## 1. Introduction

[2] Leaky waves on printed-circuit transmission lines have recently received considerable attention. Radiation into space waves, surface waves, and both wave types have been investigated for a variety of two-dimensional microstrip-like lines, coplanar lines, and various printed transmission line modifications [*Michalski and Zheng*, 1989; *Shigesawa et al.*, 1991, 1995, 1996; *Carin and Das*, 1992; *Bagby et al.*, 1993; *Nghiem et al.*, 1995, 1996; *Yakovlev and Hanson*, 1997; *Nyquist et al.*, 1997]. Experience gained in the study of leaky wave open boundary waveguides has resulted in the development of novel microwave and millimeter wave devices and components, such as leaky wave couplers [*Niu et al.*, 1993] and leaky wave antennas, although many studies have concentrated on the potentially harmful effects of unintended crosstalk, coupling, and radiation due to leaky waves on integrated circuits.

[3] In many practical applications, circuit board and on-chip interconnects are constructed from finite sections of transmission lines. The possibility of leaky wave excitation on these three-dimensional interconnects has received relatively little attention [*Das*, 1996; *Carin et al.*, 1998], compared to two-dimensional structures, although semi-infinite source-excited lines have been somewhat more thoroughly studied [*Villegas et al.*, 1999; *Mesa et al.*, 1999, 2001; *Jackson et al.*, 2000; *Mesa and Jackson*, 2002; *Langston et al.*, 2003]. While it is clear that the simpler two-dimensional transmission line model can be used as a starting point for considering leaky waves on three-dimensional structures, the degree to which two-dimensional results predict three-dimensional phenomena is still an open question. For example, *Das* [1996] reported that the onset of leakage on certain three-dimensional transmission line structures seems to occur at a different point than that predicted by two-dimensional theory. Furthermore, in previous studies simplified excitations (generally, delta gaps) were considered, or the influence of the feed was ignored.

[4] In this paper we investigate three-dimensional microstrip interconnect geometries, with realistic excitations, and derive asymptotic closed-form expressions for the field radiated by such structures. The field along the air-dielectric interface is considered, since potential crosstalk with other devices may depend on the field at this interface. The results are compared to a full-wave, three-dimensional simulation in both the traveling/standing wave (TSW) regime (analogous to the bound regime on two-dimensional transmission lines; see section 3) and leaky wave (LW) regime, verifying the developed expressions. It is shown that in the leaky wave regime the angle of leakage on a three-dimensional interconnect corresponds with the usual two-dimensional ray optics result if the interconnect is sufficiently long, even for coupled interconnects. For shorter interconnect strips, the influence of interconnect length, spacing, and of the via is important. This paper is a considerably expanded version of *Hanson et al.* [2004] and *Hanson and Yakovlev* [2004].