HOW DOES A YAGI-UDA ANTENNA WORK?

   The objective of the design is to make a "travelling wave" structure with currents in the elements all contributing to the far field in the forward direction. The contributions are designed to add up in phase in the forward direction, and to cancel in the reverse direction. The director elements are cut shorter than the driving element, which is itself a little shorter than a half wavelength at the design frequency. The reflector is cut to be about a half wavelength and it is longer than the driving element, and spaced closer than are the directors. The directors present a capacitative impedance, acting like two lengths of open circuit transmission line each a little shorter than a quarter wavelength to a hypothetical generator at the centre formed from the "induced emf" set up by the impinging fields. See the SMITH chart . Similarly, the reflector presents an inductive impedance to a hypothetical emf generator at its centre. The effects of the spacings and the current progressive phase shifts mean that the contributions of the current in the various elements to the radiated fields all add up in phase. 

   For a closely spaced driving element and parasitic element, isolated from each other as far a electrical conduction currents are concerned, the currents are oppositely directed as can be seen in the discussion on folded dipoles with the folds cut off. As the spacing is increased, the currents remain oppositely directed until when the spacing is a half-wavelength, the contributions to the far field add up in phase in the "endfire direction", as can be seen from the discussion on array antennas. 

   If the director elements are cut a little short, their self-impedance is capacitative and they have to be spaced a little closer than a half-wavelength in order to maintain equality of phase in the radiation contribution with the wave arriving from the previous director. The currents in successive elements thus roughly have the pattern 

....up down up down up down ...... 

but will all be very nearly equal in magnitude to each other. There is also some progressive phase shift as the wave advances, caused by the fact that the directors are cut short (capacitative). 

   The field pattern on the yagi directors therefore advances as a travelling wave in the forward direction, with wavelength approximately equal to three director spacings. This can be seen in the table at the top of this page; at 30MHz the wavelength (lambda) is 10 metres so for a 15 element Yagi array, the length given as 47 metres is nearly five wavelengths, or 15 elements divided by 3.

   So the travelling wave structure supports a non-attenuating wave in the forward direction, and the currents in the directors are all approximately the same size, although with a progressive phase delay. It is for this reason that, for moderate numbers of elements, the forward gain is proportional to the number of elements. 

   The reflector has an induced current in it that contributes a wave in the backwards direction that just cancels the backward wave from the driven element. Only a little power is radiated backwards. The net power radiated by the reflector current has to go somewhere, so it appears as a contribution in the forward direction. The length and the spacing of the reflector have a strong influence on the residual backward radiation from the Yagi-Uda. Typically the reflector will be spaced by 1/8 to 1/4 of a wavelength, and the directors by about 1/3 wavelength each. 

   The array factor gain of a Yagi-Uda is therefore limited to the number of elements, and the element gain is that of a dipole of length about half a wavelength, which is 1.66. 

   Therefore the maximum gain we can reasonably expect from the Yagi-Uda is 1.66 times the number of elements, over isotropic, (or just a factor [equal to the number of elements] over the gain of a single half-wave dipole).