A

For the full HPBW we write ©A = b (l / d) and hence find for the factor b = 2 uA / p. Over the range 0.1 < t < 1 the factor b can be approximated very well by the expression ([Mat.4.6], see also Fig. 4.6):

In the pattern calculations of Fig. 4.5 [Mat.4.5] we have also computed the position and level of the first sidelobe as function of the illumination taper. Thus the first sidelobe level for uniform illumination is at -17.57 dB, decreasing to -24.64 dB for the full quadratic function.

taper

Fig. 4.6. The factor b in the HPBW formula as function of the taper t.

taper

Fig. 4.6. The factor b in the HPBW formula as function of the taper t.

We see a significant decrease in the level of the first sidelobe if the illumination becomes more tapered, which corresponds to a smaller value of t. Next to the desire to minimise spillover radiation along the edge of the reflector, the lower sidelobe level is an important factor in choosing a tapered illumination. Fig. 4.7 illustrates the

taper

Fig. 4.7. The level of the first sidelobe in dB as function of the taper. The red line is the approximation of Eq. (4.14a), black is Eq. (4.14b).

taper

Fig. 4.7. The level of the first sidelobe in dB as function of the taper. The red line is the approximation of Eq. (4.14a), black is Eq. (4.14b).

sidelobe level in dB as function of the taper parameter t [Mat.4.7]. To an accuracy of a few tenths of a decibel the relation can be approximated by the simple formula

The calculated points are closely fit by the relation

S (dB) = -24.682 + 5.7121 + 7.5212 - 6.15613 . (4.14b)

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