D-CRLH unit-cell analysis

The proposed antenna is designed based on a D-CRLH unit cell. The dispersion propagation coefficient (β) along D-CRLH TL can be extracted by applying the periodic analysis of the infinite number of cells of length (d) as [Reference Caloz24]

(1)$$\cos ( \beta d) = \cos ( \theta ) + \displaystyle{1 \over 2}\,\,Z\,Y\,\cos ^2\,\left({\displaystyle{\theta \over 2}} \right) + i\,\,\displaystyle{1 \over {2\,}}( {Z_o\,Z + Y_o\,Y} ) \,\,\sin \,\left({\displaystyle{\theta \over 2}} \right)\,, \;$$

where θ is the hosting transmission line electrical length, Z ₀ and Y ₀ are the right-handed characteristic impedance and admittance, respectively. An example of dispersion diagram of D-CRLH transmission line is given in Fig. 1(a) where it demonstrates two passbands separated with a sharp stopband in between.

Fig. 1.

(a) The dispersion diagram of an unbalanced D-CRLH transmission line. (b) The equivalent circuit model for a general D-CRLH unit.

The equivalent circuit of the realized D-CRLH cell is shown in Fig. 1(b). In the equivalent circuit, the elements L_R, L_L, C_R, and C_L are representing the distributed loading elements of the hosting microstrip transmission line. To account for any patristic elements of the hosting transmission line that may exist, the elements (L_par and C_par) are introduced. Also, the inductor L_PC represents the series parasitic inductance of the employed distributed capacitor (C_L).

Following the above-discussed equivalent circuit then, the total equivalent series impedance Z, and shunt admittance Y are found to be as follows:

(2)$$Z = Z_1 + \displaystyle{{Z_2\,\,\,Z_3} \over {Z_2 + Z_3}}\,, \;\,Z_1 = j\omega L_{\,par}\,{\rm and}\,\,Z_2 = j\omega L_R\,{\rm and}\,\,Z_3 = j\omega L_{CP} + \displaystyle{1 \over {\,j\omega C_L}}\,\,, \;$$

(3)$$Y = Y_1 + Y_2\,\,{\rm and}\,Y_1 = j\omega C_{Par}\,{\rm and}\,Y_2 = \displaystyle{1 \over {\,j\omega L_L + 1/j\omega C_R}}.$$

To calculate the cut-off frequencies for the D-CRLH cell and assuming small hosting line length (θ→0), βd in equation (1) should have either π or zero. Then satisfying with equations (2) and (3), equation (1) will be

(4)$$\,\left({\,j\omega L_{Par} + \displaystyle{{\,j\,\omega \,L_R\,( {1-\,\omega^2\,L_{cp}\,C_L} ) } \over {( {1-\,\omega^2\,( {L_{cp} + L_R} ) \,C_L} ) \,}}} \right)\times \,\left({\displaystyle{{\,j\,\omega \,( {C_R + C_{\,par}} ) \,-j\,\omega^3\,C_{\,par}\,C_R\,L_L} \over {1-\omega^2\,L_LC_R}}} \right) = A, \;$$

where A is a constant = (−4) or (0) for βd = π or βd = 0, respectively. The condition βd = π yields the cut-off frequencies (f_{c 1} and f_{c 2}) whereas the condition, βd = 0, the lower (f_{c 0}) and upper cut-off frequency (f_{c 3}) and (f_{c 4}) in Fig. 1. For example, for βd = 0, the cut-off frequencies can be calculated as

(5a)$$Z = 0\,\Rightarrow \,\,f_{c 3}{\rm} = \displaystyle{ 1 \over { 2\,\pi }}\,\sqrt {\displaystyle{{L_R + L_{\,par}} \over {C_L\,( {L_RL_{CP} + L_{\,par}\,( {L_R + L_{CP}} ) } ) }}} \,, \;$$

(5b)$$Y{\rm} = {\rm 0\ }\Rightarrow \,\,f_{c 4}{\rm} = \displaystyle{ 1 \over { 2\,\pi }}\,\sqrt {\displaystyle{{1 + {{C_{\,par}} / {C_R}}} \over {C_{\,par}\,L_L}}} .$$

The characteristic impedance for the D-CRLH will be employed in the matching process as

(6)$$Z_{{\rm DCRLH}} = \sqrt {\displaystyle{{Z\,} \over Y}} = \sqrt {{{\left({\,j\omega L_{\,par} + \displaystyle{{\,j\,\omega \,L_R\,( {1-\,\omega^2\,L_{cp}\,C_L} ) } \over {( {1-\,\omega^2\,( {L_{cp} + L_R} ) \,C_L} ) \,}}} \right)} / {\,\left({\displaystyle{{\,j\,\omega \,( {C_R + C_{\,par}} ) \,-j\,\omega^3\,C_{\,par}\,C_R\,L_L} \over {1-\omega^2\,L_LC_R}}} \right)}}.} $$

From (6) it can be concluded that the D-CRLH TL does not have constant impedance over the propagation bands. The propagation constant profile in (1) is a non-linear function. Neglecting the effect of parasitic elements (L_par, L_PC, C_par), the definition for the propagation constant in equation (1) may be further simplified for a short length of hosting transmission line to be as in (7)

(7)$$\beta \,d = \omega \sqrt {\displaystyle{{L_RC_R} \over {( {1-\omega^2L_RC_L} ) \,( {1-\omega^2C_RL_L} ) }}} = n\,\pi , \;\,\,n = 0, \;\pm 1, \;\,\pm 2, \;..$$

Moreover, it is clear that the cut-off frequencies, characteristic impedance, and progressive phase shift are controlled by the values of the loading elements. This will be emphasized in the following sub-section.

Initial design

To meet the final proposal, filtering D-CRLH cell is designed to have passbands at 3 and 5.1 GHz with stopband between the two passbands, at 4.1–4.8 GHz. This is applied to design a dual-band self-filtering antenna serving WLAN applications. The equivalent circuit element values that fulfil the desired frequency bands are found to be; L_par = 1.2, L_PC = 2.335, L_L = 4.804, L_R = 2.0874 (all in nH), C_L = 0.2942, C_R = 0.1.2872, C_par = 0.8 (all in pF). The calculated equivalent circuit is simulated using ADS (Advanced Design System) with the results shown in Fig. 2.

Fig. 2.

Comparison between the equivalent circuit and EM simulation results for the transmission coefficient (S ₂₁) magnitude.

The designed equivalent cell elements are translated to 3D design. Rogers RO4350 substrate with 0.813 mm thickness is selected as a hosting material with coplanar waveguide (CPW) configuration for the cell. As shown in Fig. 3, the D-CRLH cell is realized with a parallel tank circuit formed with a six-finger interdigital capacitor and one series strip inductance. This is represented by the lumped elements L_R and C_L in Fig. 1(b). Similarly, the thin transmission line's length (L_{L_SH}) and width (W_{L_SH}) are connected to a parallel plate capacitor (L_p) on one side of the CPW grounds. It is worth noting that the green color denotes the metallic cell, while the grey color represents the substrate. This proposed geometry was suggested to achieve high gain for the antenna. These elements are corresponding to the lumped components C_R, and L_L in Fig. 1(b).

Fig. 3.

The realized 2D shape of the D-CRLH unit cell.

All equivalent elements are translated to 3D structures based on [Reference Simons and Simons44]. The realized 3D cell is shown in Fig. 3 with detailed dimensions shown in Table 1. The cell is simulated using CST simulation tool and the simulation results are compared to equivalent circuit simulation as in Fig. 2. As shown, there is a passband from around 2.6 to 3.7 GHz and from 4.9 to above 5.9 GHz. The two passbands are separated with a stopband with ranges from 4.1 to 4.8 GHz, insuring filtering specification of the cell. The EM simulation results are compared with the equivalent circuit simulation with a high agreement between them.

Table 1.

The detailed dimensions for the unit-cell

All design parameters are in mm.

To ensure the correct design steps, the phase of the transmission coefficient (S ₂₁) for both EM and circuit simulations is shown in Fig. 4(a). As shown, the deigned cell has −180 degree at 3 GHz and 180 degree at 5.1 GHz of the transmission coefficient phases for circuit simulations and EM simulations. Finally, the dispersion diagram of the designed filtering cell based on EM simulations is shown in Fig. 4(b). As shown, the dispersion diagram result agree with the magnitude and the phase results of the transmission coefficient as shown in Figs 3 and 4(a), respectively.

Fig. 4.

(a) Comparison between the equivalent circuit and EM simulation results for the phase of transmission coefficient. (b) The dispersion diagram of the proposed D-CRLH unit cell.

The dual-band D-CRLH antenna results

The simulated and measured reflection coefficients of the designed D-CRLH antenna are shown in Fig. 6. As noticed, the prototype exhibits dual-band resonances along with the stopband in-between the resonant bands. The simulated first band ranges from 2.8 to 3.2 GHz (fractional bandwidth of 13.33%) and has a center frequency at 3.0 GHz, at which the reflection coefficient is −22 dB. The measured one is wider and extends from 2.73 to 3.7 GHz (fractional bandwidth of 32.33%) with the center frequency at 3.0 GHz, at which the reflection coefficient is −44 dB.

Fig. 6.

The simulated and measured reflection coefficients of the dual-band D-CRLH antenna.

On the other hand, the simulated second band ranges from 4.9 to 5.2 GHz (fractional bandwidth of 6%) and has a center frequency at 5.1 GHz, at which the reflection coefficient is −11.4 dB. The measured one is slightly wider and extends from 4.9 to 5.4 GHz (fractional bandwidth of 9.8%) and has a center frequency at 5.1 GHz with the reflection coefficient of −16 dB. Hence, the simulated and measured results confirm the first and second band center frequencies at 3.0 and 5.1 GHz, respectively. Such discrepancies between the simulated and measured results may be claimed due to the fabrication resolution accuracy.

The stopband center frequency, possessing maximum isolation, occurs at 4.25 GHz, which is indicated by the fact that the reflection coefficient is almost 0 dB. Furthermore, the −3 dB bandwidth covers from 3.7 to 4.52 GHz.

Comparing the antenna size, at the two resonant frequencies, to a conventional patch antenna, it can be determined that the conventional patch antenna footprint is 62 × 48 mm² and 42.4 × 36.4 mm² at 3.0 and 5.1 GHz, respectively. Hence, the proposed antenna has a very small size which is only 17% at 3.0 GHz and 31% at 5.1 GHz when benchmarked against the conventional patch antenna.

The performance analysis of the designed antenna can be understood by demonstrating the surface current distribution at the resonant frequencies for the same current levels. These simulated results are plotted in Figs 7(a) and 7(b) at 3.0 and 5.1 GHz, respectively. It can be observed that the current is concentrated around the series branch than the shunt branch at 3.0 GHz. However, at 5.1 GHz, the current starts to increase and focus in the shunt branch in comparison to the series branch, as depicted in Figs 7(a) and 7(b), respectively. Furthermore, to confirm the good stopband in-between the two operating bands, the surface current distribution at 4.25 GHz is plotted in Fig. 8, for the same current levels as those in Fig. 7. It can be observed that the current, at the two resonators, follows a complete rotation cycle, which in radiation calculation cancel-out one other. The currents flow in opposite directions; thus, they result in a total bandstop filtering outcome. This observation confirms the almost 0 dB reflection coefficient, signifying total reflection, at that frequency, as was observed in Fig. 6.

Fig. 7.

The current distribution of the DCRLH antenna at (a) 3.0 GHz, (b) 5.1 GHz.

Fig. 8.

The current distribution of the D-CRLH antenna at 4.25 GHz, indicating no radiation due to cancellation of currents.

The antenna radiation properties

The radiation and filtering properties of the proposed antenna have been emphasized in two main steps. The first one is by depicting the maximum antenna realized gain and antenna total efficiency as a function of frequency, as shown in Figs 9 and 10, respectively. Moreover, tabulated in Table 2 are the simulated and measured realized gains and total efficiencies at the two resonant center frequencies and the stopband mid-frequency.

Fig. 9.

Comparison between simulated and measured realized gain of the D-CRLH antenna.

Fig. 10.

Comparison between simulated and measured total efficiency of the D-CRLH antenna.

Table 2.

The proposed D-CRLH antenna simulated and measured realized gain and total efficiency

Now, observing Fig. 9, it is evident that the simulated and measured realized gains highly agree, where the proposed antenna achieves good realized gain of 2 and 2.7 dB at 3.0 and 5.1 GHz, respectively, despite its highly compact size.

Moreover, the proposed antenna measured total efficiency agrees with the simulated one in the low resonant frequency, as portrayed in Fig. 10. However, there is a considerable discrepancy between both efficiency outcomes in the high resonant band.

It is worth to comment that the antenna reflection efficiency e_r = 10 log (1–|S ₁₁|²) can be calculated from Fig. 6 as follows. At 3 GHz, simulated S ₁₁ is −11 dB and hence e_r = 92% = −0.36 dB and at 5.1 GHz, S ₁₁ is −21 dB and hence e_r = 99% = −0.034 dB. Also, without considering the reflection efficiency, the simulated antenna gain values were 2.26 dB at 3 GHz and 3.2 dB at 5.1 GHz. So, this gain increase compensates the difference in reflection efficiency so that the realized gain and total efficiency are almost identical as in Figs 9 and 10, respectively.

In addition, to further justify the stopband at 4.25 GHz, the proposed antenna displayed very low gain and total efficiency values, whether simulated or measured. At 4.25 GHz, it exhibited simulated and measured realized gain values of −11 and −10 dB, respectively, as tabulated in Table 2, demonstrating no radiation. Furthermore, it exhibited simulated and measured total efficiency outcomes of 3.2 and 4.5%, respectively, as tabulated in Table 2.

Illustrated in Fig. 11 is the setup for measuring the proposed antenna normalized gain radiation pattern. Near-field measurements were conducted, where the StarLab Antenna Measurement – MVG was incorporated.

Fig. 11.

Setup for the D-CRLH antenna radiation pattern measurement.

Displayed in Fig. 12 are the normalized polar plots of the gain radiation pattern at both resonant frequencies in the principal planes, where the E-plane denotes the XZ-plane (∅ = 0°), while the H-plane describes the YZ-plane (∅ = 90°). As portrayed in Figs 12(a) and 12(c), the antenna exhibits the figure-of-eight gain radiation pattern at both resonant frequencies in the E-plane, with a high agreement between the simulated and measured polar plots. Similarly, demonstrated in Figs 12(b) and 12(d) are the isotropic gain radiation patterns at 3.0 and 5.1 GHz, respectively, where it is clear that the simulated and measured polar plots highly agree. Hence, the antenna displays the omni-directional radiation pattern type. Next, the 3D gain radiation patterns at 3.0 and 5.1 GHz are portrayed in Figs 13(a) and 13(b), respectively. It is observed that the two radiation patterns are almost typical and exhibit the conventional omni-directional pattern with the same null direction along the Y-axis. This is due to the current cancellation witnessed along the CPW-ground planes.

Fig. 12.

Comparison between the simulated and measured normalized gain radiation patterns, in polar formats, in the principal planes at: (a) 3.0 GHz (E-plane); (b) 3.0 GHz (H-plane); (c) 5.1 GHz (E-plane); (d) 5.1 GHz (H-plane).

Fig. 13.

The 3D gain radiation pattern of the D-CRLH antenna at (a) 3.0 GHz, (b) 5.1 GHz.

The proposed D-CRLH antenna is benchmarked against other dual-band antennas holding the self-isolation feature, as tabulated in Table 3. The aspects at which comparison was conducted included the antennas resonant frequencies, the antenna electrical size with respect to the free-space wavelength, the peak value of the reflection coefficient at the stopband center frequency, the realized gain, and the total efficiency. It can be seen that the proposed antenna is highly compact and competes with the other references in terms of size. Moreover, it displays a better out-of-band suppression than [Reference Khan and Mandal35], and almost the same as [Reference Dhwaj, Tian and Itoh34, Reference Hu, Pan, Wa and Zhang36, Reference Zhang, Zhang, Pan and Duan38], and [Reference Abdalla, El Atrash, El-Sobky and Zahran40]. Finally, despite its low profile, it exhibits a good realized gain and total efficiency at the two resonant frequencies. Hence, the proposed D-CRLH antenna could be nominated for wireless communication applications.

Table 3.

Comparison between the proposed D-CRLH antenna and dual-band self-filtering antennas