A transmitarray consists of a source antenna, which operates as the focal source, and an array structure that adjusts the waves radiated from the source to achieve the desired performance. The unit cells constituting the array are designed to have specific transmission coefficients, T_pq, while the waves transmitted from all the elements are combined to determine the far-field characteristics of the transmitarray, as expressed in the following equation:

where E_pq(θ, ϕ) denotes the far-field pattern pertaining to (p,q)_th element at center frequency f_c, while θ and ϕ are the elevation and azimuth angles, respectively. Furthermore, d_x and d_y denote the spacing of the elements along the x and y directions, respectively, and λ_c is the wavelength at the center frequency [9].

Assuming that the magnitude of the transmission coefficient of each cell is unity, the beam steering of the RTA can be controlled by adjusting the transmission phase of the unit cells. Notably, in this process, the phase difference of the waves received by each unit cell as a result of focal source excitation must also be accounted for. Based on the geometry presented in Fig. 2, the distance from the focal source to the (p,q)_th element can be calculated as follows:

The phase distribution of the elements required to steer the beam at a specific angle (θ₀,ϕ₀) can therefore be calculated as follows:

Subsequently, this phase distribution can be quantized according to the bit resolution of the RTA to determine the actual phase distribution. Fig. 3 shows the continuous and 1-bit quantized phase distributions for 0° and 30° beam steering angles, calculated using Eqs. (1)–(3).

As discussed, the beam steering of an RTA can be achieved by controlling the phase distribution of its elements, which remains static over time. However, RTA can also be controlled using periodic time-varying signals through a method known as the space-time coding scheme [9].

In this context, the periodic time-varying control signal can be represented as the time-dependent transmission coefficient T_pq(t), which changes the equation for the far-field pattern as follows:

Assuming T_pq(t) is a periodic function, indicating a linear combination of shifted pulse functions, it can be expressed as follows:

where the Fourier series coefficients apqm of the periodic function T_pq(t) can be derived using Eq. (7) below:

Eq. (7) implies that the magnitude, Apqm, and phase, φpqm, of the transmission coefficient of (p,q)_th element at m_th harmonic frequency can be controlled by adjusting the time code, as follows:

Finally, when a space–time coding scheme is applied to the RTA, the far-field pattern at m_th harmonic can be calculated as:

These results suggest that the far-field pattern at harmonic frequencies can be controlled using a periodic time-varying control signal.

Fig. 4(a) depicts the linear time code that can be applied to a 10×10 RTA. Assuming that all elements in the x direction have the same value, only one of the ten rows can have a 180° phase, while the rest will have a 0° phase at each time step. The results obtained by applying this phase-modulated linear time code, calculated using Eq. (10), are presented in Fig. 4(b) as a 2D radiation pattern. It is evident that the center frequency maintains forward radiation, while the harmonics exhibit harmonic beam steering with the sequential beam steering angle (12°, 24°, 36°,…).

Notably, the applied linear time code assumes a plane wave incidence, where all elements receive the wave with the same phase. Therefore, an additional calculation process is required to apply the space-time coding scheme to the RTA with focal source excitation. The phase distribution that each element of the RTA must have to implement harmonic beam steering can be calculated by applying the linear time code to the phase distribution for 0° radiation with focal source excitation. Fig. 5 illustrates the calculated phase distribution as the time step progresses from 0 to 6.

The structure of a 1-bit RTA unit cell can be categorized into two types: the frequency selective surface (FSS) type and the Rx–Tx type. An FSS-type unit cell utilizes the scattering characteristics of conductive elements to control its transmission phase [14]. In contrast, an Rx–Tx type unit cell consists of two antennas—one for signal reception and the other for transmission—connected using a delayed line with specific phase differences that cause phase variations in the transmitted waves. In this study, the Rx–Tx type unit cell structure was employed to ensure accurate 180° phase variation and low insertion loss. Fig. 6 illustrates the working principle of the Rx–Tx type unit cell. The Rx antenna on the top layer is illuminated by the incident wave, following which the signal is transmitted through the center via to the Tx antenna at the bottom layer, where it is reradiated. The path of signal flow changes based on the on/off state of the PIN diodes, resulting in a 180° phase difference.

The explosive view in Fig. 7(a) shows that the unit cell structure consists of two antenna layers, one bias layer, and a common ground layer. The receiving and transmitting antennas used in the proposed unit cell structure are elliptical patch antennas with a U-slot whose direction could be switched according to the on/off state of the PIN diodes on the transmitting patch [15]. A PIN diode—MADP-00907-14020x from MACOM— is used in the design to ensure low transmission loss and fast switching speed [16]. Furthermore, the bias layer was designed to deliver a bias signal to control the PIN diodes mounted on the transmitting patch. In addition, to minimize the impact of the bias layer on the RF signal, an RF/DC decoupling circuit was employed. Among the various available RF/DC decoupling techniques—radial stubs, meander lines, resistive films, and capacitive loads—the capacitive load method was chosen to filter out RF signals from the bias lines, owing to its good isolation performance and low transmission loss [17].

The proposed unit cell comprises four layers of metal with three substrate layers: two layers of Rogers RO4003C substrate (ɛ_r = 3.55, tanδ = 0.0027) and one layer of Rogers 4450F bonding film (ɛ_r = 3.52, tanδ = 0.004). The specific dimensions and stack-up of the unit cell are noted in Fig. 7(b)–7(e) and Table 1.

To verify the transmission characteristics of the designed unit cell structure, a full-wave simulation was conducted using ANSYS HFSS [18]. In addition, a Floquet port simulation was performed using the periodic boundary condition, assuming plane wave incidence. The amplitude and phase of the scattering coefficients are illustrated in Fig. 8, showing that the proposed unit cell structure attained a high transmission amplitude of more than −1 dB at around 10 GHz in States 1 and 2, with the state of one of the two PIN diodes being on. Additionally, it exactly demonstrates an 180° transmission phase difference between the two states, which makes it highly suitable for use as a 1-bit RTA unit cell.

To verify the performance of the overall RTA structure, the validated unit cells were arranged in a 10×10 array, maintaining a unit spacing of λ/2 along both the x and y axes. As shown in Fig. 9(a), the gain characteristics were simulated using a 3D full-wave solver, where a horn antenna with a maximum gain of 11 dBi was considered the focal source. The F/D ratio, defined as the distance between the focal source and the RTA aperture divided by the maximum dimension of the RTA, was set to an optimal value of 0.9, accounting for spillover and illumination efficiencies [19]. Furthermore, as discussed in the previous section, a 1-bit quantized phase distribution for broadside radiation was applied. Fig. 9(b)–9(d) depict the gain characteristics of the antenna with and without RTA in both 2D and 3D. With the introduction of the RTA, the maximum gain of the antenna improved significantly, from 11 dBi to 19.6 dBi.

As explained in the previous section, the requirements for fabricating a control board that can not only control all unit cells of a 1-bit RTA but also apply the space–time coding scheme are as follows: a sufficient number of output pins, adequate output voltage, and sufficiently fast and accurate switching speed.

Since the 1-bit RTA designed in this study is a 10×10 array, the control board must be able to independently control more than 100 output pins in order to manage all the unit cells separately. Additionally, since the active components controlled by the control board are PIN diodes mounted on transmitting patches, the output voltage of the control board must exceed the forward voltage of the PIN diodes. Finally, to achieve frequency modulation effects by applying the space–time coding scheme, the switching of each unit cell must be performed at a sufficiently fast rate while also maintaining accurate timing. Considering these requirements, a field-programmable gate array (FPGA)-based control board was considered the most suitable for the proposed 1-bit RTA. As shown in Fig. 7, the proposed unit cell was configured to control two PIN diodes using a single bias signal per unit cell, which required maintaining the ground layer at a specific potential. Fig. 10(a) presents a block diagram of the control board used for this operation. The space-time code matrix for 100 independent unit cells was loaded into the FPGA via a PC. As its output, the FPGA produced digital signals, which oscillated between 0 V and 3.3 V through 100 different GPIO (general purpose input/output) pins at a consistent clock frequency. These signals were transmitted to each unit cell through bias lines—they passed through the bias via, receiving patch, and central via to reach the center of the transmitting patch depicted in Fig. 7(e). Meanwhile, the midpoint voltage of the ground layer of the RTA was maintained at 1.6 V, achieved through an additional DC supply and a voltage divider circuit. This setup enabled the operation of switching the digital signal from 0 to 1 to turn on only one of the two diodes in the unit cell. Fig. 10(b) illustrates the control board fabricated using Xilinx Kintex-7 FPGA to achieve the abovementioned functionalities.

Fig. 11 presents the 10×10 RTA structure, designed and validated using full-wave simulation, that was fabricated for conducting measurements. The layout of the RTA was designed to interface with the control board via four D-sub connectors, each with 25 pins, accounting for their compatibility and connectivity requirements.

For the measurement, a spacing jig was employed to control the distance between the RTA aperture and the horn antenna. Fig. 12 shows the measurement setup for RTA gain measurement constructed in an anechoic chamber. Applying the phase distribution discussed in Section II, the gain of the fabricated RTA system was measured for beam steering angles of θ = −45° to 45° at 15° intervals, while a standard gain horn antenna operating within the frequency range of 8.2 GHz to 12.4 GHz was employed as the calibrating antenna. Fig. 13(a) shows the 2D radiation pattern of the RTA for 0° radiation. The measured peak gain of the RTA system was 17.51 dBi, while the simulated peak gain was 18.89 dBi. This discrepancy can be attributed to the increase in the equivalent resistance of the PIN diodes caused by insufficient current supply from the FPGA-based control board. Notably, the R, L, and C parameters of the PIN diodes used in the full-wave simulation were based on typical values specified in the datasheet for a current of 10 mA [16]. However, due to power constraints pertaining to the FPGA control board, each PIN diode experienced a lower current, resulting in higher resistance than initially assumed. However, this gain degradation can be mitigated by employing a control system that provides a higher current supply, thereby reducing losses in each unit cell. Additionally, using an excitation antenna with a narrower beamwidth can improve the spillover efficiency of the RTA, thereby further enhancing the gain. Overall, as evident from Fig. 13(b), the proposed RTA system demonstrated excellent beam steering performance.

After validating the gain characteristics and beam steering performance of the fabricated RTA, the harmonic beam steering performance attained using the space-time coding scheme was verified through measurement. Notably, measurements of harmonic beam steering require the detection of modulated signals, meaning that it is impossible to measure it using a vector network analyzer. Therefore, to capture the modulated signal, a measurement setup involving a signal generator and a spectrum analyzer were utilized, as shown in Fig. 14.

Subsequently, the normalized patterns of the RTA were measured by applying the linear time code discussed in Section II with a modulation frequency of 10 MHz. As shown in Fig. 15(a), the radiation pattern level at the center frequency decreased, while the power at this frequency dispersed into harmonic frequencies, as illustrated in Fig. 15(b). Additionally, the harmonic beam steering results show that radiation patterns at the harmonic frequencies are sequentially steered by 12°, which matches the calculated results shown in Fig. 4(b).

Table 2 presents a performance comparison of the proposed RTA system and previously established transmitarrays and reflectarrays. Compared to the RTAs presented in [4, 20, 21], the most notable advantage of the proposed RTA system is its ability to apply time codes with fast switching speeds while maintaining antenna performance similar to that achieved in the other studies. Furthermore, while the RTA in [22] allowed for the application of time codes, the proposed RTA system features a more compact design, which not only enhances efficiency but also allows for the implementation of time codes at significantly faster speeds. Furthermore, with regard to time code implementation, both [23] and [9] applied time codes to reflectarrays to achieve various functionalities. However, the current study offers a significant advantage by demonstrating the availability of time codes within a transmitarray configuration.