1 Introduction

Frequency scanning antenna (FSA) is used as an integral part of the low-cost beam scanning systems developed for different applications, such as imaging [1,2,3,4], radar [5, 6], and weather measurement [7]. Particularly, at millimeter-wave frequencies, the front-end cost contributes largely to the total system expenses [8], whereas beam scanning with frequency, eliminates the need of costly phase shifters and power combination network used in the conventional phased array systems. In many microwave imaging applications, for example concealed object detection, one of the key requirements is the symmetrical scanning of the object or space, which implies the coverage of broadside direction during beam-steering. Besides, to distinguish objects located in different distances from the antenna aperture, a large bandwidth is required to form a 3D image [9]. Furthermore, the cost and weight of such systems should be as low as possible for both portability and commercialization. Therefore, the main purpose of this work is to design a low-cost and broadband frequency scanning antenna with symmetrical beam scanning at Ka-band.

FSAs can be classified into two main categories, namely, antenna arrays [2, 7] and leaky-wave antennas (LWA) [10,11,12]. In array structures, a frequency-dependent phase shift is applied to each element to steer the main beam. As shown in Fig. 1a, this frequency-dependent phase shift is produced by the difference between the physical feed length (L) and elements spacing, denoted by (d). On the other hand, frequency scanning is an intrinsic characteristic of LWAs [13].

Fig. 1
figure 1

General structure of frequency scanning antennas. a Antenna array FSA. b Leaky-wave FSA

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Usually array-based FSAs cannot provide a wide scanning range [2, 7]. For instance, in [2], a Ku-band FSA array with meandering line feed and T-junction power dividers scans 35° using 3 GHz bandwidth. However, the radiation of feed lines and non-uniform power distribution in array elements lead to high side-lobe level (SLL) and low antenna gain. In [14], a four-layer slot array structure is implemented, in which meander lines on layers 2 and 3 feed the slots. Therefore, a low SLL is achieved with the price of increasing the fabrication cost and complexity.

In [10,11,12], and [15], LWAs are employed for beam-steering, using substrate integrated waveguide (SIW) structure. The scanning range in SIW-based FSAs depends on structure complexity rather than bandwidth; for example, 47° scanning range is reported in [10] by varying frequency from 10.2 to 11.7 GHz; however, it does not cover the broadside direction.

Recently, FSAs have been designed for frequencies near or above 100 GHz. Despite using a large bandwidth, the angular scanning range needs to be improved. For example, in [16], a dielectric grating antenna made of high-resistivity silicon is designed at 100 GHz. This structure has 84% radiation efficiency, while it scans 20° by varying frequency from 97 to 103 GHz.

In this paper, we propose a meandering microstrip structure with mitered corners as a frequency scanning antenna, which is low-cost, simple (printed on a single-layer substrate), via-less, and wideband. The proposed FSA covers a wide scanning range in comparison to the previous FSAs including broadside angle as well. This work is compared with different FSA structures in Table 2.

The rest of this paper is organized as follows. Section 2 describes the analysis of the proposed FSA structure. The role of design parameters in the proposed antenna performance is discussed in Section 3. The simulation and measurement results are presented in Section 4. Finally, concluding remarks are given in Section 5.

2 Proposed Antenna Structure

In this section, we study the general relations of the two FSA classes, and explain why conventional LWAs cannot cover the broadside. Next, we describe the proposed FSA structure and its radiation mechanism in details.

2.1 General FSA Structures Analysis

In a uniform linear array designed for frequency scanning, shown in Fig. 1a, the array factor is given by:

$$ AF = \sum\limits_{q = 0}^{N - 1} {{e^{jq\left( {{2\pi } \over \lambda } d \sin \theta - {\Delta} \varphi\right )}}}, \hspace{.2in} 0 \le \theta \le \pi , $$
(1)

where N is the number of elements, 𝜃 is the scanning angle, and λ is the free-space wavelength. The added phase shift, Δφ is defined as

$$ {\Delta} \varphi = \beta L = {{2\pi } \over {{\lambda_{g}}}}L = {{2\pi } \over {{v_{p}}}}Lf, $$
(2)

where, β is the propagation constant, λg is the guided wavelength in substrate, vp is the propagation velocity, and f is the frequency. Equation 2 shows that the phase difference (Δφ) changes with frequency, so does 𝜃, causes beam-steering.

In LWAs, the frequency scanning method is different. In a uniform LWA, steering angle is given by [11]:

$$ \theta = \sin^{- 1} {{{\lambda_{0}}} \over {{\lambda_{g}}}} =\sin^{- 1}\left( \sqrt {{\varepsilon_{r}} - {{\left( {c \over {2wf}}\right)}^{2}}} \right), $$
(3)

where εr is the dielectric constant, w is the width of the waveguide, and λ0 is the center wavelength.

Fig. 2
figure 2

Top: The exploded view of the proposed periodic FSA structure. Bottom: a detailed view of the unit cell with all design parameters

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For a periodic LWA, infinite number of harmonics can be excited. To get only one radiating harmonic, n = − 1 harmonic is chosen. The frequency scanning angle is given by [13]:

$$ \theta \approx {\sin^{- 1}}\left( {{{\beta_{- 1}}} \over {{k_{0}}}}\right), $$
(4)

In (4), β− 1 varies with frequency and provides beam scanning. Since 𝜃 cannot be zero in either (3) or (4), LWAs cannot cover the broadside direction by frequency scanning without solving this drawback. In the following, we introduce an FSA using an array structure with a wide scanning range, covering the broadside direction, and a relatively high scanning rate with frequency.

2.2 Antenna Structure

The 3D exploded view of the proposed structure for FSA, as well as a unit cell geometry, is shown in Fig. 2. The antenna consists of N cells with cell spacing d, and a uniform ground plane. Each cell consists of straight feed lines, and 3 microstrip sections with the total length denoted by L in including 4 bends. The whole FSA structure is similar to a distributed antenna array, where each cell plays the role of an element in the array. The antenna has two ports: input port used to excite the antenna, and termination, which is terminated to the matched (50Ω) load. This cell geometry has been used in microwave circuits for delay or phase generation or in antenna literature for polarization control [19] or collinear antenna arrays [20], but not as a radiating element of a frequency scanning antenna. For the sake of comparison, in [19], the antenna bandwidth is less than 5%, while it is over 30% in this work. Although the proposed structure looks like the Franklin-type antenna [20, 21], it follows a different design concept and purpose. The proposed antenna is designed for frequency scanning over a wide bandwidth with a symmetrical wide angular coverage, while the Franklin type antenna does not provide a wide bandwidth.

Fig. 3
figure 3

a 2D Amplitude and phase of the X and Y components of the near-E-field. b analysis of the main beam direction using near-field and far-field radiation

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2.3 Radiation Mechanism of the Proposed Antenna

It is well known that any discontinuity in a microstrip line causes radiation [22]. The proposed FSA is fundamentally an array formed by a series of bends in a line. Each mitered bend individually generates a diagonally polarized radiation. If these bends have a certain phase difference, they can form an array producing a constructive radiated field in a desired direction. Wood [23] explains the radiation from microstrip elements similar to the cell in Fig. 2, in terms of magnetic currents located at the edges of the line. With the quasi-TEM mode assumed in this structure, the sources along the vertical sections (L1) are oppositely directed and therefore, cancel each other out. But at each corner, there is an excess current along the outer edge, which acts as the dominant radiation source. Each source generates an electric field polarized diagonally [23]. Assuming the negligible attenuation of the wave along the line and the matched bends, the total radiated field from one cell in φ = 90° plane (YZ plane) is given by [19]:

$${E_{\varphi} }(\theta ) = A\cos \theta .exp\left[-j\left( \frac{L_{1} + L_{2}} {2}\right)\beta + j\left( \frac{u}{2}\right)\right]\sin \left( \frac{L_{1}}{2}\beta\right) $$
$$ \times \sin\left ({{{L_{1}} + {L_{2}}} \over 2}\beta - {u \over 2}\right). $$
(5)
$${E_{\theta} }(\theta ) = jA~exp\left[-j\left( \frac{L_{1} + L_{2}} {2}\right)\beta + j\left( \frac{u}{2}\right)\right]\sin \left( \frac{L_{1}}{2}\beta\right) $$
$$ \times \sin \left( {{{L_{1}} + {L_{2}}} \over 2}\beta - {u \over 2}\right), $$
(6)

where u = −k0d sin𝜃, and β and k0 denote the microstrip and free-space wave numbers, respectively. The coefficient A is determined by the traveling-wave amplitude, substrate dielectric constant, substrate thickness and line width.

Results of the near-field analysis of the unit cell is depicted in Fig. 3a, which shows that the Y component (Y is the arraying direction) of the E-field has a confined and uniform amplitude and phase, while the X component radiates randomly, considering its phase distribution, with a weaker amplitude. Thus, the Y component plays the main role in antenna radiation pattern and polarization. Figure 3b illustrates the extracted main beam direction of the array from dispersion diagram, which is generated from the near-field analysis of the E-field Y component.

Now, the total radiation pattern of the whole structure can be calculated by multiplying the radiation pattern of the E-fields in (5) and (6) by the array factor of a linear array AF(𝜃), given by [24]:

$$ AF(\theta ) = \frac{\sin \left[\frac{N}{2}(\beta d sin\theta -{\Delta} \varphi )\right]} {\sin\left[\frac{1}{2} (\beta d sin\theta -{\Delta} \varphi )\right]}. $$
(7)

3 Antenna Design Parameters Variation

In this section, the effect of design parameters variation on FSA performance is discussed briefly, using EM simulation. The simulation results in this paper are achieved for a 6.6 mil substrate with εr = 3.66 and tanδ = 3.7 × 10− 3 at Ka-band. The proposed FSA unit cell has six design parameters defined in Fig. 2, and Table 1, which are studied in this section.

Table 1 Design parameters of the proposed antenna
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3.1 Number of Cells

As the number of cells, N, increases, the beamwidth narrows and the antenna gain increases, as depicted in Fig. 4 (for f = 32 GHz and the given values in Table 1). For large N, delivered power to the last cells would be low, preventing the antenna gain from increasing considerably as N further increases. In the following simulations, number of ce lls is fixed at 10, corresponding to 9 dBi gain at 32 GHz.

Fig. 4
figure 4

Antenna beamwidth and realized gain versus the number of cells (N)

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Fig. 5
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a 2D beam-steering with frequency scanning for the proposed FSA with N = 10, simulated in MATLAB. b Broadside 3D radiation pattern at 32 GHz, simulated in HFSS

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3.2 Feed Length

By changing the feed length, L, the range of scanning angle varies with frequency. To point the beam to the broadside direction at the center frequency, which implies symmetrical beam scanning, L must be an integer multiple of the guided wavelength (λg0):

$$ L =n{\lambda_{g0}}, \hspace{.2in} n \in {N} $$
(8)

Choosing n = 2 is a safe option to balance the beam scanning range and antenna gain. If center frequency is selected to be 32 GHz (λg0 = 5.35 mm), the physical feed length will be L = 10.7 mm for n = 2. The steered 2D radiation patterns for this design calculated from (5)–(7) are depicted in Fig. 5a, for f = 29, 32, and 35 GHz. Figure 5b illustrates the 3D fan-beam pattern in antenna coordinates at the center frequency, corresponding to the broadside direction.

3.3 Cell Geometry

The cell spacing parameter, d, is selected to avoid grating lobes at the highest frequency of operation. When d is determined, the parameters L1 and L2 can be calculated consequently. The parameter L1 can be found considering that in Fig. 2, L − d = 2L1. For example, for d = 0.45λ0

$$ {L_{1}} = {\lambda_{g0}} - 0.225{\lambda_{0}} $$
(9)

The horizontal section length, L2, is calculated from d and line width value, w1. The parameter w1 is usually designed for 50 Ω impedance to match the excitation source. The horizontal section width, w2, controls the radiation of cells.

The best value for L2 is the one which results in the best impedance matching (S11). In Fig. 6, the effect of L2 variation on FSA impedance bandwidth is studied for the design parameters fixed at L1 = 2.82mm, w1 = 0.34mm, w2 = 0.43mm, N = 10 and m = 0.27mm. We can conclude that for some middle values of L2, such as L2 = 1.2, or 1.3 mm the best impedance matching can be obtained. Parameter L2 does not affect the scanning range of the antenna.

As the derived design formulas for the proposed FSA are general, if the substrate and its thickness are selected properly, the design procedure could be extended to any frequency with any reference impedance.

Fig. 6
figure 6

Reflection coefficient of the proposed FSA for different vlaues of L2

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4 Simulated and Measured Results

This section describes the simulation and measured results for the fabricated FSA at Ka-band. A complete comparison of the results of this work and the aforementioned FSAs are done in the Table 2.

Table 2 Comparison of this work with similar frequency scanning antennas
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4.1 Final FSA Geometry

The proposed FSA layout was designed and optimized for the maximum bandwidth and scanning range with reasonable gain using a 6.6 mil RO4350B substrate (εr = 3.66). The center frequency was set to 32 GHz, corresponding to a guided wavelength (λg0) of 5.35mm. To point the main beam to the broadside at 32 GHz, n was selected to be 2, and L was fixed at 10.7mm. Table 1 summarizes the final FSA parameters.

The top and side views of the fabricated FSA are shown in Fig. 7a, and b, respectively. The input port of the fabricated antenna is connected to an end-launch connector (Southwest, 1093-02A-5), and the output port is terminated to a 50-Ω matched load (Pasternack, PE6085) using the same connector. The size of connector and matched load are shown in Fig. 7b. The net antenna size, including 10 cells, is 45.2 mm. To assemble connectors, the 50-Ω feed line is extended by 7.4 mm from each side, thus the antenna board length is 60 mm. Moreover, the width of the feed line is tapered from 0.34 to 0.18mm to provide better matching to the launch-pin of the connector with 0.17-mm diameter. The antenna board width is 23 mm. Since the antenna board thickness is only 170 μm, the antenna ground plane is mounted on an aluminum carrier to avoid board warpage.

Fig. 7
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Fabricated antenna. a Top view. b Side view

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Fig. 8
figure 8

Comparison of simulated and measured S11 and S21 over the Ka-band

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Fig. 9
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Normalized simulated and measured radiation patterns at a 27.5 GHz, b 29 GHz, c 30.5 GHz, d 32 GHz, e 33.25 GHz, f 34.5 GHz, g 36.5 GHz, and h measurement setup

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4.2 Impedance Bandwidth

Figure 8 displays the simulated and measured reflection coefficients (S11) of the designed FSA from 26 to 40 GHz. Achieving such a high bandwidth is a result of the design techniques used in this work. For example, the structure is designed based on a matched 50-Ω line and the bends are optimized to be perfectly matched to remove the main source of the reflections.The measured S11 is in very good agreement with simulation, indicating that the designed FSA is properly matched from 28 to 40 GHz. The slight mismatch in the measured results from 26 to 27 GHz is due to the practical frequency limits of the connector and matched load, which are designed for Ka-band, while Ka-band starts from 26.5 GHz. The best agreement between the measured and simulated impedance matching is observed at 32 GHz, which is the center frequency of this design. The measured and simulated (S21) are also plotted in Fig. 8, and show that about -6 dB of the input power is absorbed by the matched load at 32 GHz. The amount of absorbed power decreases as the the number of elements increases, since a larger amount of the input power is radiated.

The antenna radiation patterns in E-plane or YZ-plane in Fig. 5b were measured at seven frequencies. The simulated and measured radiation patterns are illustrated in Fig. 9a–g, corresponding to 27.5 GHz, 29 GHz, 30.5 GHz, 32 GHz, 33.25 GHz, 34.5 GHz, and 36.5 GHz, respectively. The measurement setup is shown in Fig. 9h. For this frequency range, the main beam scans from − 52° to 42°. It is shown in Fig. 9d that the beam corresponding to 32 GHz frequency points to the broadside angle, exactly as we expected in the FSA design. The measured half-power beamwidth decreases from 18 to 11° versus frequency. The maximum beam-pointing error is less than 2°, which is within the measurement error. Due to the presence of bulky connectors and matched load shown in Fig. 7, the measured SLL is degraded in comparison with the simulation value of −10 dB, particularly at 33.25 GHz and 34.5 GHz.

Finally, Fig. 10 compares the measured and simulated radiation patterns in H-plane or XZ-plane at the center frequency of 32 GHz. The measured backlobe radiation is 20 dB below the mainlobe level.

Fig. 10
figure 10

Measured and simulated H-plane radiation patterns at 32 GHz

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After examining the proposed antenna, it is proved that the antenna with a low-cost structure has capability of wide beam-steering and covering the broadside, while in [14] the complicated structure used for covering the broadside and in [10] a large beam-steering was reported without covering the broadside.

4.3 Gain

The measured gain and simulated realized gains are compared in Fig. 11. The radiated gain is measured at seven frequencies, i.e., 27.5 GHz, 29 GHz, 30.5 GHz, 32 GHz, 33.25 GHz, 34.5 GHz, and 36.5 GHz. At each frequency, first we search for the gain direction, which is found with ± 1° error limited by the measurement setup precision. Figure 11 shows a very good agreement between the simulated realized gain and measured gain. The measured gain increases from 3.8 dBi at 27.5 GHz to 10.8 dBi at 36.5 GHz. The difference between simulation and measured results is less than 1 dB, which is due to extra losses of the connectors and matched load, and metal surface roughness, as well as the impedance mismatch shown in Fig. 8. The minimum difference is obtained at 32 GHz (only 0.43 dB), where the best agreement between the simulated and measured reflection coefficients is observed.

Fig. 11
figure 11

Measured and simulated gain versus frequency

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The simulated radiation efficiency of this antenna, extracted from HFSS varies from 55 to 70% over the designed FSA bandwidth.

5 Conclusion

In this paper, the design steps of a compact, low-cost, and wideband frequency scanning antenna is presented, which scans a wide angular range. The proposed structure consists of periodic meandered microstrip lines with mitered corners without requiring via-interconnections, or a multi-layer feed network. Hence, it is suitable for applications where cost or weight matters.

A sample of this structure designed for covering the Ka-band is fabricated and successfully measured. It is shown that the proposed FSA is able to scan a large angular range of 94° around broadside direction. The measured results are in very good agreement with simulation, showing over 12 GHz of impedance bandwidth and an average gain of 7.5 dBi. The beam-pointing error between design and measured values is less than 2°. The proposed structure can be easily scaled to design antennas with the desired gain or beamwidth, for different applications such as low-cost millimeter-wave imaging.