Signal Integrity and Radiated Emission of High-Speed Digital Systems

Appendix D

Formulae for Simple Radiating Structures

This appendix provides closed-form expressions for calculating radiated fields from wire structures, as often found in PCBs with attached cables. A method for considering also the metallic reference plane of a semi-anechoic chamber for measurements is given. A low-frequency approximation method for computing radiated fields from an aperture is introduced and explained for the case of a rectangular aperture.

D.1 Wire Structures

Formulae for calculating the radiated E-field in the Far-Field (FF) region when the currents on the wires are known are shown in Table D.1. It is important to make the following observations:

• Infinitesimal dipole. In general, the EM fields radiated by an infinitesimal dipole have components in spherical coordinates that depend on 1/r, 1/r², and 1/r³ [1]. However, as the interest is focused on E-field prediction at a distance r ≥ 3 m, where the observation point is normally in the far-field region, the expression for the E-field can be simplified and becomes dependent on 1/r only, as shown in Table D.1. Note that, in the far field, E and H are mutually orthogonal and E/H = 377Ω.
• Electrically short differential-mode structure. As a first consequence of using the far-field approximation for an infinitesimal dipole, the simple expression in Table D.1 is obtained for the case of two parallel electrically short wires with opposite currents. This is a practical case of signal current and its return path. Note ...