This section describes the design methodology of the filtering antenna. The expected behavior of the new device will also be shown through simulations. In this work, all the simulation analyses have been carried out with the CST Microwave Studio. The filters used in the work are designed from [
49]. The configuration of the IM-GWG is identical to the one analyzed in [
49] and has the same basic geometric parameters. The proposed IM-GWG filtering antenna is depicted in
Figure 1, which is mainly composed of three layers. The bottom layer is the full metal square array of pins that makes up the artificial surface named the bed of nails. This surface behaves like a perfect magnetic conductor in a frequency range, enabling the operation of the Gap Waveguide. As shown in
Figure 1a, the upper layer of the GWG consists of an aluminum plate in which the rectangular slot antenna is made. In the middle of these two layers is the substrate on which the inverted microstrip feeding line and the EBG resonators are printed as
Figure 1b shows. The substrate is a Rogers 4003 with thickness hs = 0.79 mm and permittivity
. The manufacturer characterizes the material losses with a
at a frequency of 10 GHz. Between the substrate and the top cover of the waveguide, there is a 1mm thick air gap, as shown in
Figure 1b. This distance, between PMC and PEC layers, is much smaller than
, so there is no possibility of exciting parallel plate electromagnetic modes. In the space between the microstrip line and the upper part, this condition is broken, allowing the local propagation of the QTEM mode. In essence, electromagnetic energy propagates in air, which is why the GWG technology allows the signal to propagate with low losses even at high frequencies.
2.3. EBG Dual-Band Filter Analysis
Typically, the implementation of the direct coupling method to filtering antennas requires the separate design of a PBF and a broadband antenna. In these cases, the performance of the whole system is determined to a greater extent by the filter [
12]. In what follows, the method used to obtain a bandpass filter, with the appropriate individual response to be later integrated with the antenna, is described. The EBG filters that we are going to use are those proposed in [
49]. They consist of a finite periodic set of mushroom-type resonators that coplanarly load the microstrip line. The resonators are formed by a rectangular patch with a small gap between the line, gx1 or gx2 in
Figure 4, and connected on its side to the upper plate of the GWG by a short-circuit element. Two sets of resonators, with different patch sizes, have to be used to suppress two different frequency bands. Each of these sets corresponds to an EBG filter in
Figure 1 and
Figure 2 and is primarily responsible for one of the stopbands. In [
49] the effect of the numerous geometric parameters that this type of filter has is studied in detail. For simplicity, except for the size of the patches, the rest of the parameters are the same for the two EBG filters. For example, the patch-line gap allows widening of the band, in this case a small gap gx1 = gx2 = 0.2 mm has been chosen to obtain a sharp selectivity. Another critical parameter in the design is the radius of the metallized via hole. In this case, it was decided to use short-circuit elements with the same radius for both filters. It would be possible to use short circuit elements of different radius, which would add one more degree of freedom to the design and would allow tuning the response. Another essential aspect is the rejection capability of the filter. As the number of resonators increases for the filter, it offers a frequency response with higher levels of rejection. To facilitate the comparison with [
49], filters with five resonators were chosen, which offers a high level of rejection but a limited size. The structure chosen to analyze the combined response of the two filters is presented in
Figure 5.
A numerical analysis of the resonator sizes needed to center the rejected bands, at f = 9 GHz for filter 1 and around f = 12 GHz for filter 2, has been carried out. Although it an approximately independent response can be observed for each filter, it is evident that some coupling exists. In order to avoid the coupling, taking into account that we do not want to introduce any extra element in the circuit, it is necessary to control the combined response by means of the separation distance between filters (df in
Figure 4).
Figure 6 shows the S parameters simulation of the dual-band filter for different distances between the two EBG filters. It can be seen in the graph how from a certain distance the coupling level decreases, allowing a considerable passband and a flat response.
Table 1 shows the resulting parameter values for the dual-band EBG filter.
The response of this type of EBG filter is greatly influenced by the short circuit element. First, its position modifies the working frequency and allows compacting the resonators if it is placed on the edge of the patch. Second, the variation of the radius of the short-circuit element strongly modifies the inductance of the cell [
49]. This behavior, which is clearly explained in terms of the resonator circuital model included in [
21], produces significant variations in the resonance frequency and therefore in the filter band.
Figure 7 shows the variation of the dual-band filter response with different shorting elements. The simulations corresponding to the metallic via modeled as a cylinder of radius r and those obtained for more complex models of screws, such as those proposed in [
49], are included in the figure.
Figure 5a clearly shows the position of the screws that connect the top cover of the GWG to the patch of the resonators. This configuration was already used in [
49] with good experimental results. The necessary parameters for the modeling of screws of different metrics are included in
Figure 5b.
Figure 7 shows how the rejected bands are located approximately at the considered frequencies to allow the propagation of the signal between 10 GHz and 11 GHz. After [
49], we know that the prototypes made with screws shift their response towards lower frequencies, which implies that the effective radius of the short-circuit element is less than the nominal of the model. For this reason, to obtain a realistic model for the screw that is going to be used, the radius of the via is decreased from re = 0.7 mm and ri = 0.65 to values of re = 0.55 mm and ri = 0.45 mm. It is verified in the graph that for this size, considering the via as a cylinder of radius r = 0.5 mm, we obtain similar results. To simplify the procedure as much as possible, in what follows this value will be used in the models. In this case, it can be seen how the lower band is located according to frequencies with the measurements made in [
49]. In the
Figure 7, a flat passband with low insertion losses of the order of 1 dB is obtained. All materials are lossy in simulations but SMA connectors are not included. This tuned filter, with parameters given in
Table 1 including the cylindrical via of radius r = 0.5 mm, is considered for integration with the antenna.
Figure 7 shows two stopbands in the transmission that will be combined with the antenna, we can consider, as in [
49], that a sufficient rejection level will be
less than −20 dB. The designed filter has a lower stopband centered at f = 8.85 GHz with a fractional bandwidth of 12.4% and with a maximum rejection level of 53 dB. For the upper stopband, the center frequency is f = 12.4 GHz with 11.6% fractional bandwidth and a maximum rejection of 54 dB. Finally, from
Figure 7, we can see a passband centered at f = 10.7 GHz with a 12.4% width (3 dB FBW); in this case, the minimum insertion losses are 0.98 dB at a frequency of 10.85 GHz.
2.4. Filtering Antenna Integrated Response
According to the method used in [
10], the design of a slot antenna with considerable bandwidth was employed using full wave simulations. From an impedance 50
feeding microstrip line, w = 4.5 mm, a T-shape feed line section was used as shown in
Figure 4b. The dipole-type end line width, dipx = 13.8 mm in
Figure 4c, allows power to be coupled to the slot whose width is slx = 14.8 mm. All geometric values of the reference antenna obtained in the fitting process are included in
Figure 8. The simulations of the frequency response of the slot antenna, impedance matching and broadside realized gain are included in
Figure 8. We can see that
dB results in an operating band from 9.8 GHz to 10.7 GHz, corresponding to an FBW of
at a frequency of
GHz. The maximum simulated realized gain for the antenna is 4.3 dBi at 9.85 GHz. We can also observe the characteristic behavior of this IM-GWG antenna. At frequencies included in the bandgap corresponding to the pins, also represented in
Figure 8, the conventional response of an inverted microstrip feeding slot antenna can be seen (in this case including the self-package). Below and above this bandgap, the reflection coefficient response, in
Figure 8, corresponds to the excitation of undesired modes in the parallel plate waveguide.
As discussed in the introduction, size reduction, low losses and filtering capabilities are a trend in antenna design. In our case, a trade-off between filter size, passband width and rejection level is necessary. For this reason, the filter’s antenna integration approach has two requirements. First, our objective is a very simple design that includes the possible integration of the filters without modifying the feeding lines of the antenna or the array. Second, IM-GWG antenna feeding networks are usually already complex and have space limitations, so if our goal is to integrate coplanar-EBG filters they must necessarily be as compact as possible. Two consequences follow from this argument. On the one hand, for the antenna filtering, we are going to use three-cell-based EBG-filters, as shown in
Figure 1 and
Figure 4c, instead of five resonators as we did when designing the filter in
Section 2.3. With this, we expect a lower selectivity of the filtering, although the rejection level will be close to 20 dB [
49]. On the other hand, if we do not want to introduce any extra network that matches the filter, we can basically adjust the combined filter–antenna response with the distance that separates the dual-band filter from the antenna and the separation between EBG-filters (ds and df in
Figure 4c, respectively). Direct filter–antenna connection, as is our case, produces an impedance mismatch [
13]. This can cause the filter’s performance to deteriorate, especially at the band edges, which in our design significantly affects the passband of the filter [
25]. Usually, an extra matching network could be implemented to solve it [
12], which is avoided here to make the filter integration compatible with already existing networks with strong space constraints.
To make the dual-band filter compact, the decrease in the distance between filter 1 and filter 2 is initially analyzed. The effect of varying the spacing between filters has already been shown in
Figure 6, although in that case the filters had five resonators. After the evaluation of the coupling and even if an increase is observed, a value of df = 7 mm is taken as distance, which ensures a certain passband in the simulations. Next, a parametric study was carried out to evaluate the coupling between the antenna and the filter. The combined filter–antenna frequency response is shown in
Figure 9 for different spacings, ds in
Figure 4c, between the filter and the T-shape feed line of the antenna. Although a mismatch between the two devices can be seen in this case, it is partially corrected by adjusting the variable (ds) to improve the overall system. The values considered for the proposed filtering antenna are indicated in
Table 2, including the adjusted distances between filters (df = 7 mm) and with the slot (ds = 6.4 mm). It should be noted that both the slot size and the rest of the parameters related to the feeding line, including the T-shape section, remain the same.
Finally,
Figure 10 shows the effect on the frequency response of the antenna depending of the type of short-circuit element used. The results obtained using an M1.4 metric screw model are included together with others of slightly smaller metrics. The effectiveness of having used a simplified via model with effective radius r = 0.5 mm is verified.
Figure 10 also shows the return losses for the reference antenna slot without the filter. For the case with r = 0.5 mm, the simulated impedance band for the filtering antenna (
dB) extends from 10.6 GHz to 10.85 GHz (only an FBW of
). This reveals that the integration of the EBG dual-band filter limits the bandwidth of the proposed antenna system as expected [
12].
The performance comparison between the filtering antenna and the reference, both in impedance and radiation, is depicted in
Figure 11. From the impedance response, the greater frequency selectivity that the filtering antenna has with respect to the reference case is verified. The realized gain for the proposed antenna reaches a maximum value of 2.8 dBi at a frequency of 10.5 GHz. If we relax the matching level condition,
dB, the working band of the proposed antenna would be an FBW of 7.6% with central frequency at
GHz. It could be seen in
Figure 11 that the gain values obtained in this passband by the filtering antenna are similar to those of the reference one, except in the lower part where they are slightly lower. From
Figure 11, we can draw conclusions concerning the design filtering operation. Compared to the slot reference, the proposed antenna effectively suppresses unwanted signals out of the band. The rejection level between both radiators reaches more than 10 dB between 8.75 and 9.75 GHz for the lower band and between 12.1 and 13.6 GHz for the upper band case. These rejected bands reasonably coincide with the stopbands for the designed filter in
Section 2.3, also included in the graph, as shown in
Figure 11. This is consistent with the direct integration method used, which initially considers that the responses of the filter and of the antenna, are independent.
In order to clarify the operational mechanisms associated with the filtering slot antenna over a wide frequency range, the calculated electric field distributions for different frequencies are illustrated in
Figure 12. As predicted by the fundamentals of the GWG, the parallel plate waveguide excites modes that can propagate through the structure up to the frequency at which the artificial surface begins to behave like a PMC. As
Figure 3 shows, this frequency is in our case f = 7.8 GHz. This is clear also from the return loss results obtained for the filter and the filtering antenna, as shown in
Figure 11. The field distribution shown in
Figure 12a at 7 GHz represents the propagation of these unwanted modes in the parallel plate waveguide. Something similar is also observed for the field distribution at 15 GHz included in the
Figure 12e, since this frequency is located above the bandgap of the GWG structure. In the other three field distributions included in
Figure 12, the GWG is working on the bed of nails bandgap. At the working frequency (f = 10.5 GHz in
Figure 12c), the filtering antenna is excited in a similar way to the reference antenna since it corresponds to the passband of the integrated filter. While for the frequencies of 9 GHz and 12.5 GHz, included in
Figure 12b,d, the band notches produced by filter 1 and filter 2, respectively, reject the energy propagated by the IM-GWG line.
The simulated 3D radiation patterns for the reference slot and the filtering antenna are compared in
Figure 13 for 9, 10.5, 12.5 and 13 GHz frequencies, all included in the bandgap of the GWG parallel plate. It can be concluded from
Figure 13 that the radiation patterns at f = 10.5 GHz are similar, both in shape and gain levels, for both antennas. That is, the integrated antenna preserves the power transmission, as observed in
Figure 12c. In the bands rejected by the dual-band filter, at 9 GHz for filter 1 and at 12.5 and 13 GHz for filter 2, the filtering antenna’s radiation patterns maintain symmetry but theirs power are significantly reduced by approximately 12 dB and 20 dB, respectively.
To facilitate the comparison between the proposed antenna and the slot antenna without the filter, the polar radiation patterns for the E and H planes of the antenna are included in
Figure 14. As expected, the patterns at the operating frequency for both planes are very similar, as shown in
Figure 14c,d, while at the rejection frequencies produced by the EBG-filters there is a very significant decrease in the radiated power as observed in
Figure 14a,b and
Figure 14e,f for the lower f = 9 GHz and higher f = 12.5 GHz filter frequencies, respectively.