# A 0.3 V, Rail-to-Rail, Ultralow-Power, Non-Tailed, Body-Driven, Sub-Threshold Amplifier
## 4 Amplifier Design and Simulation Results
### Results and Comparision  
Table 6 compares the simulated performance of the proposed amplifier with other ULV, ULP implementations from the literature. In order to compare the performance of several different designs, we have considered the usually adopted four figures of merit (FOMs) defined as follows:  
\[FOM_{1}=\frac{GBW\cdot C_{L}}{I_{\text{TOT}}} \tag{29}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(T[C]\) & \(-10\) & \(0\) & \(27\) & \(50\) & \(80\) & \(110\) \\ \(Gain[dB]\) & \(55.05\) & \(57.76\) & \(64.6\) & \(67.51\) & \(61.36\) & \(50.07\) \\ \(GBW[kHz]\) & \(1.87\) & \(2.228\) & \(3.58\) & \(3.89\) & \(2.49\) & \(1.159\) \\ \(m\varphi\)\([deg]\) & \(59.74\) & \(61.06\) & \(53.76\) & \(48.45\) & \(67.84\) & \(83.52\) \\ \(SR_{+}[V/ms]\) & \(1.11\) & \(1.28\) & \(1.7\) & \(1.96\) & \(2.16\) & \(2.29\) \\ \(SR_{-}[V/ms]\) & \(0.14\) & \(0.15\) & \(0.15\) & \(0.15\) & \(0.14\) & \(0.13\) \\ \(Pdiss[nW]\) & \(12.0\) & \(11.9\) & \(9.9\) & \(10.9\) & \(11.1\) & \(11.96\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Amplifier performance vs. temperature. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **TT** & **SS** & **FF** & **SF** & **FS** \\ \hline \(Gain\)\([dB]\) & \(64.60\) & \(59.85\) & \(68.83\) & \(64.96\) & \(62.90\) \\ \(GBW\)\([kHz]\) & \(3.58\) & \(2.56\) & \(4.15\) & \(3.59\) & \(3.18\) \\ \(m\varphi\)\([deg]\) & \(53.76\) & \(59.04\) & \(45.77\) & \(52.22\) & \(60.98\) \\ \(CMRR\)\([dB]\) & \(61\) & \(59.83\) & \(67.51\) & \(65.02\) & \(62.85\) \\ \(PSRR_{+}/PSRR_{-}\)\([dB]\) & \(26/28\) & \(23/26\) & \(28/29\) & \(27/28\) & \(24/26\) \\ \(SR_{+}/SR_{-}\)\([V/ms]\) & \(1.7/0.15\) & \(1.19/0.15\) & \(2.31/0.15\) & \(2.46/0.15\) & \(1.09/0.15\) \\ \(SR_{AVG}\)\([V/ms]\) & \(\approx\)\(0.93\) & \(\approx\)\(0.67\) & \(\approx\)\(1.23\) & \(\approx\)\(1.31\) & \(\approx\)\(0.62\) \\ \(noise\)\([\mu V/\sqrt{Hz}]\) & \(0.76\) & \(0.71\) & \(0.78\) & \(0.77\) & \(0.74\) \\ \(P_{DISS}\)\([nW]\) & \(10.9\) & \(11.8\) & \(10.95\) & \(9.9\) & \(11.36\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Amplifier performance for different process corners. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Mean** & **Std\_dev** \\ \hline \(Gain[dB]\) & \(65.48\) & \(7.43\) \\ \(GBW[kHz]\) & \(2.33\) & \(1.21\) \\ \(m\varphi[deg]\) & \(50.14\) & \(13.7\) \\ \(CMRR[dB]\) & \(46.5\) & \(10.7\) \\ \(SR_{+}[V/ms]\) & \(2.51\) & \(0.062\) \\ \(SR_{-}[V/ms]\) & \(0.183\) & \(0.006\) \\ \(Pdiss[nW]\) & \(11.35\) & \(0.831\) \\ \(V_{offset}\)\([\text{mV}]\) & \(2.91\) & \(5.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Monte Carlo simulations. \[FOM_{2}=\frac{SR_{AVG}\cdot C_{L}}{I_{TOT}} \tag{30}\] \[FOM_{3}=\frac{GBW\cdot C_{L}}{P_{DISS}}\] (31) \[FOM_{4}=\frac{SR_{AVG}\cdot C_{L}}{P_{DISS}}\] (32) \[FOM_{4_{W\mathrm{C}}}=\frac{SR_{W\mathrm{C}}\cdot C_{L}}{P_{DISS}} \tag{33}\]  
where the large signal \(FOM_{4}\) has been computed both referring to the average slew rate and to the worst case one (\(FOM_{4_{W\mathrm{C}}}\)). The comparison in Table 6 shows the effectiveness of the proposed approach: Extremely high values of the small signal FOMs (\(FOM_{1}\) and \(FOM_{3}\)) are achieved. \(FOM_{3}\) is particularly high thanks to the adoption of an extremely low supply voltage. This result is due to the combination of an Arbel-type approach, that doubles the gain of the first stage and thus the GBW product, and a dual-path second stage that allows achieving stability without sacrificing the bandwidth. Similar values of the small signal FOMs are obtained only by [22], that however uses a higher supply voltage, resulting in a lower \(FOM_{3}\), and [18]. This latter however is a single-stage amplifier with limited input common mode range and which provides a much lower gain, and is biased at an extremely low current; no additional circuit is used to stabilize the dc current, that therefore presents large variations in PVT conditions.