Experimental method for deriving accurate information
Direct evaluation of boom corrections by building long yagis with high Q (narrow bandwidth) is very tedious. One has to change all the elements to get reasonable accuracy so the amount of work required is really frightening!Rather than building a large number of antennas we have increased the Q of a single "director" by placing it in a cavity. The cavity was made from ordinary household aluminium foil, 1x1x1.6 meters. It was placed on the lab bench as you can see in fig.1 below.
Fig.1. The "boom correction" cavity from the outside.
When a typical director from a 144 MHz antenna is placed at the center of the cavity it will see mirror images of itself in four directions in the vertical walls. These images are reflected again and again so the final result is like a twodimensional "yagi" structure that extends in the plane with one element in each square meter. There are also mirror images in the top and the bottom, but radiation is lower along the element axis so these are less significant although they surely contribute.
A small capacitive probe is placed at the top and the bottom of the cavity and a signal is fed through the cavity by use of these two probes. The element can couple energy between the two capacitive probes only over a very narrow frequency range, typically 100kHz or so at the -3dB points.
The resonance is a "collective resonance" for the twodimensional director structure with mirror images separated by 1 meter (0.5 wavelengths) in the horisontal plane. When a boom tube is placed on the element, all the mirror images will be placed through mirror images of the boom tube and the frequency of the resonance changes. See fig. 2. We think it is well justified to assume that the length correction needed to compensate for the frequency change due to the boom tube is the same as the boom correction needed in a yagi antenna.
Fig 2. A boom tube, 35 mm in diameter, 260 mm long placed on a
6 mm director element inside the cavity.
The hole is 13 mm so the insulator is 3.5 mm thick.
The frequency of the resonance is stable and easily measured within 5kHz. Rotating the boom tube around the element does not affect the frequency. The boom tube has to be placed symmetrically around the element midpoint within a few millimeters. A 1 centimeter offset causes a frequency shift of 50kHz typically. The frequency is highest with the boom tube at the center position and it is lowered in proportion to the square of the offset.
The distance from an element to the end of the boom tube affects the boom correction. In our cavity setup, there are two boom tube ends to account for and this effect can not be neglected.
Theoretical justification (sort of)
One way of understanding long yagi antennas is to interpret the row of directors as a structure through which the waves propagate slower than the speed of light. When the speed is slower by that amount that makes the phase shift about 90 degrees between the ends of the structure as seen from the forward direction the antenna is near it's optimum frequency. When looking into the structure from the forward direction the the front and the back ends are both 45 degrees away in phase from the center part of the structure. The fields do not add too well in the forward direction but there is no cancellation either. When looking into the antenna from some angle away from the forward direction the phase shift between the ends increases rapidly with angle. That is the secret behind the yagi and the explanation why it provides more gain than a end fire array in which the elements are fed in phase (as seen from the forward direction).
A director has to be shorter than a half wavelength, the total phase shift has to be in the order of 90 degrees so the directors of a long yagi are shorter than the directors of a short yagi because the phase shift per meter of boom length has to be smaller. Close spaced directors are shorter than wide spaced directors because the total phase shift is a sum of contributions from all elements.
It is unknown to what extent the boom corrections vary with element lengths. We need boom corrections for the director structure of long yagis and therefore we have designed the experiment in such a way that we can measure the change in the phase shift caused by boom tubes when a director is operated at the frequency where it will operate in a real antenna.