Matrix-Based Interval Arithmetic for Linear Array Tolerance Analysis With Excitation Amplitude Errors

This communication proposes a novel matrix-based interval arithmetic (mIA) method for linear antenna array pattern tolerance analysis with excitation amplitude errors. It derives the closed-form array power pattern bounds in an analytical fashion, which can predict the maximum deviations with respect to the referenced value efficiently. The array power pattern upper bound is its midpoint value summing two error items, the first-order derivative and the array error pattern, while the lower bound is its midpoint value subtracting the first-order derivative. The new expression derived by the mIA method only involves matrix manipulation and requires no condition judgment, which inherits simple coding and easy implementation. Representative numerical examples are presented to validate and demonstrate the effectiveness of the proposed mIA method.