## 2 Electromagnetic Model  
As a model of the antenna cell, we use a double slot antenna. These antennas have been tested with various sensors, such as bismuth bolometers [13], quasioptical SIS mixers [14], and so on. The concept of double slot antenna has also been applied in the seashell antenna [11; 12; 15; 16] which has been designed for use with CEBs and suggested for COrE project [17]. To make a single cell of the antenna matrices, we actually take one frequency channel of the seashell antenna. This antenna cell represents double-folded slot antennas connected by a coplanar line [18; 19]. We started with simple double-slot antennas but could not achieve the required bandwidth of 5%. Then we tried double-folded slot antennas and managed to approach this value of the bandwidth. The peculiarity of this antenna with the CEB is that we do not simply match the resistance of the bolometer but must first compensate for the capacitance of the SIN junction, and then match it with the resistance of the bolometer. As a sensor, we use a CEB inserted into a cut in the middle of the coplanar line (Figure 1a). This antenna cell is characterized by a narrow bandwidth, which is one of the critical requirements for the ancillary channels of the LSPE project. Since a single bolometer has rather low saturation power, to make the antenna system operating at a larger optical load, these cells are proposed to be combined into an array [20]. The cells can be connected by DC conductors either in series or in parallel, to provide either current or voltage bias to CEBs, respectively. The required radiation diagram of the receiving system will be provided by a special back-to-back horn. We perform numerical simulations of a single antenna cell in the CST Microwave Studio software package. The method of calculation of frequency characteristics of the antenna cell is described in [15; 16]. First, we calculate the S-parameter of the system, and then Z-parameter in 3D electromagnetic simulations using the frequency domain solver. We place the discrete port to the position of the CEB. As the proposed antenna operates near serial resonance, i.e., near frequency \(\mathrm{f_{res}}\) where \(\mathrm{ImZ}\mathrm{(f_{res})}=0\) and \(\mathrm{d(ImZ)}/\mathrm{d}t>0\), in the vicinity of this resonance, the impedance of the antenna can be represented as \(\mathrm{Z=ReZ_{e}+2\pi fL_{e}+1/(2\pi fC_{e})}\) (Figure 1b). Here \(\mathrm{L_{e}}\) and \(\mathrm{C_{e}}\) are the equivalent inductance and capacitance of the slot antennas and coplanar lines near \(\mathrm{f_{res}}\), respectively. Then, for CEB modeling the RC-chain (Figure 1b) is used. Here \(\mathrm{R_{abs}}\) is the resistance of an absorber; \(\mathrm{C_{SIN}}\) is the two serial SIN junction capacitance of the bolometric system. We calculate \(\mathrm{R_{abs}}\) and \(\mathrm{C_{SIN}}\) values using these relations: \(\mathrm{C_{SIN}}=(2\pi\mathrm{f_{0}ImZ(f_{0})})^{-1}\), \(\mathrm{R_{abs}=ReZ(f_{0})}\). Here \(Z(f)\) is the Z-matrix diagonal component calculated in the electrodynamic part. We select \(\mathrm{C_{SIN}}\) values in the way that total \(\mathrm{C_{SIN}}\) and \(\mathrm{C_{e}}\) capacitances form a series resonance with \(\mathrm{L_{e}}\) at frequencies of 220 and 240 GHz, respectively. The value of \(\mathrm{R_{abs}}\) is chosen such to achieve the maximal coupling efficiency of an antenna system and a CEB. This parameter selection method is applicable only if \(\mathrm{ImZ(f_{0})}>0\) and if \(\mathrm{\ |\mathrm{S_{mn}}\ (f_{0})|}<<1\). Here \(\mathrm{S_{mn}}\) are off-diagonal components in the S-parameter matrix, which we calculate in the electrodynamic part. These relations lead to resonance at the operating frequency \(\mathrm{f_{0}}\). The numerical simulation takes into account the effect of direct current conductors on the antenna electrodynamics. We simulate DC conductors by lumped capacitances, which we connect between the central coplanar line ends and the ground plane. The value of these capacitances is 350 fF.