Spaceborne synthetic aperture radar (SAR) that uses satellites and other space vehicles as the movement platform has all-day, all-weather and global observation capabilities. It has important application prospects in national defense and military, ocean observation, terrain mapping, crop yield estimation, disaster prevention and mitigation, etc., and has become an indispensable means of earth observation. Phased array antenna is an important and widely-used part of the spaceborne SAR system, and its technology level largely determines the performance of the radar.

One of the important directions in the development of spaceborne SAR is ultra-high resolution, which requires phased array antennas with a large aperture, a large bandwidth and a large scan angle capability. In the case of a large signal bandwidth and a large scan angle, the phased array antenna will have aperture crossing and beam dispersion problems, which will cause directional map distortion and deterioration of the imaging quality. The main method to mitigate the aforementioned problems is to use the broadband true time delay line (TTDL) in conjunction with a phase shifter. The main methods of broadband TTDL implementation are: optical delay line^[1], acoustic delay line^[2], and electrical delay line.

The optical delay line has a low loss, a wide bandwidth, and a high interference immunity, however, the optical device structure is complex and requires additional photoelectric conversion devices, which poses difficulty in the miniaturization process. Acoustic delay lines have high delay efficiency, high accuracy, no dispersion, and good stability, but they suffer from a significant loss in the microwave band and require additional acoustoelectric conversion devices, which also hampers miniaturization. Electrical delay lines have a variety of implementation options, which can meet the requirements of a large delay, a large bandwidth and miniaturization.

In recent years, research work relating to electrical delay lines with large bandwidths, large delays, low error and miniaturization has been carried out. In Ref. [3], the microstrip line is bent to form a meander line (MDL), which is 2.4 times longer than the length of the microstrip line and has a delay multiplier of 3.6 times in X-band. However, the MDL inevitably generates interline coupling problems, which cause a large delay fluctuation of 16.6 %. A left-handed (LH) material transmission line method was proposed by Caloz and Itoh^[4]. The method used interdigital capacitors and stub inductors to form a LH transmission line, which is proved to have delay characteristics with a relative bandwidth of 100 %. However, this structure is still immature and has limitations, showing a return loss of -10 dB and large delay fluctuations.

Uchimura et al.^[5] proposed the substrate integrated waveguide (SIW) structure that can simulate the rectangular waveguide characteristics in the PCB. The authors considered the advantages of waveguide and microstrip, which could be highly integrated with other microwave circuits on the same substrate. This provided a new idea for the study of delay lines. Zhou et al.^[6] proposed an SIW slow-wave effect enhancement method. This method consisted of adding a certain number of metal blind holes in the SIW to separate the electrical and magnetic fields, thus achieving a 2.5 times slow-wave effect. However, this method has a large return loss and delay fluctuation, and it increases the processing and fabrication difficulty.

In Ref.[7], microstrip polylines were loaded on the SIW to increase the equivalent capacitance and inductance values of the transmission line to effectively separate the electrical and magnetic fields in the SIW with a delay multiplier of 1.7 times. However, the delay fluctuations in the frequency band were considerably large, reaching 60 %. Furthermore, the overly complex microstrip polyline pattern increased processing and fabrication difficulties.

In summary, the main limitations of the current delay line research are: 1) the amount of delay in the band fluctuates significantly and the delay error is not low enough; 2) the delay efficiency is low and the delay multiplier is small; 3) some structures are complex that causes impedance mismatch and consequently increases the loss.

To solve the aforementioned problems, this paper proposes the design of a SIW wideband delay line loaded with the electromagnetic bandgap(EBG) structure. As Fig. 1 shows, the delay line consists of three parts: EBG, SIW and tapered transition. The EBG structure increases the equivalent inductance and capacitance of the transmission line through a reasonable layout of microstrip multi-segment lines to realize the slow-wave effect. The bandpass structure that covers X-band is realized by loading the EBG structure with a low-pass effect on the upper surface of the SIW with a high-pass effect. The tapered transition structure achieves the impedance matching function to simultaneously extend the bandwidth and reduce the line loss. Measurements show that the delay line can effectively separate electrical and magnetic fields in X-band (8-12 GHz) with a significant slow-wave effect. The delay multiplier of the delay line reaches 4 times. The delay fluctuation is only 2.5 %. The insertion loss is >-2.4 dB and the return loss is < -15 dB. All these performance indicators are within a reasonable range.

1 Design and simulation 1.1 SIW structure

As Fig. 2 shows, the SIW is grounded on the upper and lower surfaces of the substrate, and the sidewalls are formed by two rows of metal vias with a spacing represented by w. The adjacent vias are placed with a spacing of s and the diameter of the vias is d.

$ s / d<2, $

(1)

$ d / w<0.2, $

(2)

$ w_{\mathrm{eff}}=w-1.08 d^2 / s+0.1 d^2 / w, $

(3)

$ w_{\text {eff }}=c /\left(2 f_{\text {TE10 }} \sqrt{e_{\mathrm{r}}}\right) . $

(4)

where w_eff is the equivalent rectangular waveguide width, c denotes the free-space speed of light, f_TE10 represents the designed TE10 mode cutoff frequency, and e_r is the substrate relative permittivity. In this paper, Rogers RO3006 plates with a relative permittivity of 6.15 are used.

To control the radiation loss caused by the discontinuous metal vias sidewalls, Xu and Wu^[8] concluded that the transmission characteristics of the SIW could be equivalent to a rectangular waveguide only when Eqs.(1)-(4) are satisfied.

The change of return and insertion losses near the cutoff frequency will cause large fluctuations in group delay. Therefore, in order to maintain a low delay error, the high-pass cutoff frequency f_TE10 of the SIW is set to 5.5 GHz, far from the low X-band cutoff frequency. Considering the actual engineering process, the metal through-hole diameter d and the through-hole spacing s are set to 0.2 mm and 0.3 mm, respectively. The width w of the SIW is obtained as 11.5 mm according to (3). The structure is simulated using the commercial finite element method (FEM) software Ansoft HFSS, and the S-parameter simulation results are shown in Fig. 3. In the X-band (8-12 GHz), the return and insertion losses are less than -28 dB and greater than -1 dB, respectively, and the S-parameter performance fully meets the design requirements.

1.2 EBG structure

The EBG structure with slow-wave and filtering characteristics can be loaded onto the SIW to form an ultra-wideband (>25 %) bandpass filter^[9]. The cell length of the EBG structure in this case can be derived from the Bragg scattering theory as follows:

$ 2 k=k_{\text {bragg }} \frac{2 \pi}{L_1}. $

(5)

where k is the wave number and L₁ is the length of the EBG unit. The relationship between L₁ and the guided wave wavelength λ_g is

$ L_1=\lambda_g / 2 . $

(6)

$ \lambda_g=\frac{2 \pi}{\beta} . $

(7)

$ \beta=\sqrt{k_0^2 e_{\mathrm{r}}-\left(\frac{\pi}{w_{\mathrm{eff}}}\right)^2}, $

(8)

$ k_0=\frac{2 \pi f_0}{c} . $

(9)

where f₀ is the designed bandpass filter center frequency and w_eff is the equivalent rectangular waveguide width. The value of L₁ is 0.7 mm according to Eqs.(6)-(9). Next, the internal structure of the EBG unit is designed within the width of 0.7 mm.

The slow-wave effect of the EBG structure is enhanced, i.e., the equivalent inductance and capacitance are increased. At the same time, the equivalent inductance and capacitance should be increased proportionately as much as possible in order to ensure that the line characteristic impedance $Z_0=\sqrt{L / C} $ remains unchanged. Figuer 4 shows the EBG structure designed in this paper, which contains five EBG cells. Each cell is composed of a cross structure of thin wires to provide the inductance characteristics, and W₁, L₁, and L₃ determine the equivalent inductance value. The parallel line gap within the cell provides the capacitance characteristics, and L₂ and L₄ determine the equivalent capacitance value. A low error delay in the frequency range is ensured by setting the cutoff frequency of the EBG structure to 14.5 GHz, which is far from the high X-band cutoff frequency.

The EBG structure is loaded onto the upper surface of the SIW, and the simulation is optimized using HFSS for L₁, L₂, L₃, W₁, W₂, and W₃. The optimization objective maximizes the delay time, and the optimized results are rounded to the following parameter values: L₁ = 0.63 mm, L₂=0.45 mm, L₃=0.78 mm, W₁=0.1 mm, and W₂=W₃=0.09 mm. Figuer 5 shows the final obtained S-parameters and the group delay results. Five EBG structures with a total length of 3.78 mm are loaded, achieving a delay of 1λ with significant slow-wave effect, with an fourfold delay efficiency.

1.3 Tapered transition structure

We can gather based on the results provided in the previous section that although the slow-wave effect is obvious after loading the EBG structure and the delay multiplier reaches a value of four. However, the return loss deteriorates to -5 dB and the delay fluctuation is 20 %. There are three main reasons for this deterioration:

1) The optimization objective of HFSS in subsection 1.2 is to maximize the delay time, but this does not take into account the impedance matching problem, because the equivalent inductance and equivalent capacitance grow in different proportions, which leads to changes in the characteristic impedance of the transmission line and generates an impedance mismatch.

2) The original impedance matching structure is destroyed when the electromagnetic bandgap structure is added to the substrate integrated waveguide, which also brings about the impedance mismatch phenomenon.

3) In the above, the HFSS simulation directly connects the microstrip line to the substrate integrated waveguide without considering the abrupt change at the connection. Here too, good impedance matching is necessay, otherwise it will cause great losses and delay fluctuations.

Therefore, this paper introduces the tapered transition structure used in Ref. [10] for impedance matching. The reason for introducing this structure is that microstrip lines have long been one of the most commonly used planar transmission lines in PCBs, and efficient passive transition sections are required for interconnecting substrate integrated waveguides with microstrip circuits, and the microstrip line-substrate integrated waveguide tapered transition structure shown in Fig. 6 has been shown to be very effective and has a significant broadband effect^[10-12].

The inclusion of this tapered transition structure in the delay line design in this chapter can solve most of the impedance mismatch problems. After the design based on the theory of microstrip-substrate integrated waveguide transition, the impedance matching structure suitable for the broadband true delay line in this paper can be obtained by fine-tuning using the optimization simulation of HFSS.

The transition structure of the microstrip line to the substrate integrated waveguide is essentially a tapered microstrip line connecting the microstrip line of width W_a and the substrate integrated waveguide of width w. Considering that the input and output impedance of the device is required to be 50 Ω for impedance matching in general systems, the characteristic impedance of the microstrip line must be designed to be 50 Ω. Therefore, the value of W_a is usually fixed, so the two main design parameters are the transition width W_t and the transition length L_t.

The design of this transition structure is mainly achieved by optimizing the magnitudes of W_t and L_t while monitoring the results of full-wave simulations. Nevertheless, it is possible to estimate the initial values of these parameters in order to narrow down the range of the parameter simulation. Before starting the optimization, the starting point of the optimization can be determined starting from the following relation.

$ W_{\mathrm{t}} / w \simeq 0.4, $

(10)

$ \lambda_g / 2<L_{\mathrm{t}}<\lambda_g . $

(11)

where W_t is the width of the tapered transition section, w is the width of the substrate integrated waveguide in Fig. 2, and λ is the wavelength of the quasi-TEM mode propagating in the microstrip line. It can be found by the following equation

$ \lambda_g=\lambda / \sqrt{e_{\mathrm{r}}}, $

(12)

$ \lambda=c / f . $

(13)

After the HFSS optimization simulation, a wideband tapered transition structure suitable for the delay line structure in this paper is designed, which is shown in Fig. 6.

The optimized indicators in Fig. 6 are W_a=0.36 mm, W_t=0.74 mm, and L_t=4 mm, and the optimized target is return loss < -20 dB, where W_a is the width of 50 Ω microstrip line on a 0.254 mm thick RO3006 dielectric substrate. The optimized S-parameters and group delay results are shown in Fig. 7, where the insertion loss >-0.2 dB, the return loss < -25 dB, the group delay is stable at 1.6λ, and the delay fluctuation is 2.5 %. It can be observed that the S-parameters and delay error are significantly improved after matching.

The electric field and magnetic field distribution of the delay line structure in this paper are shown in Fig. 8. It can be gathered that the electric and magnetic fields are effectively separated in the structure, which is a typical feature of the slow-wave effect. This proves that the delay line in this paper has a prominent slow-wave characteristic.

This paper simulates the delay line loaded with 5, 10, and 20 EBG units. As the measurement requires the installation of SMA connectors, it is necessary to add a 9 mm long 50 Ω microstrip transmission line at each end of the delay line structure in this paper. Figure 9 shows the simulation results after adding the transmission line.

2 Fabrication and measurement

The delay line structure proposed in this paper is designed on the dielectric substrate of RO3006. RO3006 dielectric substrate is a commonly used PCB substrate. The manufacturing process of this delay line structure belongs to the processing and manufacturing process of PCB board. The delay lines after fabrication and processing are shown in Fig. 10 with 1λ, 2λ, and 4λ delays. However, the actual delays are 3λ, 4λ, and 6λ due to the incorporation of the transition structure and a certain length of microstrip lines.

The measured and simulated results are shown in Fig. 11, where a vector network analyzer is used to measure the S-parameters as well as the group delay.

The measured results show that the insertion losses of the three delay lines are greater than -0.96, -1.4, and -2.4 dB respectively, and the return loss is less than -15 dB. The measured loss shows deterioration compared with the simulation data, where the error is mainly due to the SMA connector and SMA adapter losses, and the influence of the delay line substrate conductor oxidation. The measured group delay is close to the simulated data, and the delay fluctuates smoothly.

Table 1 compares the parameters used in this study with those used in the existing studies. The microstrip MDL structure described in Ref. [3] has a large delay fluctuation due to the effect of interline coupling. Compared with the MDL structure, the delay multiplier in this paper is higher, while the delay fluctuation is only 15 % of that in Ref. [3]. Compared with the two novel slow-wave SIWs proposed in Refs. [6-7], this paper has a better delay multiplier and delay fluctuation. Subsequent improvements can be made based on the ideas of these two papers. Reference[13] improved the left-handed transmission line with a large delay and miniaturization compared to Ref. [4], with a delay multiplier of 14.5 times. However, it has a narrow bandwidth and large fluctuations, and the structure proposed in this study has a larger bandwidth and a lower delay error compared to it. Similarly, a slow-wave bandgap waveguide and a slow-wave slot-gap waveguide were proposed in Refs. [14-15], respectively, which have the advantages of a large bandwidth and a low loss, but a lower delay multiplier. In Ref. [16], an ultra-wideband delay line with a delay multiplier of up to 14.28 and a delay fluctuation of only 3.6 % was achieved using a 0.18 μm CMOS process. The prominent advantage of the results of this paper over the aforementioned delay line methods is the reasonable insertion loss, which is as high as 22.5 dB achieved by the CMOS process.

In summary, compared with most of the existing studies, this paper is superior in terms of delay multiplier and delay fluctuation. Furthermore, the insertion and return losses are also within a reasonable range, therefore, its advantages are more obvious. However, it must be pointed out that the delay fluctuation of the delay line designed in this paper should be smoother in order to meet the requirements of the phased-array antenna system of a spaceborne SAR, and there is still considerable room for improvement.

3 Conclusion

In this paper, a wideband large delay structure was designed to realize the slow-wave effect by loading a suitable EBG structure on the SIW. The actual measurement results showed that the delay line could function in the whole X-band (8-12 GHz), the delay multiplier reached a value of four times, and the delay fluctuation was only 2.5 %. The design had certain advantages compared with the current research, and basically achieved the research objective of having a delay line with a large bandwidth, a large delay, and low delay error. The delay line is suitable for various wide-band SAR phased array antenna systems, and the loaded EBG structure can be further improved in the subsequent design to achieve a greater delay efficiency and smoother delay fluctuations.