Radio Antenna Engineering is a free introductory textbook on radio antennas and their applications. See the editorial for more information.... 
Home LowFrequency Antennas Radiation Resistance  
Search the VIAS Library  Index  
Radiation ResistanceAuthor: Edmund A. Laport
When there is capacitive top loading attached to such a vertical antenna, its electrical length is effectively increased. The current I_{t} at the top of the vertical is no longer zero but has a value that is proportional to the capacitance of the top loading. In almost every practical case I_{t} is less than the base current I_{b}. With top loading, the plot of relative current against position along the vertical now becomes a rightangled trapezoid, which as a practical limit may ultimately approach a rectangle. This is realizable only with an electrically short vertical section having a very large amount of top loading. The radiation resistance of an antenna less than an electrical quarter wavelength long is increased by top loading and by increasing height. A straight vertical radiator of height 30 degrees or less has a radiation resistance Rτ following the equation where G_{0} is the electrical height in radians.
(One radian is 57.3 degrees.) Referring again to the geometric form of current distribution with height (Fig. 1.1), this relation holds for the triangular distribution. If the base current I_{b} is always taken as 1.0 for comparative purposes, we can say that radiation resistance varies as the square of the area of the degreeampere plot. We can transform this relation into a very useful form that shows the radiation resistance as a function of the degreeampere area A of the plot of current distribution. This is
The utility of this relation is that it holds for any shape of inphase current distribution. It permits direct computation of the radiation resistance from a known current distribution for an electrically short antenna. A toploaded antenna having a trapezoidal current distribution has a degreeampere area where Gν is in degrees of vertical height and I_{t} and I_{b} the currents at the top and at the base of the vertical, respectively.
These relations can be used for any arbitrary system where the current distribution in degreeamperes is known, the value of A can be computed, and the base current is taken as unity. A chart of the values of radiation resistance as a function of physical height Gν in electrical degrees and the ratio I_{t}/I_{b} is shown in Fig. 1.2 over the domain where the vertical current distributions are linear.


Home LowFrequency Antennas Radiation Resistance 