**Hirokazu Yamakura,* Michihiko Suhara***

Department of Electrical and Electronic Engineering, Tokyo Metropolitan University, 1-1, Minami-Osawa, Hachioji, Tokyo, 192-0397 JapanNano-Micro Conference, 2017, 1, 010001

Published Online: 15 September 2017 (Article)

DOI:10.11605/cp.nmc2017.01001

*Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.This email address is being protected from spambots. You need JavaScript enabled to view it.This email address is being protected from spambots. You need JavaScript enabled to view it.

## How to Cite

Hirokazu Yamakura, Michihiko Suhara. Modeling and Analysis of Bow-Tie Antenna Integrated Resonant-Tunneling-Diode Relaxation Oscillators for Wireless Radio Applications, *Nano-Micro Conference, *2017, **1**, 01001. doi: 10.11605/cp.nmc2017.01001

## History

Received 19 May 2017, Accepted 12 June 2017, Published 15 September 2017.

**Abstract**

We propose a self-complementary bow-tie antenna-integrated resonant-tunneling-diode relaxation oscillator and investigate its oscillation/radiation characteristics. In the investigation, we establish a physics-based equivalent circuit model of the oscillator for taking the all physical phenomena related to the diode and the antenna into consideration simultaneously. In this paper, we report the equivalent circuit modeling and the large-signal oscillation/radiation analysis of the oscillator.

**Introduction**

Terahertz (THz) technology has been received great deal of interest in terms of applications for spectroscopy, imaging, wireless communications, etc. In the wireless communication, the THz range is specifically one of the most attractive regions owing to the existence of the non-allocated frequency band. One of the main challenges of the THz wireless communication is the shortage of the emission RF power of the oscillator. We guess the challenge can be overcome by using the wideband-spectrum relaxation wave, whose entire emission RF power exceeds that of the narrowband sinusoidal wave, as the carrier.

From this perspective, we have proposed an oscillator consisting of a resonant tunneling diode (RTD) and a broadband bow-tie antenna [1] for generating a wideband-spectrum relaxation wave and their theoretical models expressed by equivalent circuits respectively [2,3]. Such a semiconductor-based oscillator for THz applications is generally fabricated as a monolithically-integrated configuration of an oscillation device, a radiation antenna, etc. As the performance of such an oscillator depends upon a both of their physics, which usually differ from each other, the performance evaluation method and the design guideline for the oscillator should be established as a physical-coupled scheme considering the all effects regarding the oscillator simultaneously.

In this paper, we focus on a physics-based modeling for the entire oscillator-structure we proposed and its oscillation/radiation performance evaluated by using the physics-based model.

**Modeling**

Schematics of the proposed oscillator are illustrated in Fig. 1.

Fig. 1 Schematics of a proposed oscillator |

A peripheral circuit in front serves as a bias circuit and that in back is added for adjusting the total impedance of the peripheral circuits. We establish a physics-based equivalent circuit model of each component, RTD, BTA, and the circuits, since it is considerably impossible to analyze the quantum phenomena of the RTD together with the electromagnetic (EM) properties of the other components by a single solver.

Simple block expressions of the oscillator are described in Fig. 2.

Fig.2 Block expressions of an equivalent circuit for the oscillator shown in Fig. 1 |

The impedance variables, Z_{f}(ω,D,w_{shunt}), Z_{b}(ω,D,w_{shunt}), and Z_{BTA}(ω,D), correspond to the equivalent circuit of the peripheral circuit in front, that in back, and the BTA, respectively. The RLC expression of Z_{BTA}(ω,D) has been reported in Ref.[2]. Additionally, the circuit model of the RTD and its theoretical expression has also been reported in Refs. [3,4], respectively.

The variables, Z_{f}(ω,D,w_{shunt}) and Z_{b}(ω,D,w_{shunt}), are composed of several RLC elements which can be explained by the electromagnetic properties: the surface impedance due to the skin effect [5], the straight micro stripline [6], fringe capacitance [7], and parasitic components regarding the semi-insulating substrate. The circuit elements involved in Z_{f}(ω,D,w_{shunt}) and Z_{b}(ω,D,w_{shunt}) are evaluated by the EM field distribution in the vicinity of the circuits calculated by the finite element method-based simulator, namely, COMSOL. Their approximate numerical values of the elements are also estimated by the physical interpretation based on the structural and material properties. More precise values are numerically de-embedded by using the optimization method, namely, the particle swarm optimization [8]. More details regarding the circuit identification process have also been reported in Ref. [2].

Fig. 3 summarizes the typical fitting results of the impedance and radiation characteristics regarding the peripheral circuit/entire oscillator.

From Fig. 3, the equivalent circuit expression is quantitatively valid for the evaluation of the radiation/oscillation characteristics by the circuit analysis around the first resonance frequency of the oscillator. Oscillation AnalysisThe non-linear oscillation analysis of the proposed oscillator is performed by using the equivalent circuit above mentioned. The non-linearity of the RTD is involved by considering the measured current-voltage (I-V) characteristics [9]. The supplied voltage, V_{b}, is set to a constant value to keep the negative differential conductance of the RTD maximum. More details regarding the oscillation analysis methodology have been reported in Refs. [10,11].

Fig. 4 displays the current density-voltage (J-V) characteristics of the RTD and the time-dependent orbit of the current density, i_{rtd}(t)/S, in the RTD, where S indicates the mesa area.

We classify the oscillation modes depicted the dotted and chain lines in Fig. 4 designated as the "sinusoidal" and the "relaxation" mode, respectively. The modes are quantitatively distinguished by the cycle number of the i_{rtd}(t)/S trajectory in Fig. 4; if the cycle number is unity, the mode is a "sinusoidal mode"; else, it is a "relaxation mode". The entire emission RF power of the relaxation mode shown in Fig. 4 is ~ 6 dBm greater than that of the sinusoidal mode when the upper limit value of band is approximately set to 400 GHz. It is suggested that the relaxation wave can compensate for the shortage of the emission RF power if we employ a certain band appropriately. Moreover, it is found that the oscillation mode can be designed by adjusting the two parameters, D and w_{shunt}, appropriately. According to Shannon-Hartley theorem [12], the capacity of a wireless channel is directly proportional to the channel bandwidth. Therefore, the wideband-spectrum relaxation wave can contribute to the possibility of large-capacity wireless transmissions together with compensating for the RF power shortage.

**Conclusion**

We investigated radiation/oscillation characteristics of the resonant tunneling diode-based relaxation oscillator by using its physics-based equivalent circuit model. The advantage of a wideband-spectrum relaxation wave as the carrier was revealed in terms of the entire emission RF power. Our further studies will represent the link-budget analysis of the relaxation carrier wave-based THz wireless link to clarify the advantage of the relaxation carrier regarding the link performance.

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