Figure 3 shows the geometry of the biconical antenna. The conducting antenna surfaces are defined by the conical surfaces в = ф and в = n — ф, and the two spherical end surfaces at r = a. The analytical procedure of the biconical antenna will be outlined below. In region I, the electric and magnetic fields are represented as a sum of the outward — and inward — traveling TEM principal modes and an infinite number of complementary (higher) transverse magnetic (TM) modes. In region II, the fields are represented by an infinite series of complementary radiating modes. Boundary conditions on the aperture indicated by the dashed lines in Fig. 3 and the end

Figure 5. Measured input resistance of a conical unipole versus length in electrical degrees showing broadband characteristics with increasing cone-angle (from 10). |

Figure 3. Symmetric biconical antenna. |

Antenna length h (deg) |

Figure 6. Measured input reactance of a conical unipole versus length in electrical degrees showing broadband characteristics with increasing cone-angle (from 10). |

Antenna length h (deg) |

surfaces of the cone at r = a are used to obtain an infinite set of linear algebraic equations from which the amplitudes of the complementary modes and the principal mode reflected back at the aperture are determined.

The input admittance of the biconical antenna is represented by the equivalent transmission line circuit as shown in Fig. 4, where K is the characteristic impedance given by Eq. (3). The terminal admittance Yt represents the effect of the truncation of the biconical transmission line at r = a, that is, the transformation of the outward-traveling TEM mode into the complementary modes in both regions and the reflected TEM mode, which eventually determines the input admittance of the biconical antenna Yi.

Schelkunoff (2) has formulated the above boundary value problem rigorously and has discussed in detail special cases of a vanishingly thin antenna and a very wide-angle cone, or a spherical antenna with a very narrow equatorial gap. Tai (4) has obtained the exact analytical solution of the terminal admittance of the vanishingly thin antenna, which has been found to be identical to the expression obtained ingeniously by Schelkunoff. Tai (5) has also made an important contribution to the development of the theory for biconical antennas by applying Schwinger’s variational method. He has given the first order variational numerical solution for the specific wide cone-angles ф = 39.23°, 57.43°, and 66.06°.

The recent development of computers has made feasible the numerical solution of Schelkunoff’s formulation. However, it is still not easy to solve the infinite set of linear determining equations with reasonable accuracy because of slow convergence of the infinite series when the cone-angle decreases. For example, 15 or more modes for ф = 5° (7), and 13 modes for ф = 5° (8) are necessary for computation of the input impedance. A conical monopole above an image plane

K

a

driven by a coaxial line has been numerically analyzed by using the finite difference time domain method (9).

When the upper half-cone of the biconical antenna is mounted on an infinite conducting plane (ground plane), the antenna forms a conical unipole having one half of the input impedance of the biconical antenna. Figures 5 and 6 [Brown and Woodward, Jr. (10)] show respectively the measured input resistance and reactance of a conical unipole having flat caps instead of spherical caps. It is clear that the antenna tends to have a constant input resistance and a small reactance around zero versus frequency, showing broadband characteristics as the cone-angle is increased.

The radiation pattern of the biconical antenna has been computed by Papas and King (6) and by Bevensee (11). Figure 7 shows the far-zone electric field pattern (6) for the cone angle of ф = 30°. It is found that the patterns are not much different from those of a straight wire antenna.

Theoretical analysis of biconical antennas loaded with and/or immersed in dielectric, lossy, and ferromagnetic mate-

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rials has been provided by Schelkunoff (2), Tai (4), Polk (12), and others. These topics are reviewed by Wait (13). The theory of an asymmetric biconical antenna was also discussed by Schelkunoff (2). The variational approach by Tai was extended to a semi-infinite asymmetric conical antenna consisting of an infinite cone and a finite cone (14).

To reduce wind resistance and/or weight, a solid biconical antenna can be replaced by a skeletal conducting wire structure using several radial rods (15,16). It has been found, however, by analysis using the moment method that a considerable number of wires (e. g., 16) is required to approximate the solid biconical antenna.