by MD0MDI

or the more accurate equation:

**Figure 1**. The results show that the resonant length decreases as the structure becomes wider.

There are some important constants that are used throughout Electro Magnetic (EM) theory:

**c, the velocity of light in vacuum (or free space)****m**_{o}the permeability of vacuum (by exact definition)**e**_{o}the permittivity of vacuum (defined exactly in terms of c and m_{o})**z the real characteristic impedance of vacuum (defined exactly in terms of m**_{o }and c).

There are also some interesting relationships:

_{a }and will reserve Zo for the complex impedance that we will cover later.

In either case the approximation of Equation (6) yields:

Where s is the side of a square structure and w is the width of a lineal strip.

Thus the capacitance will be:

Where C and L can be derived from the fundamental properties of the space surrounding the structure:

Which is quite high, you could use 500:

To characterize wide structures, Hallen [reference 2] uses the parameter:

Notice:

_{T} of wide structures. The zero order equation for a dipole, an approximation is (divide by 2 for a monopole):

The first order equation takes the form of:

And the even more accurate second order equation takes the form:

_{n} and b_{n} is complex and beyond the scope of this article, but may be found in reference 2 or, according to reference 2, in table form in Hallen’s original work.

If you look at equation (25) you will see that it is 2 * equation (15) where

The d_{n} and b_{n} terms become significant as W becomes small i.e. as h / a becomes small.

Sadly the links to the Software and the Spreadsheet are not available anymore. – MD0MDI

- R.F. Harrington, “Field Computation by Moment Methods”, IEEE Press, 1992, ISBN 0-7803-1014-4
- John D. Kraus, “Antennas”, 2nd Edition, McGraw Hill, 1988, ISBN 0-07-0354 22-7, pp 359-377.
- Dr James L. Lawson, “Yagi and Antenna Design”, ARRL, 1986. ISBN 0-87259-041-0, pp 1-5 to 1-9.
- Doty, Frey, Mills, “Vertical Antennas: New Design and Construction Data”, ARRL Antenna Compendium Vol 2, ARRL, 1989, ISBN 0-87259-254-5, pp 2 – 9.
- Ralph B. Holland, “Validation of NEC2 and Zo by feedpoint reactance of monopoles”, Applied Computational Electromagnetics Society Newsletter Vol 10 – No 2, ISSN 1056-9170, July 1995, pp18 – 21.
- John D Kraus, “Antennas”, 2nd Edition, pp 848 – 850.
- Robert I. Sarbacher, William A. Edson, “Hyper and Ultrahigh Frequency Engineering”, John Wiley and Sons, 6th Edition, 1943, pp 320 – 341.
- Ralph B. Holland, “wide.xls” spreadsheet and “wide.cpp”, C++ program, Sep 1999.

Originally posted on the AntennaX Online Magazine by Ralph Holland, VK1BRH

*Last Updated : 13th May 2024*

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