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BELL SYSTEM TECHNICAL JOURNAL 



in Fig. 9. The zero frequency is always a pole for an open type antenna 

 and a zero for a perfectly conducting loop antenna. As the frequency 

 passes through a zero, the antenna impedance passes through a minimum. 

 As the frequency goes through a pole, the antenna impedance passes through 

 a maximum. The disposition of zeros and poles gives us a qualitative idea 

 of the behavior of the impedance as the frequency varies. 



As the radius of the antenna increases, the zeros and poles move farther 

 to the left of the imaginary axis. At the same time some zeros and poles, 

 which for a thin antenna are so far to the left that they have very Httle 

 effect on the impedance, move nearer the origin. For spherical antennas 

 the number of zeros and poles around the origin is considerably larger than 

 for thin doublets. 



Fig. 9 — Distribution of zeros and poles in a dipole antenna: solid circles 

 represent poles; hollow circles zeros. 



Circuit and Field Equations 



In conclusion I should like to make a few remarks on the relationship 

 between Kirchhoff's circuit equations and Maxwell's field equations. Are 

 the former approximations; and, if so, in what sense? The answer depends 

 on what is meant by Kirchhoff's equations, for their meaning has changed 

 with passing years. It was exactly a hundred years ago that Kirchhoff 

 stated his equations in a kind of postscript to his paper in Poggendorf 

 Annalen; but he contemplated only the d-c networks. Yet nowadays 

 we interpret these equations in such a way that they are applicable to a-c 

 circuits. Some thirty years went by before Maxwell thus generalized the 

 original Kirchhoff equations with the aid of Lagrange's concepts. Maxwell 

 wrote his circuit equations (not the field equations) in a form applicable 

 only to networks with a finite number of degrees of freedom; but nowadays 



