# A Temperature-Robust Envelope Detector Receiving OOK-Modulated Signals for Low-Power Applications
## 2 State-of-the-Art Passive EDs with Temperature Compensation  
As mentioned in the Introduction, the demodulation mechanism leverages the second-order non-linearities of MOSFETs in subthreshold [10]. The standard passive ED is a Dickson charge pump composed of diode-connected MOSFETs biased with zero static current and capacitances.  
The proposed ED employs the variation presented in [12] and shown in Figure 1a, where voltage \(V_{B}\) is generated by an additional PTAT block as in Figure 2. The impedance seen at the RF input is the parallel connection between a resistance \(R_{in}\) and a capacitance \(C_{in}\) and is matched to the antenna impedance by a matching network. The temperature compensation mechanism operates through a dedicated block aiming at temperature dependence reduction for \(R_{in}\) so that the temperature dependence of matching network gain \(A_{v}\) is also minimized. As detailed in Section 3.2, this ultimately reduces the temperature dependence of the overall receiving chain sensitivity.  
Temperature compensation techniques have already been presented. An alternative approach employing a different additional block was proposed in [15]. It requires both enhancement and depletion MOSFETs as it leverages the threshold difference between them and demonstrates a reduction in sensitivity temperature dependence over a \(-10\)\({}^{\circ}\)C to \(50\)\({}^{\circ}\)C operating temperature range.  
Moreover, a structure similar to the one proposed in this paper, employing a PTAT current for the biasing of self-mixer gate terminals, was proposed in [16]. Yet, a discussion of sensitivity dependence over temperature is missing.  
In [17], a dedicated block is used to drive diode bulk terminals so as to make their threshold voltage, thus their channel resistance, constant over temperature with the ultimate aim of a constant ED bandwidth. The operating temperature range is \(-10\)\({}^{\circ}\)C to \(40\)\({}^{\circ}\)C.  
Ref. [18] targets operating temperatures between \(-30\)\({}^{\circ}\)C and \(70\)\({}^{\circ}\)C. It focuses on temperature and supply robust voltage and current references, as well as comparator threshold adjustments by means of a capacitive digital-to-analog converter for temperature compensation.  
Finally, ref. [19] relies on a charge-transfer summation amplifier following the ED for temperature robustness across a \(-40\)\({}^{\circ}\)C to \(85\)\({}^{\circ}\)C operating temperature range.  
Table 1 compares the different implementations addressing sensitivity robustness through a Figure of Merit, which represents the inverse of the mean sensitivity variation across \(1\)\({}^{\circ}\)C (\((T_{max}-T_{min})/\Delta P_{sens}\)). As a result, our implementation shows FoM performances aligned with the state-of-the-art [18] over a wider temperature range.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **This Paper** & [15] & [17] & [18] & [19] \\ \hline \(P_{sens}\) at \(20\)\({}^{\circ}\)C [dBm] & \(-66.1/-68.9\) & \(-76.3\) & \(-62.5\) & \(-72.4\) & \(-70.2\) \\ \hline \(\Delta P_{sens}\) for \(T_{min}\div T_{max}\) [dB] & \(4.6\) & \(3.9\) & \(3\) & \(2.5\) & N/A \\ \hline \(T_{min}\) [\({}^{\circ}\)C] & \(-40\) & \(-10\) & \(-10\) & \(-30\) & \(-40\) \\ \hline \(T_{max}\) [\({}^{\circ}\)C] & \(120\) & \(50\) & \(40\) & \(70\) & \(85\) \\ \hline FoM= & \(34.8\) & \(15.4\) & \(16.7\) & \(40\) & N/A \\ \(1/(\Delta P_{sens}/(T_{max}-T_{min}))\) [\({}^{\circ}\)C/dB] & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Temperature stability comparison table with the state-of-the-art.  
Figure 1: (a) Passive ED as in [12] and (b) estimation of its propagation delay.  
Figure 2: Proposed ED with temperature compensation [22].