# Two-Terminal Electronic Circuits with Controllable Linear NDR Region and Their Applications
## 6 Applications
### Simulation of VCO Characteristics
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**VCO Characteristics**} \\ \cline{3-6}
**Type of Oscillator** & **Capacitance, \(C_{a}\)** & \(f_{min},f_{max}\) & \(\Delta f\) & \(PN\) (\(f_{off}\) = 10\({}^{5}\) Hz) & **Power of** & **FOM** \\
**Oscillator** & **(pF)** & \(V_{d}\) = 2 V, 12 V & **(MHz)** & **(MHz)** & **V\({}_{d}\) = 2 V, 12 V & **Dissipation, \(P_{dis}\)** & **V\({}_{d}\) = 2 V, 12 V \\ \hline MCCM (\(m=0\)) & 30 & 1555, 1915 & 360 & \(-\)99.0, \(-\)98.3 & 18.8 & \(-\)170.1, \(-\)171.2 \\ \hline MCCM (\(m=1\)) & 15 & 1376, 1586 & 210 & \(-\)97.3, \(-\)88.2 & 25.2 & \(-\)166.1, \(-\)158.2 \\ \hline MCCM (\(m=2\)) & 30 & 1235, 1380 & 145 & \(-\)97.8, \(-\)88.8 & 31.0 & \(-\)164.7, \(-\)156.7 \\ \hline MWCM (\(m=0\)) & 12 & 1510, 1791 & 281 & \(-\)111.7, \(-\)134.6 & 19.6 & \(-\)182.4, \(-\)206.7 \\ \hline MWCM (\(m=1\)) & 20 & 1325, 1480 & 245 & \(-\)134.7, \(-\)141.9 & 27.0 & \(-\)202.8, \(-\)211.0 \\ \hline MWCM (\(m=2\)) & 18 & 1191, 1298 & 107 & \(-\)144.0, \(-\)128.4 & 33.9 & \(-\)210.2, \(-\)195.4 \\ \hline MWCM (\(m=0\)) & 13 & 1532, 1841 & 309 & \(-\)130.4, \(-\)138.4 & 19.8 & \(-\)201.1, \(-\)210.7 \\ \hline MWCM (\(m=1\)) & 12 & 1325, 1478 & 153 & \(-\)135.6, \(-\)136.1 & 27.4 & \(-\)203.7, \(-\)205.1 \\ \hline MWCM (\(m=2\)) & 9 & 1191, 1295 & 104 & \(-\)139.0, \(-\)137.0 & 34.5 & \(-\)205.1, \(-\)203.9 \\ \hline \end{tabular}
\end{table} 
Table 12: Simulated characteristics of different NDR VCOs when \(R_{L}=50\)\(\Omega\). Figure 27: Phase noise versus offset frequency for VCO with multiple-output improved Wilson-current mirror when \(V_{d}\) = 2 V, \(R_{L}=50\)\(\Omega\); \(m\) = 0—purple curve (\(C_{a}=13\) pF), \(m\) = 1—blue curve (\(C_{a}=12\) pF), \(m\) = 2—red curve (\(C_{a}=9\) pF). As shown in Table 13, the highest (i.e., the worst) in-band value of the FOM insignificantly increases when connecting a 50 \(\Omega\) load to the VCO output. Indeed, the absolute FOM value decreases by 0.5 dBc/Hz for VCO with MICCM, by 1.6 dBc/Hz for VCO with MWCNT, and by 1.1 dBc/Hz for VCO with MIWCM. However, the lowest (i.e., the best) in-band FOM value changes more substantially, namely by 41.1 dBc/Hz for VCO with MCCM, by 4.3 dBc/Hz for VCO with MWCNT, and by 16.9 dBc/Hz for VCO with MIWCM. Since, when comparing the VCOs, the worst in-band FOM value is considered, we can conclude that this value changes insignificantly (maximum 0.7 %) when connecting a 50 \(\Omega\) load to the VCO output. Tables 12 and 13 show that the best VCO when \(R_{L}=50\) is the VCO with MIWCM (\(m=2\)). Table 14 compares the performance characteristics of the recently published and developed in this article VCOs and oscillators. We can draw the following conclusions from Table 14. The oscillator with MWCM (\(m=2\), \(R_{L}=50\)\(\Omega\)) designed in this study has the lowest phase noise (\(-154.6\) dBc/Hz at 0.1 MHz offset) and the best FOM (\(-221.6\) dBc/Hz) among all oscillators. The latter is an indisputable advantage of the developed oscillator since CMOS oscillators have a much lower power consumption and usually have a significant advantage over GaN and GaAs oscillators in terms of the FOM value. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Oscillator Load, \(R_{L}\) (\(\Omega\))**} & \multicolumn{4}{c}{**The Figure of Merit (dBc/Hz)**} \\ \cline{2-5}  & \multicolumn{4}{c}{**Type of Oscillator**} \\ \hline  & MCCM & MWCM & MIWCM \\ \hline \(\infty\) & \(-170.6\), \(-212.3\) & \(-204.2\), \(-215.3\) & \(-205.0\), \(-222.0\) \\ \hline \(50\) & \(-170.1\), \(-171.2\) & \(-202.8\), \(-211.0\) & \(-205.1\), \(-203.9\) \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Performance comparison of VCOs with different loads. Figure 28: Phase noise versus offset frequency for VCO with multiple-output improved Wilson current mirror when \(V_{d}=12\) V, \(R_{L}=50\)\(\Omega\); \(m=0\)—purple curve (\(C_{a}=9\) pF), \(m=1\)—blue curve (\(C_{a}=12\) pF), \(m=2\)—red curve (\(C_{a}=13\) pF).