Design
There are no simple formulas for designing Yagi-Uda antennas due to the complex relationships between physical parameters such as element length, spacing, and diameter, and performance characteristics such as gain and input impedance. But using the above sort of analysis one can calculate the performance given a set of parameters and adjust them to optimize the gain (perhaps subject to some constraints). Since with an N element Yagi-Uda antenna, there are 2N-1 parameters to adjust (the element lengths and relative spacings), this is not a straightforward problem at all. The mutual impedances plotted above only apply to λ/2 length elements, so these might need to be recomputed to get good accuracy. What's more, the current distribution along a real antenna element is only approximately given by the usual assumption of a classical standing wave, requiring a solution of Hallen's integral equation taking into account the other conductors. Such a complete exact analysis considering all of the interactions mentioned is rather overwhelming, and approximations are inevitably invoked, as we have done in the above example.
Consequently, these antennas are often empirical designs using an element of trial and error, often starting with an existing design modified according to one's hunch. The result might be checked by direct measurement or by computer simulation. A well-known reference employed in the latter approach is a report published by the National Bureau of Standards (NBS) (now the National Institute of Standards and Technology (NIST)) that provides six basic designs derived from measurements conducted at 400 MHz and procedures for adapting these designs to other frequencies. These designs, and those derived from them, are sometimes referred to as "NBS yagis."
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