist a fundamental wave and in 

 addition geometrically harmonic^'' waves. In the fundamental wave 

 the phenomena do not vary around the periphery of the cylinder. In 

 the wth harmonic wave {En- or i7„-wave) the phenomena vary around 

 the periphery as cos n{d — dn). 



Each component E- or H-wave has its own individual critical fre- 

 quency. Curiously enough the lowest critical frequency is possessed 

 by the first harmonic i/-wave; that is the iJi-wave. For this wave the 



3 68 

 critical frequency is given by the formula d > -^ — X where d is the in- 



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ternal diameter of the cylinder and X the wave-length. In general, 

 however, the critical frequency increases with the order of the harmonic. 

 In the usual transmission system, the transmission phenomena are 

 determined and described in terms of the characteristic impedance and 

 the propagation constant. By characteristic impedance the engineer 

 understands the impedance actually presented by an infinitely long 

 line to an electromotive force connected across the terminals of the 

 circuit. Now since in the hollow conducting cylinder there is only one 



' This terminology has been adopted as a matter of convenience. It is suggested 

 by equations (1) where the field is expressed in terms of £, and Hi. Another 

 terminology is transverse magvetic and transverse electric waves. 



'"This term must not be confused with frequency harmonics. 



