# Two-Terminal Electronic Circuits with Controllable Linear NDR Region and Their Applications
## 6 Applications
### Simulation of VCO Characteristics
As shown in Table 11, the VCO with MCCM has the best performance when \(m=0\). The VCO with MWCNT achieves the best performance when \(m=2\) and VCO with MIWCM--when \(m=1\). For each value of \(m\) in Table 11, VCO with MWCNT and MIWCM have significantly lower (i.e., better) FOM than VCO with MCCM. The broadest tuning frequency range, \(\Delta f=370\) MHz, has VCO with MCCM when \(m=0\). The lowest power consumption, \(P_{dis}=18.8\) mW, also has VCO with MCCM when \(m=0\). Figures 25 and 26 illustrate the dependence of phase noise versus capacitance \(C_{b}\) for VCO with multiple-output improved Wilson CM at \(V_{d}=2\) V and \(V_{d}=12\) V, respectively. We can see from Figures 25 and 26 that VCO phase noise significantly depends on the value of capacitor \(C_{b}\). Indeed, when capacitance \(C_{b}\) varies from 3 to 300 nF, phase noise decreases from \(-95.3\) to \(-137.9\) dBc/Hz at \(V_{d}=2\) V and from \(-110.9\) to \(-146.9\) dBc/Hz at \(V_{d}=12\) V. We can explain such a decrease in phase noise by reducing noise spectral density at the drain of transistor \(T_{0}\). Table 12 shows the simulated characteristics of different VCOs when a 50 \(\Omega\) load through a capacitive divider (see Figure 22) is connected to the output of VCOs shown in Figures 9-11. We select \(C_{CD1}=C_{CD2}=0.5\) pF for the VCOs with MWCNT (\(m=0,\,1,\,2\)), and MIWCM (\(m=1,\,2\)), and \(C_{CD1}=C_{CD2}=0.25\) pF for the VCOs with MCCM (\(m=0,\,1,\,2\)) and MIWCM (\(m=0\)). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{ \begin{tabular}{c} **Type of** \\ **VCO** \\ **Type of** \\ **VCO** \\ **Type of** \\ **VCO** \\ **Type of** \\ **VCO** \\ **Type of** \\ **VCO** \\ **Type of** \\ **(\(m=0\))** \\ \end{tabular}  & \begin{tabular}{c} \(f_{min}\) \\ **\(V_{d}=2\) V, 12 V** \\ **(MHz)** \\ \end{tabular}  & \begin{tabular}{c} **VCO Characteristics** \\ **\(\Delta f\)** \\ **(MHz)** \\ \end{tabular}  & \begin{tabular}{c} **PV (\(f_{od}=10^{5}\) Hz)** \\ **\(V_{d}=2\) V, 12 V** \\ **(dBc/Hz)** \\ \end{tabular}  & \begin{tabular}{c} **PV (\(f_{od}=10^{5}\) Hz)** \\ **\(V_{d}=2\) V, 12 V** \\ **(dBc/Hz)** \\ \end{tabular}  & \ \begin{tabular}{c} **PV (\(f_{od}=10^{5}\) Hz)** \\ **\(V_{d}=2\) V, 12 V** \\ **(dBc/Hz)** \\ \end{tabular}  & \begin{tabular}{c} **PV (\(f_{od}=10^{5}\) Hz)** \\ **\(V_{d}=2\) V, 12 V** \\ **(dBc/Hz)** \\ \end{tabular}  \\ \hline MCCM & 5 & 1616, 1986 & 370 & \(-99.2\), \(-139.1\) & 18.8 & \(-170.6\), \(-212.3\) \\ \hline MCCM & 12 & 1408, 1631 & 223 & \(-97.6\), \(-100.4\) & 25.2 & \(-166.6\), \(-170.6\) \\ \hline MCCM & 12 & 1262, 1410 & 148 & \(-96.8\), \(-90.4\) & 31.0 & \(-163.9\), \(-158.5\) \\ \hline MWCM & 10 & 1571, 1912 & 341 & \(-132.5\), \(-143.2\) & 19.6 & \(-203.5\), \(-215.9\) \\ \hline MWCM & 7 & 1 As shown in Table 12, the VCO with MCCM has the best performance when \(m=0\) and \(C_{a}=30\) pF. The VCO with MWCNT achieves the best performance when \(m=1\) and \(C_{a}=20\) pF, and the VCO with MIWCM--when \(m=2\) and \(C_{a}=9\) pF. As in the case of \(R_{L}=\infty\) (see Table 11), for each value of \(m\) in Table 12, VCOs with MWCNT and MIWCM have significantly lower FOM than VCO with MCCM. Figures 27 and 28 show the dependence of phase noise versus offset frequency for VCOs with MIWCM at \(V_{d}=2\) V and \(V_{d}=12\) V when \(R_{L}=50\)\(\Omega\). The best value of phase noise of \(-139.0\) dBc/Hz at an offset frequency of 100 kHz and \(V_