# Absolute and Precise Terahertz-Wave Radar Based on an Amplitude-Modulated Resonant-Tunneling-Diode Oscillator

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principle

#### 2.1. Step 1: Absolute Propagation Time Difference

_{SG}is the oscillation amplitude and the oscillation phase is taken as zero.

_{ref}and Φ

_{meas}consist of phase shifts that are due to propagation delays as well as shifts produced by intervening circuit elements such as the terahertz-wave source, detector, amplifier, etc., denoted by φ

_{ref}and φ

_{meas}below.

_{ref}and t

_{meas}are the propagation times on the reference and measurement paths, respectively, and this derivation seeks to find the difference between them.

_{wrapped}below, is accessible in the waveform, for instance on an oscilloscope:

_{wrapped}is measured at two different modulation frequencies, f and f′, the following equations are obtained.

_{air}= 1.0003:

_{target}is that it represents the distance in air between the target and the point in the measurement path where the signal takes the same amount of time to arrive from the signal generator as it takes to propagate through the whole reference path. Depending on the optical and cable configuration, that point may be virtual (not a real point in air); also, if the reference path is long, d

_{target}may be negative.

#### 2.2. Error Estimation for Step 1

#### 2.3. Step 2: Improved Precision

_{round}is exactly zero; all fluctuations produced by noise have disappeared. With this error-free value of n we can now return to the measurement of the time delay at modulation frequency f (we will not use the measurement at f′) and replace n in Equation (8) with n

_{round}:

_{round}is exactly zero; the phase difference at the numerator can be determined by fitting as explained below Equation (23) and can only affect the result by a systematic amount. Using the same numerical example as above, specifically δτ = 1 ps, the uncertainty of measuring the propagation distance is now reduced drastically, from 12 mm to 0.3 mm.

## 3. Verification

#### 3.1. Experimental Setup

#### 3.2. Measurement Results

#### 3.3. Improvement Ideas

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Dobroiu, A.; Otani, C.; Kawase, K. Terahertz-wave sources and imaging applications. Meas. Sci. Technol.
**2006**, 17, R161–R174. [Google Scholar] [CrossRef] - Song, H.-J.; Nagatsuma, T. Handbook of Terahertz Technologies: Devices and Applications; Pan Stanford Publishing: Singapore, 2015; ISBN 978-981-4613-08-8. [Google Scholar]
- Asada, M.; Suzuki, S. Resonant tunneling diodes for terahertz sources. In Handbook of Terahertz Technologies: Devices and Applications; Song, H.-J., Nagatsuma, T., Eds.; Pan Stanford Publishing: Singapore, 2015; pp. 151–185. ISBN 978-981-4613-08-8. [Google Scholar]
- Suzuki, S.; Shiraishi, M.; Shibayama, H.; Asada, M. High-power operation of terahertz oscillators with resonant tunneling diodes using impedance-matched antennas and array configuration. IEEE J. Sel. Top. Quantum Electron.
**2013**, 19, 8500108. [Google Scholar] [CrossRef] - Kasagi, K.; Suzuki, S.; Asada, M. Large-element array of resonant-tunneling-diode terahertz oscillator for high output power at 1 THz region. In Proceedings of the Compound Semiconductor Week (CSW2018), Cambridge, MA, USA, 29 May–1 June 2018. [Google Scholar]
- Nuss, M.C.; Orenstein, J. Terahertz time-domain spectroscopy. In Millimeter and Submillimeter Wave Spectroscopy of Solids; Grüner, G., Ed.; Springer: Berlin/Heidelberg, Germany, 1998; ISBN 978-3-662-30953-7. [Google Scholar]
- Cooper, K.B.; Dengler, R.J.; Llombart, N.; Thomas, B.; Chattopadhyay, G.; Siegel, P.S. THz imaging radar for standoff personnel screening. IEEE Trans. Terahertz Sci. Technol.
**2011**, 1, 169–182. [Google Scholar] [CrossRef] - Caris, M.; Stanko, S.; Wahlen, A.; Sommer, R.; Wilcke, J.; Pohl, N.; Leuther, A.; Tessman, A. Very high resolution radar at 300 GHz. In Proceedings of the 44th European Microwave Conference, Rome, Italy, 6–9 October 2014; pp. 1797–1799. [Google Scholar]
- Jaeschke, T.; Bredendiek, C.; Pohl, N. A 240 GHz ultra-wideband FMCW radar system with on-chip antennas for high resolution radar imaging. In Proceedings of the 2013 IEEE MTT-S International Microwave Symposium Digest, Seattle, WA, USA, 2–7 June 2013. [Google Scholar] [CrossRef]
- Wang, X.; Hou, L.; Zhang, Y. Continuous-wave terahertz interferometry with multiwavelength phase unwrapping. Appl. Opt.
**2010**, 49, 5095–5102. [Google Scholar] [CrossRef] [PubMed] - Nilssen, O.K.; Boyer, W.D. Amplitude modulated CW radar. IRE Trans. Aerosp. Navig. Electron.
**1962**, 4, 250–254. [Google Scholar] [CrossRef] - Hu, J.; Wakasugi, R.; Suzuki, S.; Asada, M. Amplitude-modulated continuous wave ranging system with resonant-tunneling-diode terahertz oscillator. In Proceedings of the 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), Nagoya Aichi, Japan, 9–14 September 2018. [Google Scholar]
- Ikeda, Y.; Kitagawa, S.; Okada, K.; Suzuki, S.; Asada, M. Direct intensity modulation of resonant-tunneling-diode terahertz oscillator up to ~30 GHz. IEICE Electron. Express
**2015**, 12, 20141161. [Google Scholar] [CrossRef] - Izumi, R.; Suzuki, S.; Asada, M. 1.98 THz resonant-tunneling-diode oscillator with reduced conduction loss by thick antenna electrode. In Proceedings of the 2017 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), Quintana Roo, Mexico, 27 August–1 September 2017. [Google Scholar]
- Asada, M.; Suzuki, S. Theoretical analysis of external feedback effect on oscillation characteristics of resonant-tunneling-diode terahertz oscillators. Jpn. J. Appl. Phys.
**2015**, 54, 070309. [Google Scholar] [CrossRef] - Manh, L.D.; Diebold, S.; Nishio, K.; Nishida, Y.; Kim, J.; Mukai, T.; Fujita, M.; Nagatsuma, T. External feedback effect in terahertz resonant tunneling diode oscillators. IEEE Trans. Terahertz Sci. Technol.
**2018**, 8, 455–464. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Schematic of a propagation time difference measurement setup. S.G. = signal generator. Osc. = oscilloscope. Ref. = cable carrying the reference signal. Meas. = the measurement arm, consisting both of cables and free-space propagation. Tx = transmitter. Rx = receiver. (

**b**) Time delay measurement.

**Figure 2.**(

**a**) Resonant-tunneling diode (RTD) layer structure. (

**b**) I–V curve for a typical RTD, showing a biasing interval where the differential conductance is negative. (

**c**) The RTD device containing biasing pads and a slot antenna. The device area is about 1 × 1 mm.

**Figure 3.**(

**a**) Measured I–V curve of the RTD chip used for this experiment. The chip includes a stabilization resistor connected in parallel with the RTD, as shown in Figure 2c, which explains the difference from the typical I–V curve around the NDC region. (

**b**) The dependence of the RTD output power on the bias voltage; dots: measured data; solid line: data smoothed to show the average trend. The large fluctuations are due to terahertz radiation coming back to the RTD and affecting its oscillation frequency. The strongest carrier power, almost 10 µW, is obtained at a bias voltage of around 0.60 V, but the amplitude modulation is the most efficient at 0.56 V.

**Figure 5.**Distance measured by the radar versus actual target displacement distance. After applying the second step of the algorithm, the errors become too small to see in this plot.

**Figure 6.**Errors in the distance measurement. The largest deviation after the first step is +7.7 mm (at position 70 mm); after the second step the largest deviation is −0.61 mm (at a position of 130 mm).

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## Share and Cite

**MDPI and ACS Style**

Dobroiu, A.; Wakasugi, R.; Shirakawa, Y.; Suzuki, S.; Asada, M.
Absolute and Precise Terahertz-Wave Radar Based on an Amplitude-Modulated Resonant-Tunneling-Diode Oscillator. *Photonics* **2018**, *5*, 52.
https://doi.org/10.3390/photonics5040052

**AMA Style**

Dobroiu A, Wakasugi R, Shirakawa Y, Suzuki S, Asada M.
Absolute and Precise Terahertz-Wave Radar Based on an Amplitude-Modulated Resonant-Tunneling-Diode Oscillator. *Photonics*. 2018; 5(4):52.
https://doi.org/10.3390/photonics5040052

**Chicago/Turabian Style**

Dobroiu, Adrian, Ryotaka Wakasugi, Yusuke Shirakawa, Safumi Suzuki, and Masahiro Asada.
2018. "Absolute and Precise Terahertz-Wave Radar Based on an Amplitude-Modulated Resonant-Tunneling-Diode Oscillator" *Photonics* 5, no. 4: 52.
https://doi.org/10.3390/photonics5040052