Wide-Angle Frequency-Scanning Array Antenna Using Dual-Layer Finger Connected Interdigital Capacitor Based CRLH Unit Cell

In this paper, a wide-angle frequency-scanning array antenna is presented for three-dimensional (3D) radar. Initially, a modified composite right/left-handed (CRLH) unit cell based on a dual-layer finger-connected interdigital capacitor (FCIDC) is analyzed. Compared with its conventional counterpart, the proposed unit cell eliminates the undesired high-order resonances and has a lower right/left-handed passband. Then, a broadband frequency-scanning feeding network, which has a large scanning angle, is designed using the proposed CRLH unit cell. The responses of the four output ports indicate that the network can offer desired amplitude and phase difference to scan towards both negative and positive elevation angles. To validate its performance, a tightly coupled planar quasi-Yagi antenna array is fed to synthesize an array antenna. The measured results show that the designed array antenna has an impedance bandwidth ( $\vert \text{S}_{11}\vert < -10$ dB) of 118.7% (2.55–10 GHz) and gains larger than 5dBi in the bulk of the band. Besides, the radiated beam can scan from −47° to 46° continuously when the frequency ranges from 3GHz to 9GHz.


I. INTRODUCTION
Frequency-scanning antenna array presents its good potential in three-dimensional (3D) radar, because of its many advantages such as low cost, stable operation and large scanning beam angles. In recent years, it has been studied extensively because the radiated directions of the antenna array vary with the frequencies. Leaky-wave antenna (LWA) is a general type of frequency beam scanning antennas [1]. It consists of a travelling wave structure that radiates power along its length gradually. It can be described by two parameters including a phase constant and a leakage factor.
Until now, many techniques have been used for LWAs design. Microstrip technique is an initial method in leakywave antenna design. In [2], a microstrip-based backfire planar LWA, which exhibits high radiation efficiency and low cross-pol level, is presented. Recently, spoof surface plasmon polaritons transmission lines (SSPPs-TLs) have been a good The associate editor coordinating the review of this manuscript and approving it for publication was Yasar Amin . choice to design LWAs. In [3] and [4], SSPPs-TLs have been used as guiding-wave structures for broad scanningangle LWAs. Besides, substrate integrated waveguide (SIW) technology can also be applied in the design of LWAs. In [5], a new class of SIW-based LWAs, which can scan the beam continuously from backward to forward direction, is proposed to overcome the open stopband problem of unidirectional periodic LWAs to scan the beam through the broadside direction. And a dual-band SIW slotted LWA is presented in [6]. It is composed of two back-to-back quasi-uniform slotted SIW arrays fed by a stirp line. In [7], a dual-band and dual-polarized leaky-wave antenna excited by slotted SIW has been proposed. It achieves beam scanning from +107 • to +167 • at the lower band and from −41 • to −114 • at the higher one. In [8], a broadband frequency scanning antenna with considerable gain is synthesized using TE220 mode in SIW technology. Eighth-mode SIW also presents good performance in LWA design and a high gain wide full space scanning LWA with improved broadside radiation profile has been presented in [9]. Additionally, metasurfaces have been used to design LWAs [10]- [13]. In [10] and [11], a novel concept of a leaky-wave antenna is proposed using the Huygens' metasurfaces. With the appearance of CRLH-metamaterial, the LWAs can realize a new function of generating alterable patterns in different frequencies [14]- [17]. Creatively, an LWA, which can provide beam scanning from backfire to endfire, has been designed using CRLH-metamaterial in [14] firstly. Balanced CRLH-TLs are good choice to design broadside radiation without stop band between the left-handed (LH) region and the right one. And then, a LWA with minimized sidelobe levels is designed in [15]. In [16], a wide-area innovative beam-scanning LWA for millimetre-wave applications is designed based on CRLH-metamaterial. Although these antennas present good performances in leaky wave, the radiated type is determined when the structure is fixed. And these LWAs have an inherent disadvantage of low radiation efficiency.
Using the CRLH-TLs to design a feeding network provides a new method for frequency-scanning phased-array. In this way, the frequency-scanning functionality can be achieved rather than the antenna design. As a result, the antenna element can be chosen randomly and radiation property can be designed independently. The existence of CRLH-TLs feeding network results in less influence on radiation performance. However, few frequency-scanning phased-arrays using this method have been reported. As reported in [18], a feeding network, which operates in dual-band, has been designed using CRLH-TLs pioneering. And in [19], two frequencyscanning phased-arrays separately with equal and unequal amplitude output ports have been synthesized utilizing CRLH dispersive TLs. But all of them are fabricated complexly because the lumped elements have been used. In [20], a frequency-scanning feeding network, which has a large scanning angle ranging towards both negative and positive elevation angles in wide band, has been synthesized. However, the etched slot in ground results in difficulty of encapsulation. In [21], a planar 2-D antenna array, which can be used for radar or imaging applications with the appropriate transmit/receive circuitry, is designed using CRLH-TLs for series feeding network. But it can only operate in narrow band.
In this paper, a novel dual-layer performance-enhanced CRLH unit cell based on finger-connected (FC) technology is proposed previously. The proposed CRLH unit cell has a wide band due to the elimination of the spurious spikes and realizes a degree of miniaturization. And then, a frequencyscanning phased-array feeding network with low insertion loss and less phase difference is synthesized by combining conventional microstrip lines, modified CRLH lines and power dividers. To validate the properties of the new proposed feeding network, a tightly coupled quasi-Yagi antenna array is fed by the network. Both numerical and experimental results exhibit that the antenna array has a wide bandwidth of 2.55-10GHz and gains larger than 5dBi in the bulk of the band. Additionally, the scanning angle of the antenna is from −47 • to 46 • between 3 GHz and 9 GHz. The designed array can be used in wideband radar systems that require a large scanning angle range.

II. MODIFIED CRLH UNIT CELL
According to [22], the spurious spikes can be eliminated when the fingers of the IDC on the open end at the same port are connected. And a CRLH unit cell with wide operating frequency range has been designed using wire bonded IDC because the spurious spikes are eliminated. However, the wire bonded technology is difficult to fabricate. To tackle this problem, a new method is proposed in this paper. Fig. 1 shows the layout of the proposed dual-layer CRLH unit cell based on FCIDC. Unlike the CRLH unit cell in [23], the proposed one has metallic via holes at the open ends of all capacitor fingers. Two rectangular microstrip structures on the middle layer provide two patches to connect those via holes of the alternate fingers at the same port. The specific dimensions of the proposed CRLH unit cell are given as follows: w 0 = 2.8mm, Here, substrates with a dielectric constant of 2.65 and a loss tangent of 0.001 have been used. Fig. 2 (a) presents the lumped equivalent circuit model of the IDC-based CRLH unit cell. A finger can be represented by a series inductance L i (i = 1, 2. . . , 6) and a shunt capacitance. In this model, the shunt capacitances are not shown for the sake of clarity. The capacitive coupling is modeled by the capacitances C mn , where m and n are the finger numbers. As reported in [24], the inductive coupling can be ignored in a first approximation. The shunt stubs are represented by the shunt resonant circuits composed of L 0 and C 0 . Fig. 2 (b) shows the circuit model of the FCIDC-based CRLH unit cells. The application of microstrip patches can make a new  arrangement of lumped elements in conventional IDC. In this circuit model, the rectangular slot rings on the ground provide the capacitances C p and the via holes at the open ends of the capacitor fingers provide the inductances L p . It can be seen that the circuit model in Fig. 2 (b) has fewer series resonant branches than that in Fig. 2 (a), which reveals that the new CRLH-TL has fewer spurious spikes. According to these two comparable circuit models, the improved mechanism is illustrated clearly when the patches are used to connect the fingers at the same port. Here, it should be pointed out that the common dimensions of the CRLH unit cells based on the FCIDC and the conventional IDC are the same.   Fig. 3, it can be observed that the IDC-based CRLH unit cell has four spurious spikes at 5.1 GHz, 6.8 GHz, 8.65GHz and 9.8 GHz respectively, which prevents the IDC from being used beyond 5.1 GHz. Conversely, the spurious spikes are eliminated when the fingers of IDC at the same port are connected. As a result, the FCIDC-based CRLH unit cell obtains a wide operating band. Besides, the lower frequency of the pass band is smaller than that of its conventional counterpart, which indicates that the proposed CRLH unit cell has an advantage of miniaturization.
In order to explain the mechanism of the miniaturization clearly, a classical lumped equivalent circuit model in Fig. 4 is used. The model in Fig. 2 is too complex to explain the phenomenon and a simple one is more effective, but the spurious spikes are not considered in this model. The model consists of a series LC tanks and two parallel LC tanks. The parallel LC tanks, which are composed of L L and C R , represent the shunt grounded stub in Fig.1. And the series LC tank, which is composed of L R and C L , represents the FCIDC. C L and L R are the total series capacitance and total series inductance of the unit cells, and L L and C R are separated from the total shunt capacitance and inductance.
Based on the classical circuit theory in [24], the values of the lumped elements can be calculated roughly. Then, through putting them as initial values and using the above S-parameters as optimization objectives, the final values of the lumped elements can be extracted using the Optimization Dialog Box in Serenade.
The extracted values of these elements for IDC-based CRLH unit cell are: And the extracted values of these elements for the CRLH unit cell based on the FCIDC are: From the extracted results of IDC-and FCIDC-based CRLH unit cells, we can know that larger series inductance L R , series capacitance C L and shunt capacitance C R can be obtained when the FCIDC is used. The via holes at the open ends of the capacitor fingers provide extra inductances L p for L R , and the patches on the ground provide additional capacitances C p for C R .
The new arrangement of C mn results in a larger C L because all C mn of the IDC make contribution to them. Besides, the patches enhance the mutual coupling of the fingers, which can increase the values of C mn . As a result, a larger C L can be obtained. The left/right-handed pass band can be calculated as [25]: where, According to Eqs. (1) and (2), the operating LH and RH pass bands are shifted downward because the application of FCIDC provides larger L R , C L and C R . This indicates that the CRLH unit cell based on the FCIDC can realize a degree of miniaturization.   5 presents the dispersion curves of IDC-and FCIDCbased CRLH unit cells by full-wave simulation and equivalent circuit model. It can be observed that the FCIDC-based CRLH unit cell has a lower LH pass band. The spurious spikes of the conventional IDC-based CRLH unit cell are not achieved in its circuit model, because the circuit model just provides an approximate solution and some of parasitic elements are ignored for the sake of simplicity. The CRLH can provide phase advance and phase delay in LH band and RH band, simultaneously.
The FCIDC-based CRLH unit cell has a wider operating bandwidth, because the spurious spikes of its conventional counterpart are eliminated using the proposed method. Additionally, it has a smaller electric size compared with the conventional one, because the new cell has a lower LH pass band. As a result, the novel CRLH unit cell can be applied to design devices with a wider phase response and small size.
Based on expressions (3), (4), (5) and (6), the following relations for the frequency-scanning feeding network can be obtained Combining the expressions (7), (8) and (9), the relation between the normalization incident wave voltages a i and normalization reflection wave voltages b i of the frequencyscanning feeding network can be achieved. Consequently, the S-parameters of the frequency-scanning feeding network can be expressed as (10), shown at the bottom of this page.
Based on (10), the amplitudes of the four output ports of the network are the same and the phase responses of output ports from 1, 2, 3 and 4 are 2ϕ 1 (f ), ϕ 1 (f ) + ϕ 2 (f ), 2ϕ 2 (f ) and ϕ 2 (f )+ϕ 3 (f ). So, the phase differences of the adjacent output ports can be calculated as To design a proper network, two conditions should be satisfied. On one hand, the phase differences of the adjacent output ports should be equal at arbitrary frequency. Namely, ϕ 1 (f ) = ϕ 2 (f ) = ϕ 3 (f ). On the other hand, the phase differences should be continuous. Fig. 7 illustrates the ideal phase relations between the phase shifts TLs. According to Fig. 7, it is required that ϕ 2 (f ) = ϕ 3 (f ). It can be also seen that the phase differences toward from negative to positive as frequency shifts away from ω 0 . Extra, the frequency-scanning feeding network designed in this method can reduce the number of TLs effectively. Fig. 8 illustrates the beam direction with variable phase difference. In this figure, d is the distance of adjacent elements and θ is the beam angle. The phase difference is a function of the frequency f i . MM' and PP' are the equal phase surfaces as the beam angle are θ and −θ, respectively. Assuming that the beam angle is θ at f 1 , and the beam angle is −θ at f 2 . For an antenna array designing, the coupling between the antenna elements and the grating lobe should be considered comprehensively [27]. Generally, the grating lobe is more crucial. On the basis of [28], the maximum inter-element spacing is set as

B. CRLH TLs
c is velocity of light. The phase difference at random frequency can be calculated as For phase shift lines design, three factors of antenna array including the bandwidth, the scale of beam angle and the element spacing should be taken into consideration. In this paper, the feeding network is designed to scan from −45 • to 45 • as f 1 = 3GHz and f 2 = 9GHz. Using expression (11), it can be calculated that the value of d max should be less than 19.53 mm to avoid grating lobe. So, the distance is chosen as 19.5 mm. Substituting this value into (12), ϕ(f 1 ) = 49.64 • and ϕ(f 2 ) = −148.92 • . Here, the values of the lumped elements should satisfy the equations in (13).

C. WIDEBAND WILKINSON POWER DIVIDER
A wideband power divider, whose topology is shown in Fig. 12, is designed for frequency-scanning network. Here, multi-section impedance converter is used to enhance the operating band, as the reflected wave arising from single section can be offset by other sections. The dimensions of the power divider are: w 0 = 2.8mm, w 10 = 1.3mm, l 10 = 5.5mm, w 20 = 1.3mm, l 20 = 0.7mm, w 30 = 2mm, l 30 = 5.1mm, w 40 = 1mm, l 40 = 1.5mm, l 50 = 1.5mm, d = 4.3mm. R 1 and R 2 are isolation resistances. Their values are 100 and 200 , respectively. Fig. 13 shows the simulated S-parameters of the designed power divider. It exhibits a −15 dB reflection coefficient  (|S 11 |) ranging from 2.96 to 10.68GHz and its transmission coefficients (|S 21 |, |S 31 |) present a variation of 0.03dB. Additionally, the isolation between two output ports is larger than 15dB. All results indicate that this divider can be used for wideband system.
According to the sketch map in Fig. 6, a frequency scanning feeding network, which is composed of two conventional TLs, four FCIDC-based CRLH TLs and three wideband Wilkinson power dividers, is synthesized. Among four CRLH TLs, three of them are TL2 and one of them is TL3.   It can be observed that the transmission coefficients of synthesized network are 7.5±1.5dB and the reflection coefficients are less than −13dB from 3 GHz to 9 GHz. Besides, the isolations of the output ports are less than −15dB in this band. Fig. 15 shows the phase differences of the adjacent output ports. The phase differences of adjacent output ports (P i −P i−1 , i = 2, 3, 4) are 0 • at 4.7 GHz. At 3 GHz, the phase differences are 48.6 • , 50.2 • , 52.1 • for P 2 −P 1 , P 3 −P 2 , P 4 −P 3 . And at 9 GHz, the phase differences are -149.81 • , -147.92 • , -152.12 • for P 2 −P 1 , P 3 −P 2 , P 4 −P 3 . The magnitude and phase responses are suitable for the index of the target frequencyscanning phased-array feeding network.

IV. TIGHTLY COUPLED PLANAR QUASI-YAGI ANTENNA ARRAY
Quasi-Yagi antenna, which has advantages of excellent linearly polarization, small occupied size and wide band, provides a good choice for the wideband frequency-scanning VOLUME 9, 2021 operation. Recently, tightly coupled planar quasi-Yagi antenna has been extensively studied for phased array, because large scanning angle in wideband can be realized by using this technique. Fig. 16 presents the topology of the quasi-Yagi antenna element. Due to the intrinsic characteristic of the slot line to microstrip transition, the out-of-phase power division is realized in wideband frequency. The dimensions of the structure are: w 0a = 59.5mm, l 0a = 61.75mm, w 1a = 2.8mm, l 1a = 12.2mm, l 11a = 8.05mm, l 12a = 8.8mm, w 2a = 1.7mm, l 2a = 3.15mm, l 21a = 1.7mm, w 3a = 1.1mm, l 3a = 1.5mm, w 4a = 0.6mm, l 4a = 1.5mm, r 1 = 3.2mm, r 2 = 2.5mm, l 5a = 7.5mm, l 6a = 7.6mm, g 1a = 1.2mm, g 2a = 4mm, g 3a = 2mm, w 5a = 2mm, w 6a = 4.2mm, w 7a = 7.1mm, l 7a = 18mm, w 8a = 1mm, l 8a = 8mm, g 4a = 2.3mm and θ = 160 • . Fig. 17 presents the planar quasi-Yagi antenna array. This array is composed of four elements and the arms of these elements are connected directly. The distance between the adjacent elements is 19.5 mm for matching the design principle in Section III. Fig. 18 illustrates the active voltage standing wave ratio (VSWR) of the antenna array. It can be seen that the VSWRs are less than 1.75 from 2.9 GHz to 9 GHz. The results indicate that the designed array has good impedance matching at every port. Fig. 19 depicts the simulated E-plane and H-plane at 3.5 GHz, 5.5GHz and 7.5GHz. The antenna has front-toback ratio larger than 13 dB for practical applications and has cross-polarization lower than −17.5dB. Besides, the first side lobe becomes large with the increase of frequency. The consistency of these radiation patterns indicates that the designed antenna array can be used for wideband operation.

V. SYNTHESIS OF FREQUENCY-SCANNING PHASED-ARRAY
By feeding the tightly coupled planar quasi-Yagi antenna array using the designed frequency-scanning feeding network, a frequency-scanning phased-array is simulated, fabricated and measured. Fig. 20 illustrates two photographs of the fabricated wideband frequency scanning feeding network. Fig. 20(a) is its front view and Fig. 20(b) is its back view. The frequency-scanning phased-array was tested by an Anritsu ME7808A network analyzer and a far field measurement system in an anechoic chamber. Fig. 21 presents the simulated and measured S-parameters of the frequency-scanning phased-array. The measured result  shows that the reflection coefficient of the antenna array is smaller than −10dB ranging from 2.55GHz to 10GHz, which matches well with the simulated one. Fig. 22 plots the simulated and measured E-plane scanning radiation patterns. All the results show good performances 35964 VOLUME 9, 2021  with the scan angles that agree well with the designed destinations. The measured main beam angles are −47 • to 46 • between 3GHz and 9GHz, and the corresponding simulated angles are −45 • to 45 • . In detail, the directions of the main beam angles are −47 • , −31 • , −14 • , 0 • , 16 • , 29 • and 46 • for 3GHz, 3.15GHz, 3.7GHz, 4.71GHz, 6.2GHz, 8.1GHz and 9GHz. Although the deviations exist between the simulated results and the measured ones, the fabricated array achieves elevation scanning angles towards both negative and positive.
The far field of an antenna array is equal to the product of the field of a single element, at a selected reference point, and the array factor of this array. In this paper, the antenna array is composed of four uniform quasi-Yagi antenna elements linearly. Generally, the wavelength varies with the frequency. For a single element, the physical sizes are fit and varying quantities of half wavelengths are distributed in different frequencies. If the number of half wavelength is smaller than 1, the currents of the element are in phase. In this case, the efficient currents increase significantly with frequency, which results in the far field stacking in phase. So, the directivity enhances and the half power beam width (HPBW) becomes narrow. If the number of half wavelength is larger than 1, part of the currents is out of phase, and energy in certain directions is cancelled. As a result, the pattern nulls generate and side lobes appear. The number of half wavelength has an important influence on the number of side lobes. For a linear array with n uniform elements, its array factor f a (θ) can be expressed as |f a (θ )| = sin n 2 (kd cos θ + ξ ) sin 1 2 (kd cos θ + ξ ) VOLUME 9, 2021  Here, k is the wave number, d is the element spacing and ξ is the phase excitation difference. kdcosθ is the wave path difference in the direction of θ. In this design, ξ elevates towards both negative and positive. From the expression, it can be obtained that n-2 side lobes appear and one main beam generates. Based on the above analysis, it can be obtained that the HPBW becomes narrow and more side lobes appear with the increase of frequency. Fig. 23 presents the simulated and measured gains of the frequency-scanning phased-array. It can be seen that the measured gains are lower than those of simulated ones in the same frequencies, and they are also lower than gains of the tightly coupled antenna array without feeding network.
To validate the advancement of this design, Table 1 presents the comparison between this work and other publications. It can be seen that this design has a wide band and a large scanning angle, which indicates that it can be used in those systems requiring wide scanning angle in wide band. Although the dual-layer technique is used, it can be manufactured by adopting the method of onetime forming technique. So, it can avoid the artificial error introduced by the methods of lumped loaded. Besides, it can avoid the encapsulation difficulty of defected ground structure (DGS).
The reasons of scanning angles deviation and gain decreasing can be concluded as: (1) The insertion loss of the feeding network becomes large with the frequency increasing (as shown in Fig. 14(a)). (2) The phase inconsistency of the feeding network results in the phenomenon that the radiation of the antenna elements can't be realized in-phase stack. (3) The loss of the substrate and the assembly error also can cause the amplitude/phase error.

VI. CONCLUSION
In this paper, a frequency-scanning feeding network is designed, fabricated and measured. Initially, a novel FCIDC, which can realize wide operating band and miniaturization, is proposed. The equivalent circuit model and the dispersion curves are auxiliary instructions to explain the enhanced performances of FCIDC CRLH unit cell. And then, topology of the scanning feeding network is given and its working principle is presented. Based on the topology, a wide band frequency-scanning feeding network is synthesized by CRLH TLs and wideband Wilkinson power dividers. For frequencyscanning phased-array, a tightly coupled antenna array is adopted. Finally, a phased array, which achieves elevation plane scanning towards both negative and positive, is fabricated and measured. The results indicate that the frequencyscanning feeding network has wide scanning angles in wide band. The low profile of microstrip design makes the antenna array have a good potential in conformal requirements.

ACKNOWLEDGMENT
(Bin-Feng Zong and Hui-Yong Zeng contributed equally to this work.)