# Flexible UHF RFID Tag for Blood Tubes Monitoring
## 3 Design of the Tag Antenna
### Optimization  
One of the important characteristics in the design of tag antennas is the input impedance. A good matching is needed between the IC chip and the tag antenna to avoid undesired reflections. This condition can be monitored by means of the generalized reflection coefficient calculated as:  
\[\Gamma=\frac{Z_{a}-Z_{c}^{*}}{Z_{a}+Z_{c}} \tag{1}\]  
where \(Z^{*}c\) represents the complex conjugate of the IC chip impedance and \(Za\) is the input complex impedance of the antenna. The magnitude of the generalized reflection coefficient is monitored in real conditions with the tag attached to the smallest blood tube, as shown in Figure 2c. Therefore, all the relevant elements, namely the substrate, blood and tube with the electrical characteristics discussed in Section 2, are included during the design process. Note that in order to minimize the reflections between the tag and the IC chip, the magnitude of the generalized reflection coefficient given in (1) must be minimized during the design process. The commercial electromagnetic simulator CST Studio Suite(r)was used for the optimization, analysis and design of the proposed tag. The tag attached to the smallest tube is drawn in the modeler as shown in Figure 2c, and all its element parameters (dimensions, substrate permittivity, blood permittivity, and thickness substrate), including the IC chip, are defined. The real and imaginary parts of the complex chip impedance (\(Z_{c}=16-j\ 156\ \Omega\)) are respectively specified by means of a discrete port and a lumped \(RLC\) series element. The discrete port and the lumped \(RLC\) series element are situated across the gap \(s\) between the two pads, in the same place than the IC chip (Figure 2). Then, the  
Figure 2: Proposed flexible ultra-high frequency (UHF) radio frequency identification (RFID) tag antenna. (**a**) Photograph of the tag antenna attached to a flat surface (FR4 substrate). (**b**) Structure and dimensions. (**c**) Flexible tag antenna attached to a blood tube. simulation is started from the transient solver. Once the simulation is finished different parameters such as impedance, reflection coefficient, and gain can be analyzed. For the design of the tag, the resonant frequency is mainly controlled with the length \(L1\) of the meandered substrate arms. This resonant frequency is also affected by the substrate thickness and other dielectric properties of nearby objects such as the tube and the blood [9; 10]. In addition, the maximum attainable gain and bandwidth have limitations, due to the size of the tag antenna and the frequency of operation [8]. Figure 3 shows the dependence of the input impedance of the tag antenna (Figure 2b) with the gap \(g\) between pads as a function of the frequency (0.5 GHz-2 GHz), while all other parameters are kept constant (Table 1). It can be observed that this gap controls the capacitive coupling of the two pads. The capacitive effect increases when the gap \(g\) decreases, and this results in a lower resonant frequency. Consequently, the adjustment of the gap \(g\) allows a fine tuning of the resonant frequency of the tag antenna. The insets inside Figure 3a,b shows details on the variation of the real and imaginary parts of the input impedance \(Za\) of the tag antenna with the gap \(g\) in the frequency band of interest (0.86 GHz-0.96 GHz). As it can be seen in the insets, the values of both real and imaginary parts of the input impedance \(Z_{a}\) can be fine adjusted to match the conjugate of the chip impedance \(Z_{c}\), needed to minimize the magnitude of Equation (1). This study also serves to discuss the particular case of \(g=0\). For this case, the two pads are in electrical contact, and the antenna turns from a capacitive behavior to an inductive behavior.