# Analysis of Passive RFID Applicability in a Retail Store: What Can We Expect?
## 2 Electromagnetic Characterization of Tag Antenna Attached to a Retail Product  
First, we analyze the fundamental aspects of a monostatic RFID system in free space. The minimum sensitivity level of modulated backscattered tag signal power \(P_{rx,sens}\) at the receiver can be calculated for a maximum tag range \(r_{max}\) according to the standard radar equation [15]:  
\[P_{rx,sens}=P_{tx}G_{reader}^{2}(\theta,\phi)p\frac{\lambda^{2}}{\left(4\pi \right)^{3}r_{max}^{2}}\Delta\sigma \tag{1}\]  
where \(\lambda\) is the wavelength, \(P_{tx}\) the reader's transmitted power, \(G_{reader}(\theta,\phi)\) the gain of reader's transmitting and receiving antenna in tag direction, \(\theta\) elevation angle, \(\phi\) azimuth, and \(p\) the polarization efficiency which accounts for polarization mismatch between tag and reader antenna. In our case, the polarization efficiency is 0.5 (which decreases \(r_{max}\) by \(\frac{1}{\sqrt{2}}\)) because the reader antenna is circularly polarized and tag antenna linearly polarized [16]. Differential radar cross section (RCS) \(\Delta\sigma\) of a tag depends on wavelength, impedance match between the antenna and chip, and tag antenna gain \(G_{tag}(\theta,\phi)\) in the direction towards reader, as [15]:  
\[\Delta\sigma=\frac{\lambda^{2}}{4\pi}G_{tag}^{2}(\theta,\phi)K \tag{2}\]  
where \(K\) is modulation loss caused by specific modulation details \(\alpha\) (necessary for calculating the time average signal power and here taken to be \(\alpha=1\)[17]) and reflection coefficients \(\Gamma_{low,high}\) between the tag antenna and two states of chip impedance, \(Z_{a}\) and \(Z_{low,high}\)[15], calculated by:  
\[K=\alpha\left|\Gamma_{high}-\Gamma_{low}\right|^{2} \tag{3}\]  
\[\Gamma_{low,high}=\frac{Z_{low,high}-Z_{a}^{*}}{Z_{low,high}+Z_{a}} \tag{4}\]  
Passive RFID system tags modulate backscattering power by switching the chip impedance between two modulation states. The degree of backscattering depends on this modulation efficiency; the higher the better [15]. The gain of tag antenna is a key performance parameter obtained from antenna directivity \(D\) and radiation efficiency \(e_{r}\) that accounts for dielectric and conduction losses of the antenna, \(G(\theta,\phi)=D(\theta,\phi)e_{r}\)[18]. When a tag is attached to a retail product of certain electrical properties different from air, the antenna's impedance, radiation efficiency, and directivity are changed, causing lower backscatter or backscatter in a direction different from the preferred one. In computational electromagnetics software FEKO (from the German acronym 'FELdberechnung fur Korper mit beliebiger Oberflache', in translation as 'Field Computation Involving Bodies of Arbitrary Shape') we simulated the ALN9640 tag (Alien Technology, Morgan Hill, USA), whose structure in free space is shown in Figure 1. Tag antenna consists of a meander line dipole and T-match element that acts as an impedance transformer. The copper tag structure is modeled using Method of Moments (MoM) with triangle mesh elements. As various food and packaging have different electrical properties, from metallic cans, liquids, to plastics [19], we simulated this tag attached on a cylinder presenting a retail product shown in Figure 2 to investigate the material effect. For the purpose of the analysis in this paper, the retail products' materials are generalized and represented with three basic materials: metal (representing all cans and items with metallic packaging), water (representing all liquids) and plastic (such as a low-loss dielectric for all non-metallic and non-liquid retail products). Plastic properties \(\epsilon_{r}=3.5\) and \(\sigma=0.002\) S/m are taken as a general low-loss dielectric to cover the whole range of retail products like flour, sugar, plastic products, etc. [19; 20]. Water properties are \(\epsilon_{r}=81\) and \(\sigma=0.22\) S/m (from Wireless InSite material database [21]; see Table 2). The 3D radiation patterns of these tags are simulated at a US RFID frequency of 920 MHz.