# 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
Assuming \(V_{A}=V_{GS_{5}}\) and substituting their gate-source voltage relation stated in Equation (2), it leads to Equation (17) for \(V_{B}\). Due to the current mirrors composed for \(m_{p1}-m_{p2}\) and \(m_{n1}\), the \(I_{C}\) current flows also through \(m_{10}-m_{11}\) transistors. In this case, the drain current \(I_{D_{11}}\) is equal to the \(I_{C}\) current and can be expressed by Equation (18). Furthermore, a more compact representation of the \(I_{C}\) can be obtained by substituting the gate-source voltages of the transistors \(m_{12}\) and \(m_{13}\) using Equation (2) and the \(V_{B}\) voltage established in Equation (17) into Equation (18). The result is presented in Equation (19) where \(\Delta V_{TH}=V_{TH_{5}}-V_{TH_{13}}+V_{TH_{12}}-V_{TH_{11}}\). \[V_{B}=V_{TH_{5}}+\eta V_{T}ln\Bigg{[}2\frac{k_{4}}{k_{7}}\Bigg{(}\frac{k_{2}}{ k_{1}}\Bigg{)}^{\frac{6k_{3}}{k_{5}}}\Bigg{]} \tag{17}\]  
\[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]0  
\[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]1  
A [PERSON] expansion of the exponential term can be applied to simplify Equation (19). This expansion is presented in Equation (20) up to the second term as the following values can be considered negligible. After substituting Equation (20) into Equation (19), a more insightful \(I_{C}\) expression can be obtained as shown in Equation (21) where \(k_{rc}\) is a constant that depends on the aspect ratio of the transistors \(m_{1}-m_{5}\), \(m_{7}\) and \(m_{11}-m_{13}\), while \(k_{tc}\) is a constant that fully depends on the fabrication technology; both constants are described in Equation (22). Equation (21) reveals that the \(T^{1+m}\) term presents an inversely proportional behavior over temperature as long as \(1+m<0\). On the other case, the \((\eta V_{T}+\Delta V_{TH})\) term shows a proportional temperature behavior, canceling the effect of the \(T^{1+m}\) term. However, the \((\eta V_{T}+\Delta V_{TH})\) term presents an almost constant behavior, since \(V_{T}\) increases as \(\Delta V_{TH}\) decreases. \[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]2  
\[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]3  
\[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]4  
The schematic circuits of the current and voltage reference are shown in \[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]5 These circuits make use of the \(V_{P1_{x}}\) and \(V_{P2_{y}}\) bias voltages to mirror an \(I_{P}\) current and use the \(V_{P1_{x}}\) and \(V_{P2_{y}}\) bias voltages to mirror an \(I_{C}\) current. The bias voltages were generated in the current source core shown in \[V_{DS_{3}}=V_{GS_{1}}-V_{GS_{2}}=\eta V_{T}ln\left(\frac{k_{2}}{k_{1}}\right)+ V_{TH_{1}}-V_{TH_{2}} \tag{10}\]6  
The current reference shown in Figure 7a provides a temperature-compensated current \(I_{TC}\) by sinking the \(I_{P}\) and \(I_{C}\) currents into a \(m_{14}\) diode connected transistor, creating a voltage that will be used to bias further temperature-compensated current mirrors. The current reference provides a proportional-to-temperature current conveying the \(I_{P}\) current into the \(m_{15}\) diode connected transistor, which in turn generates a \(V_{I_{P}}\) voltage that will be used to bias the current mirrors of the following stages. The implemented voltage reference is drawn in Figure 7b. The voltage reference provides a stable \(V_{REF}\) against temperature variation. This voltage can be computed by using the gate-source voltage mesh composed for \(m_{16}\) and \(m_{18}-m_{19}\) transistor as well as using the drain currents that flow through them as stated in Equation (23).