# Two-Terminal Electronic Circuits with Controllable Linear NDR Region and Their Applications
###### Abstract  
Negative differential resistance (NDR) is inherent in many electronic devices, in which, over a specific voltage range, the current decreases with increasing voltage. Semiconductor structures with NDR have several unique properties that stimulate the search for technological and circuitry solutions in developing new semiconductor devices and circuits experiencing NDR features. This study considers two-terminal NDR electronic circuits based on multiple-output current mirrors, such as cascode, Wilson, and improved Wilson, combined with a field-effect transistor. The undoubtedly advantages of the proposed electronic circuits are the linearity of the current-voltage characteristics in the NDR region and the ability to regulate the value of negative resistance by changing the number of mirrored current sources. We derive equations for each proposed circuit to calculate the NDR region's total current and differential resistance. We consider applications of NDR circuits for designing microwave single frequency oscillators and voltage-controlled oscillators. The problem of choosing the optimal oscillator topology is examined. We show that the designed oscillators based on NDR circuits with Wilson and improved Wilson multiple-output current mirrors have high efficiency and extremely low phase noise. For a single frequency oscillator consuming 33.9 mW, the phase noise is \(-154.6\) dBc/Hz at a 100 kHz offset from a 1.310 GHz carrier. The resulting figure of merit is \(-221.6\) dBc/Hz. The implemented oscillator prototype confirms the theoretical achievements. controllable negative differential resistance; cascode current mirror; Wilson current mirror; oscillator; voltage-controlled oscillator; phase noise; power consumption; the figure of merit +
Footnote †: journal: Applied Sciences  
One of the main characteristics of any NDR circuit is the peak-to-valley current ratio (PVCR), which is the ratio of the peak to the valley current. In many practical tasks, it is necessary to be able to control the PVCR. For example, in oscillators, the PVCR determines the slope of the current-voltage characteristic in the NDR region, hence the value of the differential resistance at the operating point. In turn, the self-excitation of the oscillator depends on the value of the differential resistance. The literature review (see Section 2) shows that it is impossible to control PVCR in the NDR circuits of most published studies. In studies where it is possible, the maximum current level lies in the nA or \(\upmu\)A range. This study proposes new two-terminal NDR circuits that combine a field-effect transistor (FET) with a multiple-output cascade, Wilson, or improved Wilson current mirror (CM). Possible types of FETs include a junction field-effect transistor (JFET), metal-semiconductor field-effect transistor (MESFET), high-electron-mobility transistor (HEMT), or pseudomorphic high-electron-mobility transistor (PHEMT). In the analyzed circuits, we control PVCR by changing the number of mirrored currents. Here, we show that one could set the PVCR to any desired value. There are several advantages of the proposed method of controlling PVCR. Firstly, the power supply voltage keeps constant. Secondly, the peak point and valley point voltages are not changed with increasing the number of mirrored currents. Thirdly, the types of transistors are also not changed. Fourthly, the current-voltage characteristics in the NDR region are almost linear. Fifthly, the output resistance of the CM is exceptionally high, which is a valuable property for oscillator applications. The mathematical modeling of the total current in the NDR region has been conducted for all NDR circuits using JFET and PHEMT as a FET for Shockley and Curtice drain current equations. We consider the applications of the proposed NDR circuits for microwave oscillators and voltage-controlled oscillators (VCOs). The simulation results show that the circuit with multiple-output improved Wilson CM (MIWCM) has the highest slope of the current-voltage curve in the NDR region.