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Discrete Fourier Transform Radar in the Terahertz-Wave Range Based on a Resonant-Tunneling-Diode Oscillator^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Measurement Principle

#### 2.1. Measurement Setup

#### 2.2. Single Target

#### 2.3. Multiple Target

#### 2.4. Advantage of Measuring Both Cosine and Sine Signals

#### 2.5. Resolution

#### 2.6. Distance Measurement Range

## 3. Experimental Verification

#### 3.1. Measurement Results on a Fixed Target

#### 3.2. Measurement Results on a Movable Target

#### 3.3. Distance Measurement on Two Targets

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the measurement setup. SG: signal generator; BT: bias tee; DC: power supply; BS: beam splitter; FMBD: Fermi-level-managed barrier diode detector; LNA: low-noise amplifier; LO: local oscillator input; RF: radio frequency input; IF intermediate frequency output; LPF: low-pass filter. Two power dividers are represented symbolically. The dashed rectangle is a commercial connectorized IQ mixer.

**Figure 2.**Measured IF output signals in the case of a single target, when the motor stage is placed at 0. The modulation frequency was scanned from 3 to 15 GHz in 256 steps.

**Figure 3.**The inverse Fourier transform of the signals in Figure 2. The horizontal axis is converted into distance; the vertical axis is the absolute value of the complex number produced by the Fourier transform. The inset is an expansion around the main peak and shows that the distance information is mainly contained in just three data points.

**Figure 4.**Distance measurement on one target at various positions of the motor stage, in 2 mm steps. The modulation frequency was scanned from 3 to 15 GHz in 512 steps. The top plot shows the absolute distance measured by the radar versus the stage position. As the measurement errors are too small to see at this scale, the bottom plot is added to show just the error, defined as the difference between the measured distance at each point and a linear fit through all points, with the slope fixed to 1. The standard deviation of the errors is 0.107 mm.

**Figure 5.**Measurement results on two targets, a fixed half mirror and a mobile full mirror; the modulation frequency had 512 values from 3 to 18 GHz. (

**a**) The Fourier transform when the mobile target is in its most distant position from the fixed target, with the motor stage at 200 mm. (

**b**) The distance to the two targets as measured by the DFT radar; the ranging errors included in the labels exclude the first 20 mm part of the motor stage position, where the two peaks are not clearly resolved. (

**c**,

**d**) The corresponding data for the case where a layer of cotton fabric was inserted in the beam on each side of the half mirror. The measurement errors are slightly larger.

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**MDPI and ACS Style**

Konno, H.; Dobroiu, A.; Suzuki, S.; Asada, M.; Ito, H.
Discrete Fourier Transform Radar in the Terahertz-Wave Range Based on a Resonant-Tunneling-Diode Oscillator. *Sensors* **2021**, *21*, 4367.
https://doi.org/10.3390/s21134367

**AMA Style**

Konno H, Dobroiu A, Suzuki S, Asada M, Ito H.
Discrete Fourier Transform Radar in the Terahertz-Wave Range Based on a Resonant-Tunneling-Diode Oscillator. *Sensors*. 2021; 21(13):4367.
https://doi.org/10.3390/s21134367

**Chicago/Turabian Style**

Konno, Hiroki, Adrian Dobroiu, Safumi Suzuki, Masahiro Asada, and Hiroshi Ito.
2021. "Discrete Fourier Transform Radar in the Terahertz-Wave Range Based on a Resonant-Tunneling-Diode Oscillator" *Sensors* 21, no. 13: 4367.
https://doi.org/10.3390/s21134367