Introduction
The upper millimeter-wave and THz frequency ranges are interesting for multiple applications, like material characterization and localization, medical applications, and non-destructive testing [Reference Hillger, van Delden, Thanthrige, Ahmed, Wittemeier, Arzi, Andree, Sievert, Prost, Rennings, Erni, Musch, Weimann, Sezgin, Pohl and Pfeiffer1–Reference Kueppers, Jaeschke, Pohl and Barowski5]. This frequency range is not only of importance because of the large available bandwidth, but also because of the high center frequency, as unique material fingerprints often occur in the THz range [Reference Barowski and Rolfes6]. Furthermore, the high operating frequency enables the implementation of fully integrated measurement systems because of the possibility of integrating the antennas on the monolithic microwave integrated circuits (MMIC) due to the small wavelength at these frequencies. Millimeter-wave and THz frequencies enable smaller package sizes and a higher channel count in MIMO and phased-array applications and, therefore, a higher lateral resolution [Reference Wittemeier, Ahmed, Tran, Sezgin and Pohl7].
There are also challenges associated with the high frequency of these systems. Due to the limited availability of THz-ready semiconductor technologies, designing circuits targeting this frequency range is challenging, as many circuits operate at or above the transistors’ transit frequencies. Therefore, the transmitter’s radiated power, as well as the receiver’s conversion gain is often limited. Furthermore, due to the high losses of bond interconnections [Reference Krems, Haydl, Massler and Rudiger8], integrated antennas are the primary method of interfacing the THz circuits with the environment. These antennas typically have low bandwidth and efficiencies because of the small distance between the radiating element and the ground plane of the MMIC [Reference Wang, Yi, Xu, Zheng, Che and Xue9].
In recent years, many millimeter-wave [Reference Ahmed, Furqan, Aufinger and Stelzer10, Reference Bredendiek, Pohl, Jaeschke, Aufinger and Bilgic11] and especially THz [Reference Al-Eryani, Knapp, Kammerer, Aufinger, Li and Maurer12–Reference Mangiavillano, Kaineder, Aufinger and Stelzer17] transceivers and systems based on silicon-germanium (SiGe) technologies have been published. While III–V-based systems can provide high output power [Reference Caris, Stanko, Palm, Sommer, Wahlen and Pohl18–Reference Baumann, Gashi, Meier and Zech20], demand for silicon-based systems is driven by low manufacturing cost and overall compactness, which are vital for widespread deployment [Reference Hillger, Grzyb, Jain and Pfeiffer21].
A commonly used approach to improve the measurement range of millimeter-wave and THz systems is the usage of dielectric lenses [Reference Thomas, Bredendiek and Pohl22–Reference Muckermann, Barowski and Pohl25]. These lenses narrow the beam of the on-chip antennas for improved antenna directivity and measurement range as well as suppression of unwanted targets.
An earlier version of this paper was presented at the European Microwave Integrated Circuits Conference (EuMIC) 2022 and was published in its Proceedings [Reference Starke, Wittemeier, Vogelsang, Sievert, Erni, Rennings, Rucker and Pohl26]. This paper expands the previous publication by complementing the published on-chip antennas with a dielectric lens design with high directivity, enabling higher measurement ranges and suppression of clutter from unwanted targets.
In this article, we start by detailing the system concept of the proposed radar sensor in Section “System concept”. Section “MMIC design” presents the building blocks of the developed MMIC, including the measurement results of the circuits. The dielectric lens design, complementing the developed radar MMIC, is shown in Section “Dielectric lens antenna”. After a brief comparison of the proposed THz transceiver system to the state of the art in electronic THz transceiver design in Section “Comparison to state-of-the-art electronic THz transceivers”, the article is concluded in Section “Conclusion”.
System concept
In this paper, a concept for a low-cost THz frequency-modulated continuous-wave (FMCW) radar sensor is presented, that is based on a fully integrated FMCW 
$0.48\,\mathrm{THz}$ radar transceiver MMIC [Reference Starke, Wittemeier, Vogelsang, Sievert, Erni, Rennings, Rucker and Pohl26] and a dielectric lens for antenna directivity and measurement range improvements.
A block diagram of the presented MMIC architecture is depicted in Fig. 2. A photograph of the manufactured MMIC is shown in Fig. 1. The circuit blocks previously described are shown in an overlay on the micrograph. The MMIC’s dimensions are 
$2130 \, \mu \mathrm{m}$ by 
$900 \, \mu \mathrm{m}$ with a power consumption of 
$877 \, \,\mathrm{mW}$ at a supply voltage of 
$3.3 \,\mathrm{V}$.
Figure 1. Photograph of the developed transceiver MMIC. The signal generation up to 
$240\,\mathrm{GHz}$ is depicted on the left of the figure(VCO, X2, Divider). On the top right, the transmit path is shown (PA, X2, Tx Antenna). The receive path can be seen on the bottom right (PA, IQ, SHM, Rx Antenna). This highly integrated 
$0.48\,\mathrm{THz}$ transceiver is realized on an MMIC with an area of just 
$1.92\,\mathrm{mm}^{2}$.
Figure 2. Block diagram of the developed transceiver MMIC.
In contrast to other FMCW radar sensors in the sub-THz and THz spectrum, which use external signal generation [Reference Simic, Guo and Reynaert13, Reference Mangiavillano, Kaineder, Aufinger and Stelzer17, Reference Statnikov, Öjefors, Grzyb, Chevalier and Pfeiffer27–Reference Yi, Wang, Chen, Wang, Grajal and Han30], we developed a fully integrated sensor. The frequency stabilization and chirp generation, performed by a phase-locked loop (PLL), were omitted from the fully integrated approach for several reasons. A fully programmable PLL design would have added a tremendous amount of complexity to the MMIC design and would have to be based on the simulation results of the oscillator. Furthermore, the loop filter of an integrated PLL would need to be placed on the frontend PCB due to the large component values. Hence, an external PLL on the front end is much more flexible, as it can be optimized after fabrication and measurement of the radar MMIC. An integrated voltage-controlled oscillator (VCO) at a quarter of the targeted output frequency of 
$480\,\mathrm{GHz}$ generates the LO signal and can be tuned to modulate the output frequency.
For frequency stabilization by the PLL, a by-16 frequency divider lowers the 
$120\,\mathrm{GHz}$ output signal of the VCO down to approx. 
$7.5\,\mathrm{GHz}$ which, allows the use of commercial PLL components [31].
A Gilbert-cell-based frequency doubler doubles the oscillator’s frequency before the signal is split into the transmit (Tx) and receive (Rx) path. A bistatic approach was chosen for this radar MMIC as it relaxes the requirements regarding the receive mixer, as there is no direct coupling from the Tx into the Rx path, as no directional coupler is used between the transmitter and receiver. In both paths, the signal is amplified by power amplifiers (PAs) to drive the subsequent building blocks of the transceiver.
The Tx signal is frequency doubled again by a push–push frequency doubler that creates the 
$0.48\,\mathrm{THz}$ output signal. As push-push doublers convert a differential input signal to a single-ended output signal, a single-ended patch antenna is used as Tx antenna.
In the Rx path, the amplified signal at half of the output frequency is converted to quadrature signals by microstrip-based branchline couplers (IQ) and then used to drive a subharmonic down-conversion mixer (SHM). As the subharmonic mixer has a differential RF input, a differential patch antenna can be used for signal reception.
As the signal generation of this sensor is integrated into the MMIC and no external LO signals need to be routed on the front end, the highest frequency of a signal connected to the MMIC is the approx. 
$ 8\,\mathrm{GHz}$ output of the frequency divider. This enables using low-cost FR4 printed circuit board (PCB) material for the front end to create a low-cost THz radar sensor (similar to [Reference Thomas, Bredendiek and Pohl22]). Furthermore, a low-cost polytetrafluoroethylene (PTFE) dielectric lens was developed to enhance the antenna directivity of the antennas on the MMIC and to shield the MMIC and bond wires from external environmental influences.
MMIC design
In this section, the separate building blocks of the fully integrated 
$0.48\,\mathrm{THz}$ FMCW radar MMIC are detailed, as elaborated in Section “System concept”, and measurement results are discussed.
The radar transceiver discussed in this paper was manufactured in a development lot of the 130-nm SiGe BiCMOS technology SG13G3 from IHP (based on [Reference Heinemann, Rücker, Barth, Bärwolf, Drews, Fischer, Fox, Fursenko, Grabolla, Herzel, Katzer, Korn, Krüger, Kulse, Lenke, Lisker, Marschmeyer, Scheit, Schmidt, Schmidt, Schubert, Trusch, Wipf and Wolansky32, Reference Rücker and Heinemann33]). The technology offers SiGe HBTs which a transit frequency f T of 
$470\,\mathrm{GHz}$, a maximum oscillation frequency f max of 
$650\,\mathrm{GHz}$, and breakdown voltages of 
$1.5\,\mathrm{V}$ 
$\mathrm{BV_{CEo}}$ and 
$3.7\,\mathrm{V}$ 
$\mathrm{BV_{CBo}}$. The set of passive elements includes salicided and unsalicided poly-silicon resistors, metal-insulator-metal (MIM) capacitors, and MOS-based Varicaps. The metal stack consists of seven aluminum layers including five fine-structured layers and two thick top metal layers with thicknesses of 
$2\,{\mu m}$ and 
$3\,{\mu m}$, respectively, for transmission lines, inductors, and transformers.
Due to compatibility issues with software packages used at the time of circuit design, no parasitic extractions could be performed on the designed circuit cores. Parasitics capacitances were estimated based on experience made in other 
$130\,\mathrm{nm}$ SiGe technologies [Reference Bredendiek, Pohl, Jaeschke, Aufinger and Bilgic11, Reference Thomas, Bredendiek, Jaeschke, Vogelsang and Pohl34]. EM simulations of the designed circuit layouts were performed using Sonnet to optimize the performance of the developed circuit elements.
120 GHz VCO
A VCO is used to generate the signal on this fully integrated FMCW radar MMIC, in contrast to many other publications in the THz range, which use an external signal generation approach [Reference Mangiavillano, Kaineder, Aufinger and Stelzer17, Reference Baumann, Gashi, Meier and Zech20]. When deciding on a center frequency 
$\left(f_\mathrm{c}\right)$ and subsequent frequency multiplication factor to generate the targeted output frequency, careful consideration has to be taken regarding the circuit architecture, tuning range, and phase noise of the oscillator. While for lower center frequencies, the phase noise, and the relative tuning range are better compared to higher frequencies, doubling the frequency results in an addition of 
$6\,\mathrm{dB}$ to the phase noise [Reference Siddiq, Hobden, Pennock and Watson35]. Due to the unavailability of parasitic extracted circuit simulations, a center frequency of 
$120\,\mathrm{GHz}$ was chosen, due to experience based on other 
$130\,\mathrm{nm}$ SiGe BiCMOS technologies. Furthermore, a center frequency of 
$120\,\mathrm{GHz}$ ensures a large distance of the targeted fourth harmonic at 
$480\,\mathrm{GHz}$ to other unwanted harmonics, primarily the third and fifth harmonic, at 360 and 
$600\,\mathrm{GHz}$ respectively.
The VCO of this MMIC is based on the differential Colpitts oscillator topology. A common base amplifier is used at the oscillator’s output to increase the output power. It is used to drive the subsequent frequency doubler and to decouple the oscillator from influences of the following circuit stages. A voltage-controlled MOSCAP is used as the tunable circuit element of the VCO. The oscillator’s output frequency can be controlled by tuning voltages between −1 and 
$+5\,\mathrm{V}$. The schematic diagram of the implemented VCO is depicted in Fig. 3.
Figure 3. Schematic diagram of the implemented 
$120\,\mathrm{GHz}$ VCO. The length of the transmission line LB can be altered with laser fuses to configure the center frequency of the oscillator.
As circuits in this frequency range are highly susceptible to parasitic influences, like parasitic capacitances, which in this case, influence the oscillator’s output frequency and phase noise, laser fuses were implemented to compensate for these parasitic effects and manufacturing variances. These fuses can be removed after production to lower the center frequency 
$f_\mathrm{c}$ of the oscillator (119–
$108.5\,\mathrm{GHz}$). The measurement results of this fully integrated signal source can be seen in Fig. 4.
Figure 4. Measured output power and phase noise of the integrated 
$120\,\mathrm{GHz}$ VCO. No fuses were cut for this measurement. The phase noise was measured at an offset frequency 
$\Delta f$ of 
$1\,\mathrm{MHz}$.
The VCO, set to the highest center frequency of around 
$119\,\mathrm{GHz}$ can be tuned from 110.7 to 
$126.7\,\mathrm{GHz}$, which leads to a tuning range (TR) of 
$16\,\mathrm{GHz}$ and relative tuning range (rTR) of 13.7%. The output power was determined to be around 
$7.1\,\mathrm{dBm}$ with a flatness of 
$1.2\,\mathrm{dB}$ while having a power consumption of only 
$78\,\mathrm{mW}$. This leads to a dc-to-RF efficiency of up to 6.6%. The measured phase noise is between −72.5 and 
$-82\,\mathrm{dBc/Hz}$ at an offset frequency 
$\Delta f$ of 
$1\,\mathrm{MHz}$. This phase noise measurement was performed using a Rohde & Schwarz FSWP Phase Noise Analyzer at the output of the integrated frequency divider. Due to the frequency translation of the by 16 divider, the measured phase noise was corrected by 
$24\,\mathrm{dB}$. These measurements were performed on a dedicated breakout MMIC just containing the VCO and frequency divider (published in [Reference Vogelsang, Starke, Wittemeier, Rücker and Pohl36]).
Frequency divider
To stabilize the signal from the VCO with an off-chip PLL, a static by-16 frequency divider was developed. For the design of the divider, four flip-flops were utilized, which were designed in an emitter-coupled logic (ECL).
The frequency divider is directly connected to the collectors of the VCOs output amplifier and uses a buffer stage for the approx. 
$7.5\,\mathrm{GHz}$ output signal. This buffer decouples the divider from the pads and bond wires and drives off-chip loads, like PLL ICs.
We used a Keysight MSOS804A oscilloscope to measure the differential output signals of the divider. The divider generates a 
$-10\,\mathrm{dBm}$ output signal over the whole tuning range of the VCO and consumes 
$377\,\mathrm{mW}$ just for the frequency divider. The operation of the frequency divider was verified up to 
$163\,\mathrm{GHz}$ using a separate breakout MMIC (published in [Reference Vogelsang, Bredendiek, Schöpfel, Rücker and Pohl37]).
120–240 GHz Gilbert frequency doubler
A bootstrapped Gilbert-cell frequency doubler is used to double the frequency of the differential signal generated by the oscillator. This doubler architecture has differential input and output ports and is suitable for wideband applications [Reference Kueppers, Aufinger and Pohl38]. A previous version of this circuit was published in [Reference Vogelsang, Starke, Wittemeier, Rücker and Pohl36], detailing the measurement results of a breakout MMIC, containing this frequency doubler. A schematic diagram of the implemented frequency doubler is depicted in Fig. 5.
Figure 5. Schematic diagram of the developed 
$120 - 240{}\mathrm G\mathrm H\mathrm z$ frequency doubler, based on a bootstrapped Gilbert-Cell topology.
This circuit version introduced a power splitter that splits the 
$240\,\mathrm{GHz}$ signal into the Rx and Tx path between the frequency doubler and the PAs in the respective signal paths. As we used identical power amplifiers in the Tx and Rx paths, we directly split the signal instead of implementing two Wilkinson power dividers for the differential signal.
240 GHz power amplifier
After splitting the LO signal, we use parallel PA chains for the transmit and receive paths. These PAs are implemented with a two-stage, cascaded differential cascode amplifier topology. The measurement results from a previous publication [Reference Wittemeier, Vogelsang, Starke, Rücker and Pohl39] show the importance of providing as much input power to the subsequent frequency doubler in the transmit path as possible. Therefore, for the circuit revision on this transceiver MMIC, the matching between the PAs and the following frequency doubler in the Tx path and IQ-coupler in the Rx path was improved. The PA cores remain largely unchanged (compared to [Reference Vogelsang, Starke, Wittemeier, Rücker and Pohl36]), with a core current of 
$15.9\,\mathrm{mA}$ and 
$18.0\,\mathrm{mA}$, respectively. The power amplifiers provide up to 
$7\,\mathrm{dBm}$ output power with a maximum variation of the output power of 
$1.6\,\mathrm{dB}$ over a frequency range of 
$35\,\mathrm{GHz}$ (213–248 
$\mathrm{GHz}$).
240–480 GHz push–push frequency doubler
The desired output frequency of 
$480\,\mathrm{GHz}$ of the radar system is almost equal to the transit frequency f T of 
$470\,\mathrm{GHz}$ of the used transistors in the SG13G3 technology. Therefore, the second frequency doubling stage is implemented as a push-push frequency doubler, as these can reach comparatively high output powers even above the respective transit frequencies of the used transistors. Furthermore, push-push doublers achieve high fundamental suppression due to the operating principle of the frequency doubling. A downside typically brought up when using push-push doublers is the conversion from a differential input signal to a single-ended output signal. This is no drawback in this application, as a single-ended patch antenna can be used as Tx antenna. Therefore, no additional balun needs to be used to drive the antenna. A schematic diagram of the developed push–push architecture-based frequency doubler is depicted in Fig. 6.
Figure 6. Schematic diagram of the implemented 
$240-480{}\mathrm G\mathrm H\mathrm z$ push–push frequency doubler.
Frequency doublers in the lower THz range often use power combining to reach even higher output powers than possible with a single doubler [Reference Güner, Mausolf, Wessel, Kissinger and Schmalz40]. However, in this MMIC, we did not use power combining to keep the space and power consumption requirements low.
Previous research and publications [Reference Wittemeier, Vogelsang, Starke, Rücker and Pohl39] have shown the importance of the interface between the PAs and the push-push doubler circuit. This interface and the inductive load of the doubler stage were optimized in this circuit revision to improve the output power of the doubler by more than 
$6\,\mathrm{dB}$ in relation to the previous version. This improvement was achieved, influencing neither the transistor sizes, the power consumption, nor the common-base stage of the PAs. The output power of the second frequency doubling stage was characterized on a separate radar MMIC that was just manufactured for circuit measurement and system characterization purposes. It is similar to the MMIC shown in Fig. 1, but GSG probe pads at the doubler’s output and the mixer’s input are placed instead of the patch antennas.
Using this MMIC, an output power of up to 
$-12.6 \, \mathrm{dBm}$ with a supply voltage of 
$3.3\,\mathrm{V}$ and up to 
$-9.4 \, \mathrm{dBm}$ with a supply voltage of 
$4 \,\mathrm{V}$ was measured for this circuit. The measurement results of the 
$240$ to 
$480\,\mathrm{GHz}$ frequency doubler for different fuse configurations of the VCO core are depicted in Fig. 7. The output power of the circuit is measured using an Erickson PM5B power meter with a corresponding Formfactor T-Wave Probe and a WR2.2 to WR10 rectangular waveguide taper. The losses of the probe, taper, and GSG pad are de-embedded from the measured output power using measurement data of these elements.
Figure 7. Output power measurements of the second frequency doubler for different fuse configurations of the VCO. To investigate the maximum output power of the circuit, the supply voltage was increased to 
$4\,\mathrm{V}$ for the final measurement with three fuses cut.
It can be seen that the performance of the 240–
$480\,\mathrm{GHz}$ frequency doubler is mainly limited by the tuning range of the VCO. Below a frequency of 
$470\,\mathrm{GHz}$, the output power of the doubler is mainly flat, with only a minor difference between the individual measurement curves. The difference between the curves can be explained by the fact that the MMIC has to be removed from the wafer-prober to cut the fuses and re-contacted with the probes for the subsequent measurement. Slight variations in the probes’ positioning and in contact resistance lead to minor differences in the measurement curves.
480 GHz subharmonic mixer
The dynamic range of the radar MMIC is mainly influenced by the transmit power of the Tx path and the receive mixer in the Rx path. Subharmonic mixer architectures are often used for THz applications, as the receive signal frequency is above the transit frequency f T of the used technology [Reference Deng, Lu, Jia, Yang and Zhu41–Reference Zhou and Luo43]. Therefore, a subharmonic receive mixer architecture was implemented for this radar MMIC. A Gilbert cell with an integrated frequency doubler, utilizing quadrature LO signals, is used in this transceiver (similar to [Reference Kodkani and Larson44]). A schematic diagram of this implementation is given in Fig. 8. The quadrature LO signals are created by two microstrip branchline couplers fed by the PAs described in Section “240 GHz power amplifier”.
Figure 8. Schematic diagram of the implemented subharmonic 
$480\,\mathrm{GHz}$ receive mixer. The LO input signals 
$\mathrm{I}$, 
$\mathrm{\overline{I}}$, 
$\mathrm{Q}$, and 
$\mathrm{\overline{Q}}$ are generated by two microstrip branchline couplers.
One potential downside of this circuit architecture is the susceptibility of this circuit to amplitude or phase imbalances of the quadrature LO signals 
$\mathrm{I}$ and 
$\mathrm{Q}$ generated by the integrated microstrip branchline couplers. Although these couplers were carefully EM-simulated during the circuit design, the receiver circuit should still be investigated on its susceptibility to amplitude and phase errors. To perform this investigation, the LO signals 
$\mathrm{I}$ and 
$\mathrm{Q}$ are generated by microwave ports, and artificial phase and amplitude errors are introduced to this simulation for LO input frequencies between 200 and 
$250\,\mathrm{GHz}$. When simulating phase errors of up to 30∘, e.g., a relative phase between 
$\mathrm{I}$ and 
$\mathrm{Q}$ of 60∘ to 120∘, a maximum degradation of the conversion gain of just 1.39 
$\mathrm{dB}$ could be determined. By introducing an amplitude error of up to 3 
$\mathrm{dB}$ between 
$\mathrm{I}$ and 
$\mathrm{Q}$ signals, a maximum conversion gain degradation of just 1.3 
$\mathrm{dB}$ could be determined. These simulation results demonstrate the robustness of the developed receiver circuit against phase and amplitude imbalances. Combined with the carefully EM-simulated couplers generating the quadrature signals 
$\mathrm{I}$ and 
$\mathrm{Q}$, this circuit architecture ensures a robust operation over the targeted frequency range.
Using the alternate characterization MMIC, already described in Section “240–480 GHz push-push frequency doubler”, the operation of the receive mixer was successfully verified by feeding the MMIC with an artificial receive signal and generating the LO signals on-chip. Using a Keysight MSOS804A oscilloscope, a peak conversion gain of 
$-16\, \mathrm{dB}$ was achieved at a frequency of 
$474\,\mathrm{GHz}$ [Reference Starke, Wittemeier, Vogelsang, Sievert, Erni, Rennings, Rucker and Pohl26].
On-chip 480 GHz antennas
To transmit and receive the radar signals, the push–push frequency doubler and subharmonic mixer are connected to two patch antennas integrated on the MMIC. The antennas are designed for a center frequency 
$f_\mathrm{c}$ of 
$480\,\mathrm{GHz}$ and have a length of around 
$150\,\mu\mathrm{m}$. To improve the matching of the antennas, inset feeding is implemented in both the single-ended transmit antenna Tx and the differential receive antenna Rx.
For characterization purposes, the Tx antenna was manufactured on a breakout MMIC with GSG probe pads and was measured with the setup from [Reference Sievert, Svejda, Erni and Rennings45].
In Fig. 9, the measurement results for the antenna at a frequency of 
$480\,\mathrm{GHz}$ are shown as 
$\vec{E}$- and 
$\vec{H}$-plane cuts. A maximum gain of 
$3\,\mathrm{dBi}$ was measured at a frequency of 
$460\,\mathrm{GHz}$. Overall the measurements show a good agreement compared to the full-wave FDTD simulation results.
Figure 9. Realized gain at 
$480\,\mathrm{GHz}$: (a) 
$\vec{E}$- and (b) 
$\vec{H}$-plane of the Tx patch antenna.
It should be noted that, due to the high frequency, reflections from the probe contribute to the measured radiation pattern yielding the undulations on the measured patterns [Reference Boehm, Hitzler, Roos and Waldschmidt46]. Furthermore, a part of the measured radiation pattern is shadowed by the probe. Hence, the measurement results cannot be interpreted here [Reference Titz, Ferrero and Luxey47]. The Rx antenna is not characterized, as it is highly similar to Tx, and would, however, require a balun and more breakout-chip area for separate measurement.
Dielectric lens antenna
To improve the measurement range and focus the radar beam in one direction, a dielectric lens, based on the work in [Reference Thomas, Bredendiek, Jaeschke, Vogelsang and Pohl34, Reference Pohl48, Reference Pohl and Gerding49], was developed to enhance the antenna gain described in Section “On-chip 480 GHz antennas”. In addition to improving the antenna gain, the dielectric lens has the supplementary benefit of shielding the radar MMIC against outside influences and protecting the fragile wire bonds, connecting the MMIC to the FR4 frontend PCB.
The dielectric lens is based on a rotationally symmetrical elliptical lens manufactured from PTFE. This material was chosen for its low dielectric loss tangent 
$tan~\delta \approx 0.0004$, dielectric constant 
$\epsilon_r = 2.08$, and good machining properties [Reference Thomas, Bredendiek, Jaeschke, Vogelsang and Pohl34, Reference Pohl48, Reference Pohl and Gerding49]. The shape of the elliptic lens is given by a modification of the standard ellipse equation:
\begin{equation}
1= \left(\frac{x}{a}\right)^2+\left(\frac{y}{R}\right)^2.
\end{equation} When the feeding of the lens is done at the focal point F 1 of the lens, which is located at a distance f from the center C of the ellipse, and the quasi-optic rays are refracted parallel to the rotation axis in the boresight direction of x [Reference Olver and Saleeb50], the distance f can be calculated depending on the radius of the lens R and the dielectric constant 
$\epsilon_{\mathrm{r}}$ of the lens material (cf. (2)). The cross-section of this concept can be seen in Fig. 10.
Figure 10. Cross-section of the lens concept.
\begin{equation}
f=R\cdot \tan\left(\sin^{-1}\left(\frac{1}{\sqrt{\epsilon_r}}\right)\right)=R\cdot \frac{1}{\sqrt{\epsilon_r-1}}.
\end{equation} The second semi-axis a of the lens can also be calculated depending on the radius R and the dielectric constant 
$\epsilon_\mathrm{r}$, as the quasi-optic rays have to form a plane phase front at the tip of the lens. This means that the following equation has to be true:
\begin{equation}
\frac{\sqrt{\epsilon_r}}{c_0}\cdot (\,f+a) =P\cdot \frac{\sqrt{\epsilon_r}}{c_0} + a\cdot\frac{1}{c_0}.\\[4pt]
\end{equation}By rearranging (3), the length of the second semi-axis a can be calculated:
\begin{equation}
a= R\cdot \frac{\sqrt{\epsilon_r}}{\sqrt{\epsilon_r-1}}= R\cdot \frac{1}{\sqrt{1-\frac{1}{\epsilon_r}}}.
\end{equation}Substituting the results from (2) and (4) into (1) and defining the feeding point of the lens at the focal point F 1, the shape of the dielectric lens can be described in dependence of the radius R and the dielectric constant ϵr of the lens:
\begin{equation}
1 = \left(\frac{x-f}{a}\right)^2+\left(\frac{y}{R}\right)^2,
\end{equation}
\begin{equation}
\qquad\quad\hspace{6.6pt}=\left(\frac{x-\frac{R}{\sqrt{1-1/\epsilon_r}}}{\frac{R}{\sqrt{1-1/\epsilon_r}}}\right)^2+\left(\frac{y}{R}\right)^2.
\end{equation}The radius R of the lens can be chosen depending on the targeted application, antenna gain, and form factor of the radar system. To estimate the directivity D of the dielectric lens, the following estimation was used [Reference Stutzman51]:
\begin{equation}
D= \frac{4\cdot\pi \cdot A_E}{\lambda^2}.
\end{equation} In this equation, the losses of the dielectric lens antenna are neglected. Using the approximation of 
$A_E \approx \pi\cdot R^2$, a maximum theoretical directivity of 
$45\,\mathrm{dBi}$ can be calculated for a dielectric lens with a radius 
$R=18\,\mathrm{mm}$ using Eq. (7). A radius of 
$R=18\,\mathrm{mm}$ was chosen because of the aspect that a small and lightweight THz radar system is going to be implemented with this lens. Hence, this radius is a good tradeoff between the small form factor and the targeted measurement range of the radar system.
To verify this approximation, a simulation model was implemented in CST Microwave Studio. There is a large discrepancy between the feature size of the on-chip antennas, which have a minimum feature size of 
$420\,\mathrm{nm}$, and the dielectric lens, which has a radius R of 
$18\,\mathrm{mm}$. Because of this discrepancy, a simulation of the on-chip antennas in combination with the dielectric lens would take vast amounts of time and simulation power. Therefore, a two-stage approach was chosen for this simulation to assess the performance of the patch antennas in conjunction with the lens.
As a first step, the on-chip patch antennas were simulated, and near-field sources of both antennas were created. These near-field sources were included in the simulation environment of the dielectric lens. In this simulation environment, the physical construction of the MMIC in an open QFN package inside a cavity of the lens is modeled, as depicted in Fig. 11. The dielectric lens and QFN package are mounted on an FR4 PCB with a grounded metal plane as the top layer. Including the mounting interface to attach the lens to the PCB, the lens has a height of 
$43.3\,\mathrm{mm}$.
Figure 11. Cross-section of the presented assembly. The dielectric lens is visualized by a non-functional 3D-printed cut model.
The simulation results of the transmit and receive path in the 
$\vec{E}$- and 
$\vec{H}$-plane using this model and the detailed two-step simulation approach can be seen in Fig. 12(a) and 12(b).
Figure 12. Simulation results of the proposed MMIC and dielectric lens combination in the 
$\vec{E}$ and 
$\vec{H}$-plane. Squinting beams for the Rx and Tx path can be observed in the 
$\vec{E}$-plane, but not in the 
$\vec{H}$-plane. No squinting can be observed for the resulting effective beams in 
$\vec{E}$ or 
$\vec{H}$-plane. (a) Directivity: 
$\vec{E}$-plane. (b) Directivity: 
$\vec{H}$-plane.
It can be seen that both paths of the radar system, transmit path (Tx) as well as receive path (Rx), have a distinctive peak of the directivity of around 
$41.7\,\mathrm{dBi}$ with a half-power beam width (HPBW) of 1.5
${}^{\circ}$. Because of the bistatic approach, the on-chip antennas cannot be placed in the symmetry plane of the dielectric lens in the 
$\vec{E}$-plane but are shifted 
$175\,\mu\mathrm{m}$ to either side of the symmetry plane. This shift leads to two squinting beams with a beam direction of 0.5
${}^{\circ}$ in either direction.
As the presented transceiver has a separate transmit and receive path with corresponding integrated antennas, it has to be handled as a bistatic radar sensor. The radar range equation for a bistatic radar system is given by:
\begin{equation}
P_{\mathrm{Rx}}= P_{\mathrm{Tx}} \frac{D_{\mathrm{Tx}} D_{\mathrm{Rx}} \lambda^2 \sigma}{(4\pi)^3 R_{\mathrm{Tx}}^2 R_{\mathrm{Rx}}^2}.\\[2pt]
\end{equation} In this equation, the power at the receiver 
$P_{\mathrm{Rx}}$ is dependent on the power from the transmitter 
$P_{\mathrm{Tx}}$, the directivities of the receive (
$D_{\mathrm{Rx}}$) and transmit (
$D_{\mathrm{Tx}}$) antenna, the wavelength λ of the radar signal, the radar cross-section σ of the target, and the distances between the transmitter and receiver to the target, described by the factors 
$R_{\mathrm{Tx}}$ and 
$R_{\mathrm{Rx}}$. Due to the small pitch between transmit and receive antenna, the distances 
$R_{\mathrm{Tx}}$ and 
$R_{\mathrm{Rx}}$ are practically identical. Therefore the term 
$R_{\mathrm{Tx}}^2 R_{\mathrm{Rx}}^2$ in Eq. 8 can be replaced by R 4. The system can also be handled as a monostatic radar transceiver because of the small distance between the transmitter and receiver and the similar transmit and receive characteristics. The term 
$D_{\mathrm{Tx}} D_{\mathrm{Rx}}$ can be replaced by 
$D_{\mathrm{eff}}^2$, where 
$D_{\mathrm{eff}}$ describes the effective directivity of the radar system. This simplifies Eq. 8 to the following equation for a monostatic radar system:
\begin{equation}
P_{\mathrm{Rx}}= P_{\mathrm{Tx}} \frac{D_{\mathrm{eff}}^2 \lambda^2 \sigma}{(4\pi)^3 R^4}.\\[2pt]
\end{equation}This effective directivity represents the bistatic squinting assembly, with a monostatic model calculated by combining the directivities in transmit and receive operation. It can be determined by calculating the geometric mean of the Tx and Rx directivity for every angle θ and φ:
\begin{equation}
D_{\mathrm{eff}}(\theta,\varphi)= \sqrt{D_{\mathrm{Tx}}(\theta,\varphi)\cdot D_{\mathrm{Rx}}(\theta,\varphi)}.
\end{equation} The effective directivity, calculated by the equation above (10), is depicted in black in Fig. 12(a) and 12(b). The effective directivity has its peak in the boresight direction and is approximately 
$2.4\,\mathrm{dB}$ lower than the respective Tx and Rx beams in the 
$\vec{E}$-plane. Due to the small pitch of the antennas of only 
$350\,\mu\mathrm{m}$, the geometric mean of both individual beams leads to a distinctive peak of 
$39.33\,\mathrm{dBi}$ in the 
$\vec{E}$-plane. Because of the combination of the two squinting beams, the sidelobe level in the 
$\vec{E}$-plane is considerably higher than the respective individual Tx and Rx beams, with a value of 
$7.64\,\mathrm{dB}$. The HPBW of the effective directivity in the 
$\vec{E}$-plane is 0.95∘. As the on-chip antennas lie on the symmetry plane for the directivity in the 
$\vec{H}$-plane, no squinting of the Rx and Tx beams can be observed in Fig. 12(b). The effective directivity in the 
$\vec{H}$-plane reaches a value of 
$39.3\,\mathrm{dBi}$ in boresight direction with an HPBW of 0.95∘ and a sidelobe level of 
$11.91\,\mathrm{dB}$.
The simulation results show that this dielectric lens enables a compact and low-cost 0.48 THz FMCW radar system with a small beam width and high suppression of unwanted targets for high-accuracy measurement scenarios.
Comparison to state-of-the-art electronic THz transceivers
In Table 1, the proposed 
$0.48\,\mathrm{THz}$ transceiver is compared to the state of the art in electronic THz transceivers. The comparison of the size and power consumption Pdc has to be split between systems with external signal generation, typically using a laboratory signal generator, and the transceivers that generate the signal internally with integrated VCOs. As in the realization described in this manuscript, most comparable THz transceivers use lenses to improve the radiation characteristics of the antennas integrated on their respective transceiver MMICs. These lenses are manufactured from multiple different materials, like polymethylpentene (TPX), polypropylene (PP), silicon (Si), or in this case, made from PTFE.
Table 1. Comparison of state-of-the-art integrated electronic THz transceivers
* Size of all MMICs that form the transceiver.
** EIRP.
Conclusion
This paper shows a fully integrated transceiver operating in the range of 0.448–0.491 THz. Besides the transmit and receive path, the frequency divider is also integrated on the MMIC. This makes it possible to use an external PLL IC to create a complete radar system. The receiver channel features a subharmonic down-conversion mixer that enables the use of 
$240 \, \mathrm{GHz}$ quadrature signals and a differential patch antenna. The transmit signal is generated with a push-push frequency doubler and a single-ended patch antenna, reaching 
$-9.4\, \mathrm{dBm}$. This radar MMIC is complemented by a dielectric lens design to improve the directivity of the integrated patch antennas. The dielectric lens reaches directivities of up to 
$39.3\,\mathrm{dBi}$ in boresight direction and narrows the beam to a HPBW of just 0.95
${}^{\circ}$, improving the measurement range of the radar system. Furthermore, it provides a high suppression of more than 
$24.6\,\mathrm{dB}$ for clutter from unwanted targets, deviating more than 6
${}^{\circ}$ from antenna boresight in the 
$\vec{E}$- and 
$\vec{H}$-plane. In summary, the transceiver presented is the first to be fully integrated and to have an output frequency just below 
$0.5\, \mathrm{THz}$.
Acknowledgements
The author would like to thank his co-authors, Jonathan Bott, Florian Vogelsang, and Benedikt Sievert, for their invaluable contributions to the presented radar MMIC.
Funding statement
The research work presented in this paper was funded by the German Research Foundation (“Deutsche Forschungsgemeinschaft”) (DFG) under Project-ID 287022738 TRR 196 for Project C02, C03, C05, M02 and M04. Furthermore, this project has received funding from the ECSEL Joint Undertaking (JU) under Grant Agreement No. 876019. The JU receives support from the European Union’s Horizon 2020 research and innovation programme and Germany, Netherlands, Austria, Romania, France, Sweden, Cyprus, Greece, Lithuania, Portugal, Italy, Finland, Turkey.
Competing interests
None declared.
David Starke was born in Herne, Germany, in 1992. He received the B.Sc. and M.Sc. degrees in electrical engineering and information technology from Ruhr University Bochum, Bochum, Germany in 2015 and 2017, respectively. Since 2017, he has been a Research Assistant with the Institute of Integrated Systems, Ruhr University Bochum, Bochum, Germany. His current research interests include mm-wave to THz radars and monolithic microwave integrated circuit (MMIC) design using silicon-germanium technologies.
Jonathan Bott (formerly Wittemeier) was born in Lünen, Germany. He received the B.Sc. and M.Sc. degrees in electrical engineering and information technology from TU Dortmund University, Dortmund, Germany, in 2014 and 2016, respectively. Between 2016 and 2017, he worked in the automotive industry as a Software Developer. Since 2017, he has been a Research Assistant at the Institute of Integrated Systems, Ruhr University Bochum. His research interests include mm-wave radar system design, circuit and MMIC design using Silicon-Germanium, as well as MIMO DoA and imaging algorithms.
Florian Vogelsang was born in Hattingen, Germany in 1993. He received the B.Sc and M.Sc. degrees in electrical engineering and information technology from Ruhr University Bochum, Bochum, Germany in 2015 and 2017, respectively. Since 2018, he has been a Research Assistant with the Institute of Integrated Systems, Ruhr University Bochum, Bochum, Germany. His current research interests include wideband radar systems in the mm-Wave and THz range, realized as monolithic microwave integrated circuits (MMIC) in silicon-germanium technologies.
Benedikt Sievert was born in Krefeld, Germany. He received his B.Sc. and M.Sc. in Electrical Engineering/High-Frequency Systems from the University of Duisburg-Essen in 2017 and 2019, respectively. Since 2017 he is a member of the Laboratory of General and Theoretical Electrical Engineering of the University of Duisburg-Essen. His research interests include mm-wave on-chip antennas, electromagnetic metamaterials, theoretical and computational electromagnetics.
Jan Barowski was born in Bochum, Germany, in 1988. He received the B.Sc. and M.Sc. degrees in electrical engineering and the Dr.Ing. degree (with honors) in electrical engineering from Ruhr University Bochum, Bochum, Germany, in 2010, 2012, and 2017, respectively. Since 2012, he has been with the Institute of Microwave Systems, headed by Ilona Rolfes, Ruhr University Bochum, as a Research Assistant. He is currently a Postdoctoral Research Scientist with the Institute of Microwave Systems. His research interests include radar signal processing, radar imaging, and material characterization techniques. Dr. Barowski was the recipient of the IEEE Antennas and Propagation Society Doctoral Research Grant in 2016 and the IEEE MTT IWMS-AMP Best Student Paper Award in 2017, U.R.S.I. Germany Sections Young Scientist Award and the German Association for Electrical, Electronic and Information Technologies (VDE) Award for the Doctoral dissertation, in 2018.
Christian Schulz received the Dipl.Ing. and Dr.Ing. degrees in electrical engineering from Ruhr University Bochum, Bochum, Germany, in 2009 and 2016, respectively. From 2010 to 2016, he was a Research Assistant with the Institute of Microwave Systems, Ruhr University Bochum, where he has been a Postdoctoral Researcher since 2016. His research interests include 3-D electromagnetic field simulations, plasma diagnostics, radar systems, and antenna design. Dr. Schulz was the recipient of the IEEE Antennas and Propagation Society Doctoral Research Award in 2014, the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Graduate Fellowship Award in 2015, and the Gert Massenberg Award for Doctoral dissertation in 2017.
Holger Rücker received his diploma and doctorate in physics from the Humboldt University of Berlin, Germany, in 1986 and 1988, respectively. From 1989 to 1991, he was a staff member of the Humboldt University of Berlin. From 1991 to 1992, he was with the Max Planck Institute for Solid State Research in Stuttgart, Germany. He joined IHP in Frankfurt (Oder), Germany in 1992 where he is engaged in research on the physics and fabrication of semiconductor devices. His research interests include SiGe bipolar devices, the development of CMOS and BiCMOS technologies, and their application in radio-frequency integrated circuits. He led the development of IHP’s 130-nm SiGe BiCMOS technologies SG13S, SG13G2, and SG13G3.
Andreas Rennings studied electrical engineering at the University of Duisburg-Essen, Germany. He carried out his diploma work during a stay at the University of California in Los Angeles. He received his Dipl.-Ing. and Dr.-Ing. degrees from the University of Duisburg-Essen in 2000 and 2008, respectively. From 2006 to 2008 he was with IMST GmbH in Kamp-Lintfort, Germany, where he worked as an RF engineer. Since then, he is a senior scientist and principal investigator at the Laboratory for General and Theoretical Electrical Engineering of the University of Duisburg-Essen. His general research interests include all aspects of theoretical and applied electromagnetics, currently with a focus on medical applications and on-chip millimeter-wave/THz antennas. He received several awards, including a student paper price at the 2005 IEEE Antennas and Propagation Society International Symposium and the VDE-Promotionspreis 2009 for the dissertation.
Daniel Erni received a diploma degree from the University of Applied Sciences in Rapperswil (HSR) in 1986, and a diploma degree from ETH Zürich in 1990, both in electrical engineering. Since 1990 he has been working at the Laboratory for Electromagnetic Fields and Microwave Electronics, ETH Zürich, where he got his Ph.D. degree in laser physics 1996. From 1995-2006 he has been the founder and head of the Communication Photonics Group at ETH Zürich. Since Oct. 2006 he is a full professor for General and Theoretical Electrical Engineering at the University of Duisburg-Essen, Germany. His current research interests include optical interconnects, nanophotonics, plasmonics, advanced solar cell concepts, optical and electromagnetic metamaterials, RF, mm-wave and THz engineering, biomedical engineering, bioelectromagnetics, marine electromagnetics, computational electromagnetics, multiscale and multiphysics modeling, numerical structural optimization, and science and technology studies (STS). Daniel Erni is a co-founder of the spin-off company airCode on flexible printed RFID technology. He is a Fellow of the Electromagnetics Academy, a member of the Center for Nanointegration Duisburg-Essen (CeNIDE), as well as a member of the Swiss Physical Society (SPS), of the German Physical Society (DPG), of the Optical Society of America (OSA), and of the IEEE.
Ilona Rolfes received the Dipl.Ing. and Dr.Ing. degrees in electrical engineering from Ruhr University Bochum, Bochum, Germany, in 1997 and 2002, respectively. From 1997 to 2005, she was with the High Frequency Measurements Research Group, Ruhr University Bochum, as a Research Assistant. From 2005 to 2009, she was a Junior Professor with the Department of Electrical Engineering, Leibniz University Hannover, Hannover, Germany, where she became the Head of the Institute of Radio frequency and Microwave Engineering in 2006. Since 2010, she has been leading the Institute of Microwave Systems, Ruhr University Bochum. Her research interests include high-frequency measurement methods for vector network analysis, material characterization, noise characterization of microwave devices, sensor principles for radar systems. Dr. Rolfes is currently a member of the Executive Committee of the IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes. She is also a Board Member of the German IEEE MTT-AP Chapter and the German Commission for Electromagnetic Metrology of U.R.S.I.
Nils Pohl received the Dipl.-Ing. and Dr.Ing. degrees in electrical engineering from Ruhr University Bochum, Bochum, Germany, in 2005 and 2010, respectively. From 2006 to 2011, he was a Research Assistant with Ruhr University Bochum, where he was involved in integrated circuits for millimeter-wave (mm-wave) radar applications. In 2011, he became an Assistant Professor with Ruhr University Bochum. In 2013, he became the Head of the Department of mm-wave radar and high-frequency sensors with the Fraunhofer Institute for High Frequency Physics and Radar Techniques, Wachtberg, Germany. In 2016, he became a Full Professor of integrated systems with Ruhr University Bochum. He has authored or coauthored more than 200 scientific papers and has issued several patents. His current research interests include ultrawideband mm-wave radar, design, and optimization of mm-wave integrated SiGe circuits and system concepts with frequencies up to 300 GHz and above, and frequency synthesis and antennas. Prof. Pohl is a member of VDE, ITG, EUMA, and URSI. He has received the Karl-Arnold Award of the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts in 2013, and the IEEE MTT Outstanding Young Engineer Award in 2018. He was the co-recipient of the 2009 EEEfCom Innovation Award, the 2012 EuMIC Prize, the 2015 Best Demo Award of the IEEE Radio Wireless Week, the Best Paper Award at EUMIC 2012, the Best Demo Award at RWW 2015, and the Best Student Paper Awards at RadarConf 2020, RWW 2021, and EuMIC 2022.
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