502 BELL SYSTEM TECHNICAL JOURNAL 



inductive reactance. Since any variation of the magnetic field with time 

 always creates an electric field, there will be some capacitance in parallel 

 with the inductance. The same idea may be expressed by saying that the 

 inductance of the iris is not quite independent of the frequency. This 

 lack of constancy is not peculiar to ultra-high frequencies; it is true of 

 coils at low frequencies. Likewise, even at very low frequencies the in- 

 ductance varies with the frequency because of skin effect. 



In the iris shown in Fig. (7b) there are alternating charge concentrations 

 on the upper and lower partitions. The local field is largely electric and 

 the iris is capacitive. A feeble magnetic field associated with charging 

 current is unavoidable, of course; this is also true of capacitors at low 

 frequencies but this time the effect is greater. Finally, an iris of the type 

 shown in Fig. (7c) may be designed to behave as an antiresonant circuit. 



In that frequency range in which only the dominant wave is an effective 

 carrier of power to great distances, any discontinuity will behave as a 

 reactive T or Il-network — assuming that observations are made at some 

 distance from the iris where the local field is too feeble to count. This 

 could not be otherwise since there are three parameters at our disposal: 

 two reflection coefficients for waves traveling in opposite directions and 

 one transmission coefficient across the discontinuity. The Reciprocity 

 Theorem requires that the transmission coefficients in the two directions 

 be equal. These three parameters determine the ratios of the reactance 

 elements of the equivalent T or Il-network to the characteristic impedance 

 of the guide. 



If the operating frequency exceeds the second cutoff frequency, other 

 waves besides the dominant become effective carriers of power and the 

 equivalent network for the iris becomes more complicated. The iris behaves 

 not only as a dissipative impedance to the dominant wave but also as a 

 negative resistance, to one or more higher order waves. 



Boundaries 



So far we have paid little attention to the boundaries of the electro- 

 magnetic field. Strictly speaking, in any actual situation the field always 

 extends to infinity; the only boundaries there are, are the geometric bound- 

 aries between media with different electromagnetic properties. This 

 means that we should solve electromagnetic equations for each homogeneous 

 region, or region with analytically varying properties, and then match 

 the solutions at the boundaries. In many cases, however, this procedure 

 would be very complicated and quite unnecessary. In the case of a cylin- 

 drical metal tube with a dipole as a source of power the exact solution may 

 be represented as a particularly formidable integral; but experimentally 



