A substrate integrated waveguide (SIW) with transverse slots on the top plane can be used to design an effective leaky-wave antenna with good frequency beam-scanning and platform integration capability. For a main beam near end-fire, the phase constant of the radiating wave must be near to the free space wavenumber or slightly larger. In this context, the modified Hansen-Woodyard condition gives an optimum phase constant to maximize the directivity at end-fire. For the analysis of the wave propagation we have implemented a modal analysis for rectangular waveguides with transverse slots. Near end-fire, three types of modal solutions exists, a leaky improper mode, a surface wave mode and a proper waveguide mode. The leaky mode can reach phase constants larger than the free space wavenumber to fulfill the Hansen-Woodyard condition, but loses strongly its physical significance in this slow wave region, thus the excitation of the leaky-wave becomes negligible there, whereas the proper waveguide mode is dominant but exhibits only a negligible radiation loss leading to a strong drop of the antenna efficiency. Therefore, the optimum efficiency of 86 % for maximizing the gain as proposed in the literature cannot be reached with this kind of leaky wave antenna.

But it will be shown in this contribution by analyzing antenna structures with finite aperture lengths, that the efficiency can reach nearly 100 % if the phase constant of the leaky-wave meets exactly the free space wavenumber (ordinary end-fire condition) and the aperture length is adjusted with regard to the attenuation constant of the leaky-wave from the modal analysis. For a given aperture length, a procedure is outlined to adjust the attenuation constant in several steps at the desired ordinary end-fire frequency to reach maximum gain and efficiency.

Modal analysis results of the structure in Fig. 1a.

Analysis of the structure in Fig. 1b with HFSS.

Microstrip-SIW transition.

Microstrip power divider with detour line.

Figure 1a, shows the configuration with infinite length and filled
rectangular waveguide used for the modal analysis in the space domain (Liu
and Jackson, 2011). This analysis searches for the complex propagation
wavenumber

Stepwise increasing of the attenuation constant at ordinary end-fire.

This can be recognized by the behaviour of

This is due to the fact, that the leaky mode becomes unphysical beyond
end-fire and the proper waveguide mode becomes dominant with a low
attenuation only due to dielectric and metallic losses, thus

This can also be observed in Fig. 2b, where the red curve shows only
a small increase somewhat before

Obviously the leaky-wave is transformed into the surface-wave over the
aperture length in such a way that the attenuation constant for the
leaky-wave derived from the modal analysis is still valid for the radiating
mechanism of both leaky and surface-wave mode up to the frequency of
ordinary end-fire. Since the excitation of the surface wave drops down
beyond the ordinary end-fire frequency, the efficiency of 86 % at the
modified Hansen-Woodyard condition for gain maximization as proposed in
O'Connor and Jackson (2010) cannot be reached. Therefore we
propose as follows a gain improvement at the ordinary end-fire frequency by
a procedure of step-wise increasing the attenuation constant to maximize the
efficiency derived by

The attenuation constant can be increased by enlarging the slot length
and/or the slot width and/or decreasing the slot periodicity. But with fixed
width of the waveguide, also the values of

In Table 1, the

The gain is, depending on frequency, up to 1.4 dBi higher for No. 7 compared with the parameter set No. 1. A radiation exactly in end-fire direction is not possible due to diffraction effects of the finite groundplanes.

Since the antennas are fabricated in SIW-technology, we still need a
SI-waveguide with width

For the practical implementation we need also a microstrip-SIW transition, which is sketched in Fig. 5, showing a good matching behavior with low losses and a bandwidth of about 18 %.

To reach a higher gain also for frequencies below end-fire, we have also examined structures with two antenna branches. In this context we need a power divider with low losses. A suitable microstrip divider with additional detour line is outlined in Fig. 6 with the input port 3. We have used rounded bends to minimize the parasitic radiation leading to losses of only about 0.6 dB (Weisshaar and Tripathi, 1990). A power divider with mitered bends could be optimized for a good matching behaviour, but the losses amount to about 1.5 dB mainly due to the parasitic radiation of the mitered bends. A structure with two antenna branches with a center distance of 10 mm is given in Fig. 7a.

Figure 7b shows the peak gain comparison with one and two branches. Due to mechanical constraints, the SMP-connector must be located alongside the branches thus the additional detour line is needed. The SMP-connector is linked to the microstrip line with an additional matching section .

The maximum gain of the structure with one branch drops down to 18.4 dBi at

Leaky-wave antennas in SIW-technology with transverse slots are a good candidate, if a frequency scanning capability up to end-fire and a cheap fabrication is desired. To increase the directivity and gain at end-fire operation, the (modified) Hansen-Woodyard condition may be applied. To fulfill this condition, the propagation constant of the radiating mode must be slightly higher than the free space wavenumber. However, in this slow wave region the leaky-wave becomes unphysical and also the excitation of the surface wave mode drops down strongly beyond the ordinary end-fire operation. But it could be found, that the leaky-wave is transformed into the surface wave at the frequency of ordinary end-fire and that for the radiation loss computation along the aperture still the attenuation constant of the leaky-wave can be used which is derived from a modal analysis based on rectangular waveguides. With this modal analysis, we have outlined a procedure to stepwise increase the attenuation constant e.g. by decreasing the periodicity of the slots and decreasing the width of the waveguide to get a radiation efficiency of about 99 % adjusted to the length of the aperture. After a careful transformation of the rectangular waveguide into a SIW together with an efficient microstrip-SIW transition, a cheap fabrication is possible. With the use of power dividers with low losses, structures with two antenna branches can be designed leading to a gain improvement also for frequencies below end-fire operation.

There are no underlying research data for the presented work due to non-disclosure reasons. The results can be reproduced with the design methods and equations given in the paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Kleinheubacher Berichte 2018”. It is a result of the Kleinheubacher Tagung 2018, Miltenberg, Germany, 24–26 September 2018.

This paper was edited by Thomas Eibert and reviewed by three anonymous referees.