Proposal of Bow-Tie Antenna-Integrated Resonant Tunneling Diode Transmitter Utilizing Relaxation Oscillations and Its Application to Short-Distance Wireless Communications

Abstract

We propose a resonant tunneling diode (RTD)-based relaxation oscillator and an oscillator-based terahertz (THz) wireless link that compensate for shortfalls in RF-oscillator emission power by adding several relaxation carrier wave harmonic modes. We believe that the proposed link can perform as well as or superior to large component-based wireless links that suppress power dissipation using collimating lenses and/or discrete antennas to add the power output of a relaxation oscillator. This hypothesis is investigated analytically using a physics-based equivalent circuit model of the proposed oscillator and a link budget analysis of the relaxation carrier wave. The model, which incorporates effects such as the non-linearity of the tunneling diode and the electromagnetic properties of the integrated bow-tie antenna on the oscillator, is used to quantitatively investigate the link characteristics in terms of the signal-to-noise ratio (SNR) and other parameters and to demonstrate that, by applying an appropriate device size and number of harmonic modes in the occupied bandwidth, link performance comparable to that of previously reported wireless links can be achieved. Based on these results, we discuss the potential for practical implementation of the proposed link configuration in mobile link applications for use in environments such as the Internet of Things (IoT).

Appendices

Appendix A: Equivalent Circuit Parameters

Table 3 summarizes all of the equivalent circuit parameters and their basic physics with respect to antenna size, D, and line width, w_shunt. As the EM field distribution around/on the oscillator is specific and complicated, it was quite difficult to evaluate the values of several parameters, whose “physics” states are therefore given as “N/A.”

Table 3 Values of Equivalent Circuit Parameters De-Embedded by Optimization Method (Dimensions: structural length [μm]), resistance [O], inductance [pH], capacitance [fF], and ξ [dimensionless]

Appendix B: Definitions of the Radiation Efficiency

In the case of the EM simulation, the radiation efficiency, η_EM(ω, D, w_shunt), is defined as follows:

$$ \eta_{\text{EM}}(\omega,D,w_{shunt}) \equiv \frac{P_{rad(\text{EM})}(\omega,D,w_{shunt})}{P_{in(\text{EM})}(\omega,D,w_{shunt})}. $$

(24)

P_rad(EM)(ω, D, w_shunt) is the surface integral of the Poynting power on the radiated field.

$$ P_{rad(\text{EM})}(\omega,D,w_{shunt}) \!=\!\! \int \!\! \int_{S} \frac{\Re \left[\tilde{\boldsymbol{E}}(\omega,D,w_{shunt},\boldsymbol{r})\!\times\! \tilde{\boldsymbol{H}}^{*}(\omega,D,w_{shunt},\boldsymbol{r}) \right] }{2} \cdot d\boldsymbol{S}. $$

(25)

P_in(EM)(ω, D, w_shunt) is given by,

$$\begin{array}{@{}rcl@{}} P_{in(\text{EM})}(\omega,D,w_{shunt})=\frac{\left| V_{0} \right|^{2}}{2Z_{0}}\left( 1 - \left| \tilde{{\Gamma}}_{\text{EM}}(\omega,D,w_{shunt}) \right|^{2} \right), \end{array} $$

(26)

where $\tilde {{\Gamma }}_{\text {EM}}(\omega ,D,w_{shunt})$ is the reflection coefficient seen from the a-a^′ port.

For the circuit analysis, the radiation efficiency, η_cir(ω, D, w_shunt), is described as,

$$ \eta_{\text{cir}}(\omega,D,w_{shunt}) \equiv \frac{P_{rad(\text{cir})}(\omega,D,w_{shunt})}{P_{in(\text{cir})}(\omega,D,w_{shunt})}, $$

(27)

where

$$ P_{rad(\text{cir})}(\omega,D,w_{shunt})= \frac{|\tilde{V}_{rad}(\omega,D,w_{shunt})|^{2}}{2 R_{rad}(D,w_{shunt})} $$

(28)

is the power consumption by the radiated resistance, R_rad(D, w_shunt). $\tilde {V}_{rad}(\omega ,D,w_{shunt})$ is applied to R_rad(D, w_shunt), depicted in Fig. 3a. The input power, P_in(cir)(ω, D, w_shunt), is given by,

$$ P_{in(\text{cir})}(\omega,D,w_{shunt}) = \Re \left[ \frac{1}{2} \tilde{V}_{in(\text{cir})}(\omega,D,w_{shunt}) \tilde{I}_{in(\text{cir})}^{*}(\omega,D,w_{shunt}) \right], $$

(29)

where $\tilde {V}_{in(\text {cir})}(\omega ,D,w_{shunt})$ and $\tilde {I}_{in(\text {cir})}(\omega ,D,w_{shunt})$ are defined by,

$$\begin{array}{@{}rcl@{}} \tilde{V}_{in(\text{cir})}(\omega,D,w_{shunt})&= V_{0} \left[ 1 + \tilde{{\Gamma}}_{\text{cir}}(\omega,D,w_{shunt}) \right], \end{array} $$

(30)

$$\begin{array}{@{}rcl@{}} \tilde{I}_{in(\text{cir})}(\omega,D,w_{shunt})&=\frac{V_{0}}{Z_{0}} \left[ 1 - \tilde{{\Gamma}}_{\text{cir}}(\omega,D,w_{shunt}) \right], \end{array} $$

(31)

$$\begin{array}{@{}rcl@{}} \tilde{{\Gamma}}_{\text{cir}}(\omega,D,w_{shunt})&= \displaystyle \frac{Z_{in(\text{cir})}(\omega,D,w_{shunt})-Z_{0}}{Z_{in(\text{cir})}(\omega,D,w_{shunt})+Z_{0}}, \end{array} $$

(32)

where Z_in(cir)(ω, D, w_shunt) indicates the impedance seen from the a-a^′ port.

Appendix C: Fundamental Equations for Oscillation Analysis

We derived simultaneous differential equations for the variables of the equivalent circuit shown in Fig. 5. All of the oscillation characteristics presented in this paper were analyzed by solving these equations. The numerical calculations were carried out using the fourth-order Runge-Kutta method:

$$ \frac{d i_{c}}{dt} = \frac{1}{2 L_{c}} [ V_{b} - R_{b} i_{c} - R_{L} (i_{c} -i_{E2})]. $$

(33)

$$ \frac{d i_{E1}}{dt} = \frac{1}{L_{E1}} (v_{CE} - R_{E} i_{E1}). $$

(34)

$$\begin{array}{@{}rcl@{}} \frac{d i_{st}}{dt} = \frac{1}{2 L_{st}} [v_{CL} - (2 R_{st} + R_{L}) i_{st}], \end{array} $$

(35)

$$ \frac{d v_{Crtd}}{dt} = \frac{1}{C_{rtd}} (i_{mesa} - i_{rtd}), $$

(36)

$$ \frac{d v_{CE}}{dt} = \frac{1}{C_{E}} (i_{E2} - i_{E1}), $$

(37)

$$ \frac{d v_{CL}}{dt} = \frac{1}{C_{L}} (i_{E} - i_{st}). $$

(38)

$$\begin{array}{@{}rcl@{}} \frac{d i_{gap}}{dt}&\!=\!& \left[{\displaystyle 2 \xi L_{arms} \left( 1 \!+\! \frac{L_{gap}}{L_{mesa}}\right) \!+\! L_{gap}}\right]^{-1} \times \left[ v_{Cas} - 2\xi R_{arms} (i_{mesa} + i_{gap})\right.\\ &&\left.\!- \left( \frac{2 \xi L_{arms}}{L_{mesa}}\right)\! (R_{gap} i_{gap} \!+\! v_{Cgap})\!+\!\> \frac{2 \xi L_{arms}}{L_{mesa}}(v_{rtd} \!+\! R_{mesa} i_{mesa}) \right] . \end{array} $$

(39)

$$ \frac{d i_{mesa}}{dt} = \frac{1}{L_{mesa}} (R_{gap} i_{gap} + L_{gap} A + v_{Cgap} - v_{rtd} - R_{mesa} i_{mesa}), $$

(40)

where the variable A is defined as $\displaystyle A \equiv \frac {d i_{gap}}{dt}$.

$$ \frac{d i_{armin}}{dt} = \frac{1}{2 \xi L_{arms}}\left( v_{Cas} - 2 \xi R_{arms} i_{armin} - \> R_{gap} i_{gap} - L_{gap} A - v_{Cgap}\right). $$

(41)

$$ \frac{d v_{Cas}}{dt} = \frac{1}{C_{as}} (i_{armout} - i_{armin}), $$

(42)

$$ \frac{d v_{Csub}}{dt} = \frac{1}{C_{sub}} i_{sub}, $$

(43)

$$ \frac{d v_{CEsub}}{dt} = \frac{1}{C_{Esub}} i_{Esub}, $$

(44)

$$ \frac{d v_{CLsub}}{dt} = \frac{1}{C_{Lsub}} i_{Lsub}, $$

(45)

$$ \frac{d v_{Cgap}}{dt} = \frac{1}{C_{gap}} i_{gap}. $$

(46)

$$ \frac{d v_{Crad}}{dt} = \frac{1}{C_{rad}} i_{rad}, $$

(47)

where i_rad can be defined by,

$$ i_{rad}\equiv i_{E2} - i_{armout} - i_{E} - i_{Lsub} - i_{sub} - i_{Esub}. $$

(48)

$$ \frac{d i_{sub}}{dt} = \frac{1}{L_{sub}} [ v_{Crad} + R_{sub} i_{sub} - v_{Csub} + R_{rad} i_{rad}], $$

(49)

$$ \frac{d i_{Lsub}}{dt} =\frac{1}{L_{Lsub}} [ v_{Crad} + R_{Lsub} i_{Lsub} - v_{CLsub} + R_{rad} i_{rad}], $$

(50)

$$ \frac{d i_{Esub}}{dt} = - \frac{1}{L_{sub}}[ v_{Crad} +R_{Esub} i_{Esub} - v_{CEsub} + R_{rad} i_{rad}] . $$

(51)

$$ \frac{d i_{armout}}{dt}= [2 (1 - \xi ) L_{arms}]^{-1} (v_{Crad} + R_{rad} i_{rad} - v_{Cas}- 2 (1 - \xi ) R_{arms} i_{armout}). $$

(52)

$$ \frac{d i_{E2}}{dt} = \frac{-1}{L_{E2}} [ v_{Crad} + v_{CE} + R_{L} (i_{E2} - i_{c} ) + R_{rad} i_{rad}]. $$

(53)

$$ \frac{d i_{E}}{dt} = \frac{1}{2 L_{E}} [ v_{Crad} - v_{CL} + R_{rad} i_{rad}]. $$

(54)