# Two-Terminal Electronic Circuits with Controllable Linear NDR Region and Their Applications
## 6 Applications
### Negative Differential Resistance Voltage-Controlled Oscillators
A practically zero error exists in calculating the current \(I_{Z}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of NDR Circuit \(\rightarrow\)** & \multicolumn{3}{c}{**NDR Circuit with Multiple-Output**} \\ \hline
**Parameter of I–V Characteristics** & **Cascode** & **Wilson Current** & **Improved** \\ \(\downarrow\) & **Current Mirror** & **Mirror** & **Wilson Current** \\ \hline \(V_{X}\) (V) & \(1.46\) & \(1.46\) & \(1.46\) \\ \hline \(I_{X}\) (mA) & \(0.5\) & \(0.5\) & \(0.5\) \\ \hline \(V_{Y}\) (V) & \(4.6\) & \(4.6\) & \(4.6\) \\ \hline \(I_{Y}\) (mA) & \(4.3\) & \(4.4\) & \(4.5\) \\ \hline \(I_{Y}\) (mA) & \(5.8\) & \(6.1\) & \(6.2\) \\ \hline \(I_{Y}\) (mA) & \(7.1\) & \(7.6\) & \(7.8\) \\ \hline \(V_{Z}\) (V) & \(10.2\) & \(10.2\) & \(10.2\) \\ \hline \(I_{Z}\) (mA) & \(3.5\) & \(3.5\) & \(3.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulated parameters of current-voltage characteristics for different two-terminal NDR circuits (\(T_{0}\)—JFET). Figure 16: Calculated current-voltage characteristics of the NDR circuit with multiple-output improved Wilson current mirror in the NDR region; \(m=0\)—green curve, \(m=1\)—blue curve, \(m=2\)—red curve. \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 Characteristics** & \begin{tabular}{c} **Cascode** \\ **Current** \\ **Mirror** \\ \end{tabular} & \
\begin{tabular}{c} **Wilson Current** \\ **Mirror** \\ \end{tabular} &
\begin{tabular}{c} **Improved** \\ **Wilson Current** \\ **Mirror** \\ \end{tabular} \\ \hline \(V_{Y}\) (V) & 4.6 & 4.6 & 4.6 \\ \hline \(I_{Y}\) (mA) & 4.6 & 4.6 & 4.7 \\ \(m=0\) & 4.6 & 4.6 & 4.7 \\ \hline \(I_{Y}\) (mA) & 6.4 & 6.4 & 6.7 \\ \(m=1\) & & & \\ \hline \(I_{Y}\) (mA) & 8.1 & 8.2 & 8.6 \\ \(m=2\) & & & \\ \hline \(V_{Z}\) (V) & 10.2 & 10.2 & 10.2 \\ \hline \(I_{Z}\) (mA) & 3.5 & 3.5 & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated parameters of current-voltage characteristics for different two-terminal NDR circuits (\(T_{0}\)—JFET). Figure 15: (**a**) Calculated current-voltage characteristics of the NDR circuit with multiple-output cascode current mirror in the NDR region; \(m=0\)—green curve, \(m=1\)—blue curve, \(m=2\)—red curve. (**b**) Calculated current-voltage characteristics of the NDR circuit with multiple-output Wilson current mirror in the NDR region; \(m=0\)—green curve, \(m=1\)—blue curve, \(m=2\)—red curve. Now, let us simulate the current-voltage characteristics for two-terminal NDR circuits presented in Figures 3-5 when transistor \(T_{0}\) is a PHEMT. We select ATF34143 as transistor \(T_{0}\) and MRFC521 as transistors in BJT CM and choose the following resistor values: \(R_{c}=300\ \Omega\) and \(R_{d}=4\ k\Omega\). Figures 17-19 show the current-voltage characteristics for the PHEMT based two-terminal NDR circuits with different multiple-output CM. Table 4 shows the values of voltages and currents at the breakpoints of characteristics. From the analysis of Table 4, the same conclusions follow as from the study of Table 1. As in using JFET, the PHEMT based two-terminal circuits also have a linear current dependence on voltage in the NDR region. We also calculate the current \(I_{1}\) at voltages \(V_{X}\), \(V_{Y}\), and \(V_{Z}\) using Equations (3), (5) and (7) with the following data of transistors ATF34143 [54] and MRFC521: \(b=0.24\) A/V\({}^{2}\), \(V_{TH}=\) -0.95 V, \(\alpha=4\) V\({}^{-1}\), \(\lambda=0.09\) V\({}^{-1}\), \(h_{FE}=50\), \(V_{A}=15\) V, \(V_{EB3}=0.7\) V. The values of resistors \(R_{c}\) and \(R_{d}\) are similar to those used in simulation. Tables 5 and 6 show the calculated currents \(I_{Y}\) and \(I_{Z}\) and the relative accuracy of the \(I_{Y}\) current calculation \(\Delta I_{Y}\) %.