# Two-Terminal Electronic Circuits with Controllable Linear NDR Region and Their Applications
## 6 Applications
### Simulation of Oscillator Characteristics  
Let us simulate the characteristics for oscillators presented in Figures 6-8 by ADS2020. As transistor \(T_{0}\), we use ATF34143 and MRFC521 as transistors in BJT CM. We select chip inductor 0604 HQ-1N1 XJR (1.15 nH), and \(C_{1}=C_{2}=1\) pF, \(R_{c}=300\)\(\Omega\), \(R_{d}=4\) k\(\Omega\), \(C_{b}=300\) nF, and \(V_{1,2}=4\) V for all oscillators. We selected the value of capacitance \(C_{a}\) from the condition of minimizing the phase noise of each oscillator. We use FOM (22) to compare oscillators shown in Figures 6-8. Table 8 shows the results of the oscillators' simulation under the assumption that load resistance (\(R_{L}\)) is infinite. As shown in Table 8, oscillators with MCCM, MWCM, and MIWCM have the best FOM value when \(m\) is 0, 2, and 1, respectively. Among all oscillators, the best FOM of \(-227.1\) dBc/Hz has the one with MWCM when \(m=2\). For each value of \(m\) in Table 8, oscillators with MWCM and MIWCM have significantly better FOM than the oscillator with MCCM. For each value of \(m\), the oscillator with MCCM has the highest oscillation frequency, the lowest power of dissipation, and the worst phase noise. Figure 20 shows the dependence of phase noise versus offset frequency for the oscillator with MWCM. As shown in Figure 20, the best value of phase noise of \(-159.9\) dBc/Hz at an offset frequency of 100 kHz is the case when \(m=2\) and \(C_{a}=3\) pF. Figure 21 shows the dependence of phase noise versus capacitance \(C_{b}\) for the oscillator with multiple-output Wilson CM. We can see from Figure 21 that oscillator phase noise significantly depends on the value of \(C_{b}\). Indeed, when capacitance \(C_{b}\) varies from 3 to 300 nF, phase noise decreases from \(-125.5\) to \(-159.9\) dBc/Hz. We can explain such a decrease in phase noise by reducing noise spectral density at the drain of transistor \(T_{0}\) where capacitor \(C_{b}\) is connected. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{4}{c}{**Oscillator Characteristics**} \\ \cline{3-6}
**Type of** & **Capacitance, \(C_{a}\)** & **Frequency of** & **Phase Noise at an Offset Frequency of** & **Power of** & **The Figure of** \\
**Oscillator** & **(pF)** & **Operation, \(f\)** & **10\({}^{5}\) Hz, \(P\)N** & **Dissipation, \(P_{dis}\)** & **Merit, \(FOM\)** \\  & & **(MHz)** & **(dBc/Hz)** & **(mW)** & **(dBc/Hz)** \\ \hline MCCM & & & & & \\ (\(m=0\)) & 8 & 2019 & \(-125.4\) & 18.8 & \(-198.8\) \\ \hline MCCM & & & & & \\ (\(m=1\)) & 8 & 1627 & \(-104.4\) & 25.2 & \(-174.6\) \\ \hline MCCM & & & & & \\ (\(m=2\)) & 25 & 1412 & \(-104.7\) & 31.0 & \(-172.8\) \\ \hline MWCM & & & & & \\ (\(m=0\)) & 1 & 1958 & \(-150.7\) & 19.6 & \(-223.6\) \\ \hline MWCM & & & & & \\ (\(m=1\)) & 1 & 1556 & \(-151.1\) & 27.0 & \(-220.6\) \\ \hline MWCM & & & & & \\ (\(m=2\)) & 3 & 1335 & \(-159.9\) & 33.9 & \(-227.1\) \\ \hline MIWCM & & & & & \\ (\(m=0\)) & 3 & 1951 & \(-145.0\) & 19.8 & \(-217.8\) \\ \hline MIWCM & & & & & \\ (\(m=1\)) & 1 & 1554 & \(-152.0\) & 27.4 & \(-221.5\) \\ \hline MIWCM & & & & & \\ (\(m=2\)) & 2 & 1333 & \(-152.6\) & 34.5 & \(-219.7\) \\ \hline \end{tabular}
\end{table} 
Table 8: Simulated characteristics of different NDR oscillators when \(R_{L}=\infty\). Let us now consider the case when a load \(R_{L}\) is connected through the capacitive divider to an oscillator output, as shown in Figure 22. Assume that \(R_{L}=50\)\(\Omega\) and \(C_{CD1}=C_{CD2}=0.5\) pF for the oscillators with MIWCM (\(m=0\), \(1\), \(2\)) and MWCM (\(m=0\)). For the oscillators with MCCM (\(m=0\), \(1\), \(2\)) and MWCM (\(m=1\), \(2\)), we selected \(C_{CD1}=C_{CD2}=0.25\) pF. Figure 21: Phase noise versus offset frequency for the oscillator with multiple-output Wilson current mirror when \(R_{L}=\infty\); \(C_{b}=300\) nF—red curve, \(C_{b}=30\) nF—blue curve, \(C_{b}=3\) nF—purple curve. Figure 22: A capacitive divider with load resistance \(R_{L}\) at the oscillator output. Using FOM (22), we compare oscillators shown in Figures 6-8 when \(R_{L}=50\ \Omega\).