### Abstract

The relative power error of a truncated expansion is obtained from the derived modal power distribution. The result offers a convenient way to determine an appropriate truncation limit of the modes in a SWE as a function of the desired accuracy and antenna size.

This method is more accurate than the formulas given previously in the literature. Moreover, it allows one to choose the accuracy of the resulting field, contrary to the earlier formulas.

The derived truncation limit is compared with expressions given previously in the literature and with analytically and numerically determined radiation pattern examples. The modal power distributions are also compared with the calculated examples.

Original language | English |
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Pages (from-to) | 1307-1328 |

Journal | Journal of Electromagnetic Waves and Applications |

Volume | 16 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2002 |

MoE publication type | A1 Journal article-refereed |

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**Analytical solution for characteristic modal power distribution and truncation limit for spherical wave expansion of antenna radiation pattern.** / Koivisto, Päivi.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Analytical solution for characteristic modal power distribution and truncation limit for spherical wave expansion of antenna radiation pattern

AU - Koivisto, Päivi

PY - 2002

Y1 - 2002

N2 - In this paper the Spherical Wave Expansion (SWE) is used to represent an antenna radiation pattern. An analytical expression for the characteristic modal distribution of power radiated by an arbitrary antenna is derived from the assumption of equal average amplitude for each mode over the surface of the minimum sphere enclosing the antenna. The relative power error of a truncated expansion is obtained from the derived modal power distribution. The result offers a convenient way to determine an appropriate truncation limit of the modes in a SWE as a function of the desired accuracy and antenna size. This method is more accurate than the formulas given previously in the literature. Moreover, it allows one to choose the accuracy of the resulting field, contrary to the earlier formulas. The derived truncation limit is compared with expressions given previously in the literature and with analytically and numerically determined radiation pattern examples. The modal power distributions are also compared with the calculated examples.

AB - In this paper the Spherical Wave Expansion (SWE) is used to represent an antenna radiation pattern. An analytical expression for the characteristic modal distribution of power radiated by an arbitrary antenna is derived from the assumption of equal average amplitude for each mode over the surface of the minimum sphere enclosing the antenna. The relative power error of a truncated expansion is obtained from the derived modal power distribution. The result offers a convenient way to determine an appropriate truncation limit of the modes in a SWE as a function of the desired accuracy and antenna size. This method is more accurate than the formulas given previously in the literature. Moreover, it allows one to choose the accuracy of the resulting field, contrary to the earlier formulas. The derived truncation limit is compared with expressions given previously in the literature and with analytically and numerically determined radiation pattern examples. The modal power distributions are also compared with the calculated examples.

U2 - 10.1163/156939302X00787

DO - 10.1163/156939302X00787

M3 - Article

VL - 16

SP - 1307

EP - 1328

JO - Journal of Electromagnetic Waves and Applications

JF - Journal of Electromagnetic Waves and Applications

SN - 0920-5071

IS - 9

ER -