where k is an integer. Squaring either of these equations gives an equation of the form: where n is an integer, and the ± sign refers to even (+) or odd (-) n. Dividing through by u2n gives: To find the upper bound of this function, the oscillating term in parentheses on the right side must be replaced by its upper bound, which is 2. Thus, Applying this approximation to Equation 2, and substituting for Io and r gives: where r is the dimensionalized distance from the center of the radiation pattern. If c is the velocity of light and f is the frequency, then = c/f. In addition, In(r) can be set equal to the microwave safety threshold Is, and r can be set equal to the exclusion zone radius rs. These substitutions can be made in Equation 10, and the equation rearranged to give the approximate exclusion zone radius for case n:
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