# A Polarization Independent Quasi-TEM Metamaterial Absorber for X and Ku Band Sensing Applications
## 2 Design Methodology
where, \(l=\) length of microstrip line  
\(w=\) width of microstrip line  
\(t=\) thickness of microstrip line  
correction factor \(=K_{g}=0.57-0.145\ln\frac{w^{\prime}}{h^{\prime}}\)  
\(w^{\prime}=\) substrate width  
\(h^{\prime}=\) substrate thickness  
\(\epsilon_{rd}=\) dielectric constant of dielectric film  
\(d=\) distance between mutual overlapping stripline  
Width and thickness of the substrate taken as \(w^{\prime}\) and \(h^{\prime}\), respectively, to calculate a correction factor. Total inductance and capacitance based on the above equivalent circuital model gives \(L=1.166\times 10^{-4}nH\) and \(C=0.68\) pF, respectively. As mentioned in Section 1, absorbers basically have three different layers, the ground plane of the absorber comprises copper (Cu) with thickness of 0.035 mm which gives zero transmission of incident wave during propagation. Hence, the absorbance calculations have been done as follows [13]:  
\[A=1-R=1-\left|\frac{Y_{0}-Y_{in}}{Y_{0}+Y_{in}}\right|^{2} \tag{3}\]  
Figure 1: Proposed metamaterial absorber design (**a**) Equivalent circuit of prototype (**b**) unit cell absorber with dimension, and (**c**) fabricated prototype. where \(Y_{0}\) and \(Y_{in}=Y_{1}+Y_{A}\) are the characteristic admittance of air and the input admittance of the MM absorber. The input admittances \(Y_{1}\), \(Y_{A}\) are formulated as:  
\[Y_{1}=-jY_{d}\cot(kh)=-j\sqrt{\frac{\varepsilon_{r}\varepsilon_{0}}{\mu_{r}\mu_{ 0}}}\cot(kh) \tag{4}\]  
\[Y_{A}=\frac{1}{R+j\omega L-\frac{j}{\omega C}} \tag{5}\]  
where, \(Y_{d}\), \(\epsilon_{r}\), \(\mu_{r}\) and \(k=k_{0}\sqrt{(\epsilon_{r}\times\mu_{r})}\) are the characteristics admittance, relative permittivity, relative permeability, and wave number of dielectric substrates, and \(\epsilon_{0}\), \(\mu_{0}\), and \(k_{0}\) are the permittivity, permeability, and wave number of free spaces, respectively. It is clearly in Equation (3) that the transmittance parameter \(\left|S(\omega)_{21}\right|^{2}\) or \(T\) at angular frequency \(\omega\) is zero due to the complete copper ground plane. Most researchers did not put any second resonator inside the lattice, which suffers from a poor form factor. In the proposed absorber, this mirror reflexed C-shaped resonators form another set of resonances with effective absorbance parallel to the first one. This uniqueness is significant of the proposed design with increased form factor as for X and Ku-band satellites. Based on Equation (1), theoretically the transmittance should be zero, and in simulation most of the power is lost between the resonator gaps as the electric fields converge to each other. Details of this will be presented as experimental data in Section 3. However, in this article a finite-integration technique (FIT)-based simulation method was used for structural analysis of the absorber. At the initial stage, the polarization of the unit cell was a quasi-TEM mode where X-axis comprises electric field whereas magnetic field in the Y-axis and Z-axis propagation of the EM field. Tetrahedral mesh is being used for the frequency domain solver on the unit cell absorber. To verify the theoretical concept, the measurements were set-up as in Figure 2, where Figure 2a shows the simulated boundary conditions (X-axis: applied electric field, Y-axis: applied magnetic field), Figure 2b represents the necessary experimental components and accessories.