# A CMOS-Based Terahertz Reconfigurable Reflectarray with Amplitude Control: Design and Validation
## 2 Design Concept  
The reconfigurable reflectarray (RRA) element with a single switch is the simplest form of metasurface element and can be modeled as a two-port microwave network [37; 38; 39; 40], as shown in Figure 1a,b. Port 1 is the spatial wave port, and Port 2 is the switch port. The elements are divided into the tunable switch and the passive part. The switch is typically assumed to have ideal switching characteristics, with its impedance exhibiting significant variation. The passive part of the element can be equivalent to a two-port scattering parameter matrix, used to describe the response of the element's metallic structure and dielectric material to electromagnetic waves, and is typically regarded as a lossless network in the microwave and millimeter wave bands. In this lossless network, Port 1 matching is equivalent to Port 2 matching. Therefore, the lower-frequency RRA element design methodologies aim to design the passive part of the element so that the characteristic impedance of Port 2 is matched with the switch-related impedance. More specifically, when the characteristic impedance of Port 2 matches the impedance of the switch in ON or OFF state at a certain frequency point, the spatial wave Port 1 is simultaneously matched. Thus, the resonance of the element is achieved near that frequency point, causing the magnitude of the element reflection coefficient \(\Gamma\) to significantly low. When the switch is toggled to the other state, the impedance of the switch shifts dramatically, disrupting the impedance matching and the resonance. Therefore, the magnitude of the element reflection coefficient \(\Gamma\) remains high, thereby achieving amplitude control of the RRA element through switch operation.  
As the operating frequency increases to terahertz, the performance of switches deteriorates due to high-frequency parasitics, making it impossible to achieve the ideal OFF effects. The deterioration of switch performance not only leads to an increase in element loss but also makes the design of elements more challenging. Since the characteristic impedance parameters of the switch are often complex numbers, the design goal for the element becomes unclear. Additionally, the significant material losses in the terahertz frequency range prevent the two-port network from being treated as lossless.  
To address these challenges in the THz band, necessary adjustments must be made based on the lower-frequency RRA element design methodologies mentioned earlier. Since the passive part of the terahertz RRA element constitutes a lossy two-port network, simultaneous conjugate matching at both port interfaces becomes unachievable. In this case, priority must be given to ensuring conjugate matching at Port 1. It should be noted that this approach does not require conjugate matching between Port 1 input impedance and the spatial wave impedance. Instead, when Port 1 is terminated with the spatial wave impedance, the Port 2 characteristic impedance is calculated and conjugate-matched to the switch-related impedance. These two matching approaches are not equivalent in lossy networks, as will be demonstrated through numerical examples and analysis in the next section. Concretely, the design of amplitude-control RRA element has a clear goal: the passive part of the element must be designed to achieve conjugate matching between the Port 2 characteristic impedance (calculated under the condition of Port 1 matching) and the switch impedance in either the ON or OFF state.  
Figure 1: Model and microwave network equivalence of the single-switch RRA element. (**a**) Model of the element. (**b**) Network equivalence of the single-switch element.