# Two-Terminal Electronic Circuits with Controllable Linear NDR Region and Their Applications
## 6 Applications
### Simulation of Negative Differential Resistance  
By inequality (23), the steepness of the current-voltage characteristics in the vicinity of the operating point significantly affects the self-excitation of an oscillator. The less the absolute value of the differential resistance, the greater is the probability of self-excitation of the oscillator.  
Table 7 shows the simulation results of the differential resistance at the operating point \(V_{1,2}=4\) V for two-terminal NDR circuits shown in Figures 3-5 using the same input data as Table 4. As shown in Table 7, the smallest absolute value of NDR at the operating point has a two-terminal NDR circuit with an improved Wilson CM. The NDR circuit with a Wilson CM has a little greater absolute value of NDR. The circuit with a cascode CM has the most considerable absolute value of NDR for any \(m\). Thus, the improved Wilson and Wilson CM oscillators have the best start-up conditions due to inequality (23).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of NDR Circuit \(\rightarrow\)** & \multicolumn{2}{c}{**Two-Terminal NDR Circuit with Multiple-Output**} \\ \hline
**The Relative Accuracy of the** & **Cascode** & **Wilson Current** & **Improved** \\ \(I_{Y}\)**Current Calculation** & **Current Mirror** & **Mirror** & **Wilson Current** \\ \(\downarrow\) & **Current Mirror** & **Mirror** & **Mirror** \\ \hline \(\Delta I_{Y}\)\%, \(m=0\) & 12.5\% & 10.5\% & 10.3\% \\ \(\Delta I_{Y}\)\%, \(m=1\) & 17.3\% & 12.2\% & 14.1\% \\ \(\Delta I_{Y}\)\%, \(m=2\) & 20.9\% & 15.7\% & 16.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: The relative accuracy of the \(I_{Y}\) current calculation for different two-terminal NDR circuits (\(T_{0}\)—PHEMT).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of NDR Circuit \(\rightarrow\)** & \multicolumn{2}{c}{**Two-Terminal NDR Circuit with Multiple-Output**} \\ \hline
**Negative** & **Cascode** & **Wilson Current** & **Improved** \\
**Differential Resistance \(R_{diff}\) (k\(\Omega\))** & **Current Mirror** & **Mirror** & **Mirror** \\ \(\downarrow\) & **Mirror** & **Mirror** & **Mirror** \\ \hline \(m=0\) & \(-6.25\) & \(-5.56\) & \(-5.41\) \\ \hline \(m=1\) & \(-3.07\) & \(-2.70\) & \(-2.67\) \\ \hline \(m=2\) & \(-2.63\) & \(-1.85\) & \(-1.80\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Simulated negative differential resistance for different two-terminal NDR circuits (\(T_{0}\)—PHEMT).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of NDR Circuit \(\rightarrow\)** & \multicolumn{2}{c}{**Two-Terminal NDR Circuit with Multiple-Output**} \\ \hline
**Parameter of I–V Characteristic** & **Cascode** & **Wilson Current** & **Improved** \\ \(\downarrow\) & **Current Mirror** & **Mirror** & **Wilson Current** \\ \hline \(V_{Y}\) (V) & 2.8 & 2.8 & 2.8 \\ \hline \(I_{Y}\) (mA), \(m=0\) & 5.6 & 5.7 & 5.8 \\ \hline \(I_{Y}\) (mA), \(m=1\) & 8.1 & 8.2 & 8.5 \\ \hline \(I_{Y}\) (mA), \(m=2\) & 10.5 & 10.8 & 11.1 \\ \hline \(V_{Z}\) (V) & 13.6 & 13.6 & 13.6 \\ \hline \(I_{Z}\) (mA) & 3.2 & 3.2 & 3.2 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Simulated parameters of current-voltage characteristics for different two-terminal NDR circuits (\(T_{0}\)—PHEMT).