Design of the antenna

The presented antenna is based on the SIW LWA already presented in paper [Reference Machac, Lorenz, Saglam, Bui and Kraemer8]. The used transmission line can be viewed at first glance as a conductor-backed slotline with a finitely wide substrate metallized on its side walls or a low-profile flat slotted waveguide [Reference Zehentner, Machac and Zabloudil18]. The solid conducting walls are substituted by arrays of conducting pins used as the SIW side walls. A cross section of the line is shown in Fig. 1. Generally, relative permittivities are ε _r2 > ε _r1. When waveguide width b is substantially greater than substrate thickness h, we have a flat waveguide with a slot cut in the waveguide wall parallel to its longitudinal axis. The problem of the antenna presented in paper [Reference Machac, Lorenz, Saglam, Bui and Kraemer8] was in the shape of the radiation pattern. This pattern was split into two lobes in the transverse plane due to the symmetry of the slot position and the corresponding symmetry of the field distribution across the slot. Therefore, the slot in our antenna is moved out of the y-axis by distance a (see Fig. 1).

Figure 1. Cross section of the flat slotted waveguide [Reference Zehentner, Machac and Zabloudil18].

Using a standard substrate of a thickness of 0.762 mm with a permittivity of 3.48, we achieve the dependence of the angle of maximum radiation on frequency for particular slot widths w as shown in Fig. 2. The data are calculated by the CST Microwave Studio (CST MWS) time domain solver [19]. The SIW width is 20 mm, and the SIW side walls are substituted by solid PEC walls to simplify the analysis. This is acceptable as for the chosen parameters of the SIW structure with the diameter of conducting pins equal to 0.2 mm and their distance equal to 0.4 mm, the difference between the SIW width and the width of the equivalent waveguide with PEC side walls is only 0.105 mm [Reference Cassivi, Perregrini, Arcioni, Bressan, Wu and Conciauro20]. The plotted angle of maximum radiation Θ (elevation angle) is measured from the broadside direction, which is a direction perpendicular to the substrate (direction of the y-axis in Fig. 1). This elevation angle is coupled with propagation constant β by the phase condition

(1)\begin{equation}{\text{sin}}\;\Theta = \beta /{k_{\text{o}}},\end{equation}

Figure 2. Angle of maximum radiation (elevation angle) calculated by the CST MWS and plotted for different slot widths.

where k _o is the free space propagation constant. Equation (1) is accurately valid for an infinitely long leaky-wave transmission line.

Figure 2 shows that slot width equal to 9 mm offers the widest frequency band of beam steering, which starts at a frequency of 5.5 GHz and ends at 7.4 GHz. At the selected frequency, the direction of radiation depends on the slot width. Hence, when changing the slot width from 4.4 to 9 mm, the direction of radiation is reduced from 71° to 17° at the 5.5 GHz frequency.

Inserting two auxiliary conducting strips into the slot on the substrate top parallel to the z-axis gives us the chance to control the antenna radiation pattern. These strips themselves have only a minor influence to the final radiation pattern. They are connected to the original slot edges by an array of varactors. The DC bias of these varactors changes their capacitances and controls the antenna radiation pattern as the slot width is effectively changed. So, we finally arrive at the LWA structure shown in Fig. 3. The SIW width is 20 mm fabricated on the substrate 0.762 mm in thickness with permittivity 3.48. SIW side walls are constructed of conducting pins 0.2 mm in diameter located at distances equal to 0.4 mm. The radiating slot width is 9 mm and is shifted from the SIW axis by 1 mm. The feeding 50 Ω microstrip line width is 1.7 mm. The distances between varactors are d = 12 mm as will be discussed at the end of this section in conjunction with the inequality (2). The auxiliary conducting strips are 2 mm in width. They are separated from the radiation slot edges by the slot 0.3 mm in width.

Figure 3. A model of the presented LWA on the SIW. The radiation pattern is controlled by varactors connected between the auxiliary conducting strips and radiating slot edges.

The antenna length l is 350 mm because the amplitude of the space leaky mode at the end of the antenna should be lower than 5% of its magnitude on the feeding point at the mean operating frequency of 5.5 GHz.

Figure 4 documents the steering of the antenna beam by changing capacitances of the used varactors. In the CST MWS model, varactors are represented only by a single capacitor. The plot in Fig. 4 shows angles of maximum radiation (elevation angles) calculated by the CST MWS as a function of frequency for the given capacitances of varactors. The beam is directed at a frequency of 5.5 GHz at 30° by using a capacitance equal to 0.15 pF. Continuously increasing the capacitance to 0.9 pF tilts the beam to 78°. Accordingly, the beam can be steered by 48°. Similarly, the beam can be steered by 37° at 6.3 GHz by changing the capacitance from 0.65 up to 0.9 pF. However, there is not a sufficiently low antenna input reflection at this frequency.

Figure 4. Angle of maximum radiation (elevation angle) calculated by the CST MWS and plotted for given values of varactor capacitances as functions of frequency.

By comparing the plots in Figs. 2 and 4, we can determine the effective slot width w _eff that results when two conductive slots are inserted. The effective width is plotted in Fig. 5 for a given structure geometry and frequency 5.5 GHz. The effective width decreases almost linearly with increasing capacitance. This is due to the decrease in the impedances of the capacitors connecting strips to the slot edges. At zero capacitance, which corresponds to strips not connected to the slot edges, the effective width equals the actual slot width. This shows that the strips have no effect on the radiation pattern.

Figure 5. The SIW slot effective width at frequency 5.5 GHz depending on the varactor capacitance.

Radiation patterns calculated in the E-plane (parallel to the y–z plane, see Fig. 1) for the selected varactor capacitances by the CST MWS at a frequency of 5.5 GHz are plotted in Fig. 6. The level of side lobes increases with increasing capacitances. At 0.65 pF it is 5.9 dB, and at 0.9 pF it is only 0.35 dB below the level of the main beam.

Figure 6. Radiation patterns in the E-plane calculated by the CST MWS and plotted for selected values of varactor capacitances at a frequency of 5.5 GHz. The depicted varactor bias corresponds to capacitance as stated in paper [21].

Radiation patterns calculated in the H-plane (parallel to the x–z plane, see Fig. 1) for the selected frequencies between 5.5 and 6 GHz are plotted in Fig. 7. The varactor capacitance is taken 0.2 pF that corresponds in the fabricated structure to 9 V DC bias. The azimuthal angle is measured in the x–z plane from the positive direction of the x-axis. Each plot in Fig. 7 is taken not exactly in H-plane, but at the direction of the maximal radiation in elevation. These angles are according to Fig. 4 equal to 32° for 5.5 GHz, 40° for 5.6 GHz, 47° for 5.7 GHz, 51° for 5.8 GHz, 57° for 5.9 GHz, and 60° for 6 GHz. The radiation patterns are narrower at higher frequencies. The level of side lobes increases with increasing frequency as shown in Fig. 13.

Figure 7. Radiation patterns in the H-plane calculated by the CST MWS and plotted for selected frequencies.

The simulated antenna radiation efficiency is between 88% and 90% in the frequency band of the maximum gain 5.5–5.6 GHz at the applied DC bias equal to 9–12 V.

Figure 8 shows scattering parameters of the antenna calculated by the CST MWS within a frequency interval from 5.3 to 7 GHz for selected varactor capacitances. The plot shows that the antenna is able to work with sufficiently low reflection in a frequency band from 5.3 to 6 GHz. The best match is for an applied voltage of 4 V corresponding to a varactor capacitance of 0.37 pF [21]. Figure 8(b) proves that the antenna does not radiate at varactor capacitances greater than 0.65 pF, i.e., for bias voltages lower than 1.5 V as the power is transmitted, but not radiated.

Finally, the presence of two arrays of varactors in the antenna design must be mentioned. They form a periodic array with period d, as seen in Fig. 3. This structure can cause the Bragg reflection to occur. To avoid the presence of a band gap, the waveguide must preserve the following condition for the wavelength λ:

(2)\begin{equation}\lambda\,{ \gt }\,4d.\end{equation}

Figure 8. Simulated scattering parameters of the presented antenna as a function of frequency for varactor capacitance values between 0.15 and 0.9 pF. (a) S ₁₁, (b) S _21.

Condition (2) is valid using the propagation constant determined from data plotted in Fig. 4 by using relation (1) and choosing the maximum possible distance between varactors d = 12 mm.

The varactors used, which must have a sufficiently low capacity, are MA46H120 from MACOM [21]. These varactor diodes are represented in the CST MWS model only by a simple p-n junction capacitor. The dependence of these capacitances on the DC bias voltage is given in paper [21]. Mounting these diodes requires a narrow slot between the edges of the radiating slot and auxiliary conducting strips. We opted for a 0.3 mm wide slot. As mentioned above, to obtain a maximum span of elevation angles equal to 48°, we decided for auxiliary conducting strips of a width of 2 mm. The distance between varactors is 12 mm. The radiating slot is in total 350 mm long and is shifted out of the SIW axis by a = 1 mm. Finally, two rows of 29 varactors are used in the antenna design. The positive bias port is connected via a 22 kΩ resistor to ground (i.e., to the SIW edges), the negative port is connected to the auxiliary conductive strips. Thus, only one DC voltage source is used.

The radiating slot is terminated on both sides with a taper. The SIW is connected to the microstrip line using this standard taper transition transforming the SIW impedance to 50 Ω.

Experimental verification

The antenna was fabricated based on the design specifications presented in the previous section. The antenna structure is shown in Fig. 9, where the position of the varactors is indicated.

Figure 9. Photo of the fabricated antenna.

Measured reflection coefficients S ₁₁ are plotted in Fig. 10 for specific values of varactor bias and corresponding capacitances. Antenna matching deteriorates with decreasing varactor bias, which increases their capacitances. The best match is at 4 V. The measurement was done by using vector network analyzer (VNA) Rohde & Schwarz ZVA40 (10 MHz–40 GHz). Data correspond well to the simulated characteristics given in Fig. 8(a).

Figure 10. Measured input reflectivity of the presented antenna as a function of frequency for given varactor bias from 1 to 12 V.

Antenna patterns were measured in an anechoic chamber [22] and computed automatically, employing the NSI2000 far-field measuring software [23] for defined frequencies. The measuring system uses the two-port VNA Rohde & Schwarz ZVA40 as a transmitter/receiver. In this setup, the antenna under test is connected to one port of the VNA, the test probe DHR18-EX antenna [24] to the second one, and the S ₂₁ transmission coefficient is measured.

Measured radiation patterns (antenna gain) of the antenna are plotted in Fig. 11 for specific DC bias values. Angles of maximum radiation taken from Fig. 11 correspond to the calculated angles plotted in Fig. 4 at a frequency of 5.5 GHz, at which there is the biggest span of the angle of maximum radiation controlled by the varactor bias voltage.

Figure 11. Measured E-plane radiation patterns of the antenna at 5.5 GHz for given varactor DC biases.

The direction of the antenna’s maximum radiation is steered by 35°, from 30° to 65°, when changing the varactor bias from 12 to 2 V. This corresponds to the simulation shown in Fig. 6. Unfortunately, at lower values of the bias, the antenna radiation starts to be less sensitive (see Fig. 11) with the increasing frequency. The reason can be in higher S ₁₁ and lower S ₂₁ at these voltages. The experimentally obtained beam steering, however, corresponds to the calculated data shown in Figs. 4 and 6 even at these bias values.

One of the reasons for the mismatch between the calculated and measured radiation patterns is in the used coarse equivalent circuits of varactors. They comprise only the capacitance of the varactor diode junction.

The measured maximum antenna gain is plotted in Fig. 12 as a function of frequency for given DC bias of varactors. It was obtained by the gain transfer method, using the DHR18-EX antenna as the standard gain antenna [23]. The measured values correspond to the gain simulated by the CST MWS. The maximum value is 12 dBi.

Figure 12. Measured maximum antenna gain in dependence on frequency for given varactor DC biases.

The measured side-lobe level (SLL) of the antenna has a maximum value of −20 dB at 5.5 GHz with a DC bias voltage of 12 V. This is the best value of the antennas listed in Table 1.

The calculated and measured SLLs are plotted in Fig. 13. The agreement of the corresponding SLL values is relatively good. The separation between the main lobe of the radiation diagram and the side lobes decreases with increasing frequency and with increasing values of varactor capacitances (decreasing DC bias). This behavior was determined in Fig. 7 on simulated radiation patters in the H-plane using the varactor capacitance equal to 0.2 pF.

Figure 13. Calculated (a) and measured (b) SLLs for the selected (a) varactor capacities and (b) selected varactor biases.

Table 1 compares our results with those taken from literature. All structures (except [Reference Zheng, Wang, Zhao, Li, Geng, Li, Chen and Zhang17]) are planar and use varactors with their capacitances controlled by DC bias, so they enable a continuous beam scanning. The span of applied DC bias depends on the chosen varactors. Reference [Reference Xu, Eleftheriades and Hum16] proposes optimal design of selected varactors bias. Reference [Reference Zheng, Wang, Zhao, Li, Geng, Li, Chen and Zhang17] proposes the antenna controlled by coding a set of PIN diodes between their “ON” and “OFF” states. Our proposed antenna can work with rather narrow span of DC voltages using only one DC source. The presented gain has moderate value 12 dBi, but higher than most of the values given in Table 1. The measured radiation pattern shows the maximum separation between the level of the main lobe and the side lobes of the selected antennas.