# A Self-Powered UHF Passive Tag for Biomedical Temperature Monitoring
## 2 Architecture of Proposed Self-Powered Passive Tag
### Power Management
#### 2.2.2 Current and Voltage Reference  
The current and voltage reference is made up by three building blocks: a current source core, a current reference, and a voltage reference. The current source core generates a PTAT \(I_{P}\) current and a Complementary To Absolute Temperature (CTAT) \(I_{C}\) current. The current reference delivers a temperature-compensated \(I_{TC}\) current by adding the \(I_{P}\) and \(I_{C}\) currents into a current sink, while the voltage reference generates a temperature-compensated voltage. Figure 6 shows the schematic circuit of the current source core, where all transistors operate in the subthreshold region, except for \(m_{3}\) and \(m_{5}\), which operate in the linear and saturation regions [54; 55]. The \(m_{P_{3}}\) transistors and \(C_{A}\) are only used for start-up purposes. Figure 5: Shunt regulator. The \(I_{P}\) current in Figure 6 is computed by solving the mesh composed for the \(m_{1}\), \(m_{2}\), and \(m_{3}\) transistors and substituting their gate-source voltage relation stated by Equation (2), which leads to Equation (10). Since \(m_{3}\) operates in the linear region, its channel resistance can be expressed as \(R_{DS_{3}}=1/[k_{3}\mu C_{ox}(V_{A}-V_{TH_{3}})]\). Equation (10) can be also replaced in the drain current equation of \(m_{3}\) which is ruled by \(I_{P}=V_{DS_{3}}/R_{DS_{3}}\), obtaining Equation (11). \[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]  
\[I_{P}=k_{3}\mu C_{ox}(V_{A}-V_{TH_{3}})\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right) \tag{11}\]  
With the current mirrors composed by \(m_{p_{1}}-m_{p_{2}}\), the \(I_{p}\) current expressed in Equation (11) can be copied three times and then sunk into the \(m_{5}\) transistor that operates in the saturation region. In this case, the \(m_{5}\) drain current is stated as \(3I_{p}=k_{5}\frac{\mu C_{ox}}{2}(V_{A}-V_{TH_{5}})^{2}\). By substituting Equation (11) into the \(m_{5}\) drain current, a second order equation can be found and solved for \(V_{A}\), as shown in Equation (12). By replacing Equation (12) into Equation (11) and assuming \(V_{TH_{5}}=V_{TH_{3}}\), a new expression for \(I_{P}\) can be found as shown in Equation (13). \[V_{A}=6\frac{k_{3}}{k_{5}}\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+V_{TH_{ 5}} \tag{12}\]  
\[I_{P}=\frac{k_{5}}{6}\mu C_{ox}\left[6\frac{k_{3}}{k_{5}}\eta V_{T}ln\left( \frac{k_{2}}{k_{1}}\right)\right]^{2} \tag{13}\]  
In order to obtain a final expression for \(I_{p}\), the temperature dependence of the electron mobility \(\mu\) and the thermal voltage relation must be included. The behavior of \(\mu\) as a function of the temperature is shown in Equation (14), where \(\mu_{T_{nm}}\) is the electron mobility at nominal temperature, \(T_{nm}\) is the nominal temperature, and \(m\) is a technological parameter. After replacing in Equation (14) the thermal voltage and rearranging terms, a more compact equation for \(I_{P}\) can be obtained as shown in Equation (15). In this equation, \(k_{rp}\) is a constant that depends on the aspect ratio of the transistors \(m_{1}-m_{2}\) and \(m_{4}-m_{5}\) while \(k_{rp}\) is a constant that fully depends on the fabrication technology. Both constants are described in Equation (16). Equation (15) shows that a proportional temperature behavior is kept as  
Figure 6: Proposed current source core. long as \(2+m>0\); the best scenario will occur at \(2+m=1\) where Equation (15) is linearly dependent on temperature. \[\mu(T)=\mu_{T_{nom}}\Bigg{[}\frac{T}{T_{nom}}\Bigg{]}^{m}\quad m<-1 \tag{14}\]  
\[I_{P}=12k_{r}k_{t}\cdot T^{2+m} \tag{15}\]  
\[k_{rp}=\frac{k_{0}^{2}}{k_{0}^{5}}ln\Bigg{(}\frac{k_{2}}{k_{1}}\Bigg{)}\ \,\ \ k_{tp}= \eta\frac{K}{q}\frac{\mu_{T_{nom}}\mathcal{C}_{ox}}{T_{nom}^{m}} \tag{16}\]  
The complementary current \(I_{C}\), shown in Figure 6, is computed by solving the mesh composed for the \(m_{4}-m_{7}\) transistors.