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

Comparison of three interval arithmetic‐based algorithms for antenna array pattern upper bound estimation

“…By comparing (3), (7) and (10), one can see that the first items for these three algorithms are all the same. However, the latter two items denoting amplitude error introduced impacts are different.…”

“…where a = {a n } and E is a N × 1 vector with E n = exp(ju n ), k = 2p/l is the wavenumber and r(u) is the unit vector in the direction. Note that the following discussion can be applied to antenna array with any geometry and not restricted in the linear or planar case as considered in previous works [5][6][7][8][9][10]. Let the interval of the excitation amplitude of the nth element is ka mid n , a rad n l, where a mid n and a rad n are the midpoint and the radius, respectively.…”

“…Hence, the antenna array upper bound derived by the mIA algorithm should be [10] P sup mIA = a mid Qa mid T + 2|a mid Q|a rad T + a rad |Q|a rad T .…”

“…Later, Anselmi et al [8] and Tenuti et al [9] analysed the array pattern tolerance with the circular IA (cIA) algorithm by first calculating the bounds of the array factor and then squaring it. Recently, He et al [10] proposed a matrix IA (mIA) algorithm to estimate the interval of the antenna array pattern by expressing it in the quadratic matrix form. However, only numerical examples are presented for comparison in all these existing works, while the underlying relations of these IA-based algorithms have not been revealed.…”

Tolerance analysis of 3D printed patch antennas based on interval arithmetic

“…They analyzed and compared the difference between the upper and lower boundaries of three interval algorithms to calculate the power pattern of an array antenna. 24,25 However, studies on IA-based tolerance analysis of the patch are lacking.…”