# Two-Terminal Electronic Circuits with Controllable Linear NDR Region and Their Applications
## 6 Applications
### Simulation of VCO Characteristics  
Let us now simulate the characteristics for VCOs presented in Figures 9-11 by using the same transistors, resistor values of \(R_{c}\) and \(R_{d}\), inductor type of \(L\), and power supply voltage as in Section 7.3 when \(R_{L}=\infty\). We select varactors SMV1104-33. The tuning voltage \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Oscillator Load, \(R_{L}\) (\(\Omega\))**} & \multicolumn{3}{c}{**The Figure of Merit (dBc/Hz)**} \\ \cline{2-4}  & \multicolumn{3}{c}{**Type of Oscillator**} \\ \hline  & \multicolumn{2}{c}{MCCM} & MWCM & MIWCM \\ \hline \(\infty\) & \(-198.8\) & \(-227.1\) & \(-221.5\) \\ \hline
50 & \(-189.1\) & \(-221.6\) & \(-219.8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Performance comparison of oscillators with different loads. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Type of** \\ **Oscillator** \\ \end{tabular} } & \multirow{2}{*}{**Capacitance, \(C_{a}\)**} & \multicolumn{3}{c}{**Precency of**} & \multicolumn{3}{c}{**Phase Noise at an**} \\  & & **Operation, \(f\)** & **Offset Frequency of** & **DISSipation, \(P_{dis}\)** & **The Figure of Merit, \(FOM\)** \\  & & **(MHz)** & **10\({}^{5}\) Hz, \(PN\)** & **(mW)** & **(dBc/Hz)** \\ \hline MCCM (\(m=0\)) & \(28\) & \(1925\) & \(-116.1\) & \(18.8\) & \(-189.1\) \\ \hline MCCM (\(m=1\)) & \(15\) & \(1582\) & \(-103.9\) & \(25.2\) & \(-173.9\) \\ \hline MCCM (\(m=2\)) & \(25\) & \(1384\) & \(-90.0\) & \(31.0\) & \(-157.9\) \\ \hline MWCM (\(m=0\)) & \(15\) & \(1800\) & \(-143.1\) & \(19.6\) & \(-215.3\) \\ \hline MWCM (\(m=1\)) & \(3\) & \(1519\) & \(-149.8\) & \(27.0\) & \(-219.1\) \\ \hline MWCM (\(m=2\)) & \(7\) & \(1310\) & \(-154.6\) & \(33.9\) & \(-221.6\) \\ \hline MIWCM (\(m=0\)) & \(7\) & \(1800\) & \(-144.9\) & \(19.8\) & \(-217.0\) \\ \hline MIWCM (\(m=1\)) & \(5\) & \(1483\) & \(-150.8\) & \(27.4\) & \(-219.8\) \\ \hline MIWCM (\(m=2\)) & \(2\) & \(1294\) & \(-148.3\) & \(34.5\) & \(-215.2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Simulated characteristics of different NDR oscillators when \(R_{L}=50\ \Omega\). \(V_{d}\) is varied from 2 to 12 V for each VCO. Capacitance \(C_{b}\) = 50 nF for VCOs with MCCM and C\({}_{b}\) = 300 nF for VCOs with MWCM and MIWCM. As in Section 7.3, we select the value of capacitance \(C_{a}\) from the condition of minimizing the phase noise of each VCO. Figures 23 and 24 show the dependence of phase noise versus offset frequency for VCOs with MIWCM at \(V_{d}\) = 2 V and \(V_{d}\) = 12 V. The best value of phase noise of \(-\)137.9 dBc/Hz at an offset frequency of 100 kHz and \(V_{d}\) = 2 V has VCO with MIWCM when \(m\) = 2 (see Figure 23). The best value of phase noise of \(-\)152.5 dBc/Hz at an offset frequency of 100 kHz and \(V_{d}\) = 12 V also has VCO with MIWCM but when \(m\) = 1 (see Figure 24). Figure 23: Phase noise versus offset frequency for VCO with multiple-output improved Wilson current mirror when \(V_{d}\) = 2 V, \(R_{L}\) = \(\infty\); \(m\) = 0—purple curve (\(C_{a}\) = 10 pF), \(m\) = 1—blue curve (\(C_{a}\) = 7 pF), \(m\) = 2—red curve (\(C_{a}\) = 6 pF). Figure 24: Phase noise versus offset frequency for VCO with multiple-output improved Wilson current mirror when \(V_{d}\) = 12 V, \(R_{L}\) = \(\infty\); \(m\) = 0—purple curve (\(C_{a}\) = 10 pF), \(m\) = 1—blue curve (\(C_{a}\) = 7 pF), \(m\) = 2—red curve (\(C_{a}\) = 6 pF). Interestingly, at \(V_{d}=2\) V, the phase noise improvement occurs in the sequence of \(m=0,\,1,\,2\), i.e., the more mirrored currents, the lower the phase noise (see Figure 23). However, at \(V_{d}=12\) V, the phase noise improvement occurs in \(m=0,\,2,\,1\), i.e., the highest phase noise occurs at \(m=0\), and the lowest at \(m=1\) (see Figure 24). The phase noise curve at \(m=2\) occupies an intermediate position. Table 11 shows the simulated characteristics of different VCOs when \(R_{L}=\infty\), where \(f_{min}\) and \(f_{max}\) are the minimum and maximum frequency of VCO operation.