An integral equation for a single loop antenna satisfying the boundary condition is reviewed, where the tangential electric field vanishes at the surface of the perfectly conducting wire except in a narrow region across which a voltage source is applied.
Fourier-Series expansion coefficient of the current in the loop may be expressed in terms of the double integration, and Wu showed that the double integration may be changed into a single integration.
Formulation for the single loop may be applied to the array of multiple loops. The integral equations are reduced to a series of linear simultaneous equations which contain only the Fourier coefficients of the electric currents of the same order.
It has been shown that by varying the propagation constant linearly along the Yagi array, the side lobe level can be improved. This linear variation of the propagation constant may be obtained by tapering the element lengths or element spacings slowly along the Yagi array. An approximate method for the calculation of the linearly tapered long Yagi array is introduced, and the result of tapered spacing is shown to be satisfactory in reducing side lobe level.
The above calculation scheme is also applied to the design of the reflector, which improves the front-to-back ratio.
The validity of this design method is verified by experiments, testing radiation pattern of the designed Yagi loop antenna in the anechoic chamber.