1. Introduction

Terahertz (THz) heterodyne receive with high-sensitivity is in high demand in advanced communications [1–3], sensing [4–6], imaging [7–9] and astronomical observation [10–12]. The mixer is one of the key components of the heterodyne receiver, that directly determines receiver performance in the absence of a low-noise amplifier. Generally, THz heterodyne mixers are roughly classified into two categories: waveguide-based mixer with horn antennas [13–16]and antenna-coupled [17,18], namely quasi-optical mixer. Compared with the waveguide-based one, the quasi-optical mixer is easier to manufacture, integrate, and much less expensive when fabricated in large quantities [19,20]. Additionally, the quasi-optical mixer can be flexibly configured into a miniaturized THz heterodyne receiver 2-D array [21].

A wide variety of quasi-optical mixers have been realized, such as antenna-coupled Schottky diode [22], antenna-coupled high electron-mobility transistors [23], and antenna-coupled Josephson junctions [24]. In these cases, employing a common antenna loaded a lens receives the local oscillator (LO) pump signal and radio frequency (RF) signal in the free space. To avoid the irradiation of the LO obstructing RF incidence, the most common THz quasi-optical mixers apply beam splitters configuration to combine RF and LO signals and then inject into the mixer [25]. Unfortunately, the beam splitter configuration not only increases the difficulty of optical path tuning on account of a complex and hulking optical network subsystem, but increases the LO power loss and RF power loss on account of the reflection and transmission property of the beam splitter. This problem can hopefully be avoided because it is difficult to generate high LO power.

With the development of the quasi-optical mixer, many techniques are applied to achieve high-efficiency power coupling. In [26], to reduce transmission loss, a novel dual frequency operating microstrip antenna fed by a common coplanar waveguide was proposed in the quasi-optical fundamental mixer. However, there is a lack of coplanar waveguide network for achieving good isolation between LO and RF signals. Then in [27], a hybrid ring coupler was designed to improve the isolation. The conversion loss is 16 dB at 19.25 GHz, which is relatively high. The coupling efficiency of antennas can be further enhanced by adding the hemispherical lens. In [28], a composite wax/PTFE lens was mounted on the front-side of bowtie antenna while a Si lens was glued onto the back-side of the substrate. Despite the enhanced conversion gain was realized, the dual lens can deteriorate the front-to-back (FB) ratio of LO/RF antenna radiation patterns without the ground plane for isolation. Additionally, taking advantage of the offset center effect of antenna relative to the lens, a dual-beam frequency-selective THz quasi-optical mixer was reported [29], but it is still challenging to maintain each element uniformity for array because of the off-axis characteristics. All these methods suffer from insufficient utilization of LO power, which is crucially important at THz frequency band.

In this paper, we present a 170 GHz quasi-optical sub-harmonic mixer with excellent radiation properties and a high isolation between the LO and RF signal paths. Without the loss of generality, a low-cost commercial Schottky diode is utilized as the mixing element. The measured single-sideband (SSB) conversion loss is from 11.3 to 15.4 dB in the operation range of 160 to 180 GHz. Innovations for the mixer are summarized as follows. First, A new-type quasi-optical sub-harmonic mixer configuration is realized with low-cost and high performance using high-density interconnect (HDI) technology. Second, dual 3D-printed dielectric lenses are loaded on the either side of the mixer for enhancing the radiation gain of the RF and LO antennas, respectively. Additionally, the buried planar reflectors are integrated in the multilayer build-up substrate for maintaining the RF/LO radiation isolation in the free space. Third, a low-loss matching/isolation network with a quasi-coaxial via transition structure is designed to realize a compact mixer configuration. Experimental demonstrations validate the feasibility of the proposed design.

2. Architecture and operation mechanism

2.1 Architecture and mixer design concept

Figure 1 presents the architecture of our proposed quasi-optical sub-harmonic mixer, designed using HDI technology. It includes an antenna-coupled mixer, packaged by dual back-to-back 3D-printed lenses, incorporating two patch antennas, a Schottky diode, and a matching network with a quasi-coaxial via transition structure. The mixer is integrated onto a multilayer printed circuit board (PCB), comprised of four prepreg layers, one core board layer, and six conductor layers. To optimize the mixer's efficiency, we chose Megtron 7N (ε_r = 3.1, tanδ = 0.003) as the substrate material for its low loss and availability of dielectric thickness.

 

Fig. 1. Architecture of the proposed quasi-optical sub-harmonic mixer based on PCB HDI technology: (a) Schematic diagram of configuration. (b) Stack-up cross view. (c) 3D view. (Design parameters: h₁ = 250 µm, h₂ = 75 µm, h₃ = 80 µm, h₄ = 75 µm, h₅ = 100 µm, r₁ = r₂ = 2.3 mm, l₁ = 2 mm, l₂ = 1.8 mm, l_a= 0.85 mm, r_a =1.45 mm.)

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The Schottky diode, acting as the mixing element, is adjacent to the RF antenna on L6. The LO and RF antenna elements are realized on L1 and L6 for radiation at the operating frequencies of 85 and 170 GHz, respectively. In addition, a compact and low-loss matching network with a quasi-coaxial via transition structure is routed on L2 to L6 to achieve good antenna radiation and high signal isolation characteristics, thus significantly enhancing the coupling of signal power into the Schottky diode. an IF low-pass filter (LPF) on L4 is also integrated in the matching network to prevent the RF and LO signals from leaking onto the IF output port on L6. Notice that, in the HDI PCB, all the high-density circuit connections between the layers are realized in the form of stacked micro-via. Therefore, special attention should be paid to the antennas and matching network design. For instance, the minimum limit for line width, space and via diameter are set to 50/50/90 µm, and the minimum via-to-edge separation and alignment accuracy between layers are 75/60 µm [30].

Dual 3D printed extended hemispherical lenses, with respective radius r₁ and r₂, and extended thickness l₁ and l₂, are placed on the front and back sides of the antenna-coupled mixer. a flat board is extended from each lens, ensuring mechanical robustness of the mixer so that the antenna-coupled mixer and the dual lenses can be integrated firmly [31]. On the side of the RF antenna the lens has a cylindrical cavity to house the Schottky diode. These lenses can improve the RF and LO antennas radiation gain. In this design, Nylon (ε_r = 2.64) is selected as the material for the 3D-printed lenses owing to its low permittivity, which facilitates the reduction of multiple reflection loss and the enhancement of coupling efficiency. Meanwhile, the buried planar reflectors or grounds (GND) on L2 and L5, interconnected by numerous vias, preserve the radiation isolation of the RF and LO antennas in the free space.

2.2 Mixer equivalent circuit model

The proposed sub-harmonic quasi-optical mixer has three signal paths in Fig. 1 (b), where the blue, green and brown guides represent the LO, RF and IF signal circuit interconnections, respectively. Accordingly, the equivalent circuit model is illustrated in Fig. 2. The red dashed box represents the antiparallel Schottky diode, AP2 from Chengdu Terawind Co. Ltd, with the following parameters: serial resistance R_s = 8 Ω, zero voltage capacitance C_j0 = 3 fF, saturation current I_s = 50 fA, breakdown voltage V_bd = 5.5 V and reverse current I_j = 10 µA. The whole dimensions of the diode are the length 185 µm, width 75 µm and thickness 25 µm. Operating in the sub-harmonic mixing mode, the RF and LO signal sources (I_RF and I_LO) are presumed to have distinct source impedances Z_RF and Z_LO, paralleling the input impedances of the RF and LO antennas. They drive the RF and LO signals into the Schottky diode in the RF and LO paths respectively. Note that, the diode is adjacent to the RF antenna for reducing the RF path loss. Under an appropriate LO power condition, heterodyne mixing occurs inside Schottky diode and the IF is generated and received by an IF termination Z_IF (50 Ω) via the IF LPF. Considering the RF and LO signals are received by respective antennas, which naturally restrain signals below their operating frequency, two ideal isolation networks are present in the model. One (green box) suppresses LO and IF signals in RF path, and the other (blue box) RF and IF signals in LO path. As providing resonance that stops RF signal flowing while allowing LO and IF signals to pass, the double open stubs (yellow dashed box) is modeled as resonators and assign to the LO and IF paths. Moreover, the quasi-optical transition structure, as a three-port device, is substituted with a matrix of port impedance Z_c for the LO and IF paths. Additionally, an IF LPF (brown box) is designed and integrated with the quasi-optical transition structure in the IF path.

 

Fig. 2. Schematic showing the equivalent circuit model of the proposed quasi-optical sub-harmonic mixer including anti-parallel Schottky diode, antennas, signal isolation networks and IF impedance.

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3. Mixer design and analysis

3.1 RF antenna element design

At the sub-THz frequencies, it is challenging to achieve relative impedance bandwidth of 18.5% at 170 GHz based on HDI PCB technology. Since the restrictions in process capacity and cost, the commonly used approach such as reactive loading [32], thicker dielectric substrate or etched slot [33] is not suitable for RF antenna configuration. In the design, we employ a patch antenna with an insertion feed structure, derived from the topology of conventional patch antennas, as depicted in Fig. 3(a). Two symmetrical slits are introduced along the patch radiating edges that modify the electrical field distribution at fundamental and second harmonic mode [34]. by adjusting the critical parameters a₆ and b₆, the dual resonant modes resonate can be in proximity to each other, leading to a wide impedance bandwidth. Additionally, the symmetrical slits enhance the robustness against fabrication process tolerance due to the flexibility in adjusting the impedance values. On the RF side a short stub of three-quarter wavelengths is configurated, that acts as a high-pass filter at 170 GHz. It allows RF signal to flow into the diodes, but not LO into the RF antenna for radiation. Additionally, it routes the IF signal to ground. Ideally, the LO termination should be half wavelengths open stub at 170 GHz, but to reduce the effect on the RF antenna radiation, we decided to use a three-quarter wavelengths short stub at 170 GHz. Figure 3(b) shows the electric field distribution at 170 GHz. It can be observed that the three-quarter wavelengths stub effectively suppresses the RF signal, resulting in the minimal impact on the RF antenna's radiation.

 

Fig. 3. (a) Geometry of the proposed patch antenna loaded short stub. (b) the electric field distribution at 170 GHz. (Design parameters: a₆ = 95 µm, b₆ = 85 µm, c₆ = 75 µm, d₆ = 860 µm, w’₆= 75 µm, w’’₆= 875 µm, l₆ = 510 µm.)

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3.2 LO antenna element design

Due to the design of sub-harmonic mixing scheme, it is significant to take the isolation between the RF and LO signals into account. Typically, a LO LPF is used in the mixer configuration that results in a relatively large circuit size [35–37]. In the design, we employ an aperture-coupled antenna which naturally provides effective suppression of the even-order mode TM₂₀ [38]. This eliminates the requirement to design a separate LO LPF, thus facilitating the compact circuit design. Also, compared to the conventional microstrip lens antenna, the antenna offers several advantages. It enables independent optimization of the feeding network and radiation patch separated by the common ground plane, and achieves a reasonable impedance bandwidth of 15% at 85 GHz [39,40].

Figure 4(a) presents the geometry of the proposed aperture-coupled antenna. There are three metallic layers denoted as L1-L3: the radiation patch is on L1, the ground plane with a narrow aperture on L2, and the 50-Ω cross shaped microstrip feeding network on L3. The feeding net-work transmits the LO signal coupled from the radiation patch through the aperture. Details of the aperture-coupled antenna are depicted in Fig. 4(b). Two pairs of identical strip-slot hybrid structure are positioned symmetrically along the center x-axis of the radiation patch to achieve a wide impedance bandwidth and high gain. The aperture is placed beneath the center of the radiation patch, with a slight offset of a₂, b₂ along x-axis and y-axis, respectively, causing little impact on the LO antenna performance. Finally, A symmetrical 50-Ω cross-shaped microstrip feeding network, with two open-ended matching branches, is designed along the x-axis. Matching branch I and matching branch II have lengths of l₃ and a₃, respectively. Additionally, matching branch II is slightly offset by d₃ away from the center of the radiation patch along the x-axis.

 

Fig. 4. (a) Geometry build-up of the proposed aperture-coupled patch antenna. (b) Details of the aperture-coupled patch antenna on different mental layers. (c) Equivalent circuit model of the aperture-coupled antenna. (Design parameters: a₁= b₁= 75 µm, l₁= 570 µm, w₁= 670 µm, a₂= 60 µm, b₂= 75 µm, l₂= 640 µm, w₂= 75 µm, a₃= 280 µm, b₃= 75 µm, l₃= 320 µm, w₃= 75 µm, a₃= 40 µm.)

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The equivalent circuit model of the aperture-coupled antenna is illustrated in Fig. 4(c). To maximize the coupling at the aperture, it is common to design the open-ended matching branch I to be shorter than one-quarter wavelengths at 85 GHz [41]. As a result, it can be modeled as an LC series resonator. The circuit parameters L₀₁ and C₀₁ not only depend on the matching branch I length l₃, but also depend on the aperture length l₂ and the aperture position relative to the center of the radiation patch, given by a₂ and b₂. The C₀₂ represents the mirror symmetry of the open-ended matching branch II, which is designed as one-quarter wavelengths at 170 GHz to enhance the suppression of even-order mode TM₂₀. It depends on the matching branch II length a₃. The radiation patch and aperture are represented by an RLC parallel resonant circuit as a series load along the open-ended matching branch I [42]. By optimizing the dimensions of the radiation patch, aperture, and feeding network, the bandwidth requirement for the LO antenna can be effectively achieved.

3.3 Quasi-coaxial via transition

As the heterodyne mixing occurs inside the Schottky diode on L6, a transition configuration is required for the LO signal circuit interconnection from L3 to L6. Figure 5(a) illustrates the notable dimensions of the embedded microstrip-to-microstrip quasi-coaxial via transition. Similar to the structure of coaxial line, the signal mental blind via, surrounded by four grounded blind vias from L2 to L6, is designed. However, since the fabrication limitation of process capability, the largest characteristic impedance of the vertical transition is lower than 50 Ω when the diameter of the via pad, r_pad, is set to the minimum value 250 µm. Therefore, a quarter wavelengths transformer is implemented on L3 to achieve the impedance matching of port 1 close to 50 Ω in conjunction with ground layers on L2 and L5. It is important to note that the discontinuity of the characteristic impedance at the interface between the microstrip line (MS) and signal via can cause serious mismatch and spurious radiation, especially for the RF signal at sub-THz frequencies. To prevent the RF signal to flow into the transition, the double open stubs are utilized as resonators, which is also treated as an impedance tuner to match the impedance of the port 2 to 50 Ω on L6. The length of the double open stubs is close quarter-wavelength at 170 GHz, given by a₆ and c₆. Additionally, it should be mentioned that the feeding line on L6 is inverted 180° in a back-to-back structure for the convenience of simulation and measurement, without significantly impacting the performance of the transition [43].

 

Fig. 5. (a) Details of the quasi-coaxial via transition. (b) Section of the physics-based equivalent circuit model. (c) Fabricated quasi-coaxial via transition. (Design parameters: w^’₃= 180 µm, r_pad =130 µm, r_d = 365 µm, r_g = r_s = 115 µm, r_anti = 220 µm, w₆ = 75 µm, a₆ = 190 um, b₆ = 75 µm, c₆ = 320 µm, d₆ = 75 µm, e₆ = 400 µm, w_pad = 250 µm, α= 30°, β= 60°.)

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To ensure reliable return current paths and improve the RF and LO antennas performance, it is critical to optimize the impedance matching of the transition. Due to the symmetry of the transition along the x-axis, Fig. 5(b) presents one half of the physics-based equivalent circuit model. Among the various parasitic elements in the transition, including the resistance (R), capacitance (C) and inductive (L), the capacitance plays the most significant role in determining the overall electrical behavior. For simplification, the capacitance C_P represents the coupling between the signal via and the ground planes on L2 and L5, resulting from the parallel-plane mode excited by the vertical LO current through the signal via. Additionally, the capacitance C_T represents the combined effect of coupling between the signal and grounded vias, as well as the coupling between the antipad and the plane (L5) dominated by the TEM mode. To achieve optimal performance, it is desirable to minimize this capacitance by optimizing the number and location of the grounded vias, given by α, β and r_d [44], and the radius of the antipad r_anti, the via pad r_pad [45].

An 85 GHz prototype of back-to-back quasi-coaxial via transition has been fabricated with the standard HDI PCB technology as shown in Fig. 5(c). the transmission characteristics of the transition were measured using the Cascade Microtech 110 GHz GSG signal probes with 250-µm pitch. The simulation and measurement results are depicted in Fig. 6. It is observed that quasi-coaxial via transition achieves measured relative impedance bandwidth (|S11|< -10 dB) of 25.8% and insertion loss of 0.88 dB at 85 GHz, and the simulated and measured transmission characteristics agree with each other. The slight difference is mainly caused by manufacturing error and other uncertainties, such as the dielectric constant, the thickness of the substrate and the surface roughness of mental.

 

Fig. 6. Simulated and measured S-parameters of the proposed quasi-optical via transition.

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In addition, an IF LPF loaded DGS (defected ground structure) is designed and integrated on L4 and L5 as shown in Fig. 1. It is not included in the quasi-coaxial via transition for simplification in Fig. 5(a) and (b). The details of the proposed LPF loaded DGS is illustrated in Fig. 7(a) and (b). The simulated S-parameters of the LPF is presented in Fig. 7(c). It is shown that the LPF has a 3-dB cutoff frequency at 55 GHz and 20-dB suppression at 71 GHz.

 

Fig. 7. (a) Geometry build-up of the proposed LPF with DGS. (b) Details of the LPF with DGS on different mental layers. (c) Simulated S-parameters of the LPF. (Design parameters: a_4-0 =a_4-1 = 290 µm, b_4-1 = 75 µm, a_4-2 = 375 µm, b_4-2 = 75 µm, a_4-3 = 75 µm, b_4-3 = 300 µm, d₄ = 225 µm, a_5-1 = 75 µm, b_5-1 = 240 µm, a_5-2 = 15 µm, b_5-2 = 75 µm, d₅ = 168 µm.)

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3.4 Dual-lens packaged antenna-coupled mixer

Based on the analysis presented above, the overall characteristics of the quasi-optical mixer can be efficiently optimized within the operating range of 160-180 GHz using the HFSS full-wave simulator. It is noteworthy that while all antenna elements can be optimized to achieve a broader impedance bandwidth, it may not be possible to achieve a wider radiation bandwidth.

In the simulation, a lumped port with impedance of 50 Ω is used to substitute for the Schottky diode. The material models for Megtron 7N from ANSYS's material library are employed. Figure 8(a) and (b) present the optimized outcomes for LO lens antenna, revealing an impedance bandwidth (|S11| < -10 dB) that spans from 74.2 to 90.4 GHz (19.6%), and a radiation bandwidth (Gain > 11 dB) extending from 80 to 90 GHz (11.8%). Despite the possibility of achieving a broader relative impedance bandwidth depending on the coupling between the patch antenna and feeding line, the radiation pattern is not desirable throughout the frequency range of interest. Benefiting from the well-designed matching network, the LO lens antenna also exhibits a significantly good aperture efficiency according to Eq. (1) and (2) [46],

 

Fig. 8. (a) Simulated S-parameter of the proposed LO lens antenna. (b) Simulated gain and efficiency of the LO lens antenna. (c) Simulated S-parameter of the proposed RF lens antenna. (d) Simulated gain and efficiency of the RF lens antenna. (Light blue area: antenna radiation bandwidth. Dark blue area: impedance bandwidth.)

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With the simulated realized gain G_a and radius of the lens r, the estimated aperture efficiency of the LO antenna varies from 73% to 96% within the radiation bandwidth. Figure 8(c) and (d) further illustrate the optimized results for RF antenna. Here, the impedance bandwidth (|S11| < -10 dB) lies within 152.6 to 183.2 GHz (18.2%), and the radiation bandwidth (Gain > 16.1 dB) ranges from 160 to 180 GHz (11.8%). Within the radiation bandwidth, the estimated aperture efficiency of the RF antenna varies from 60.2% to 88.7%. These outcomes provide significant insights into the design and optimization of antenna performance in the quasi-optical mixer.

Figure 9 demonstrates the simulated radiation patterns at LO and RF operating frequencies, 85 GHz and 170 GHz, respectively. These patterns exhibit notable directivity. The LO antenna's radiation pattern is oriented toward the positive Z direction, yielding a FB ratio of 33.3 dB. Conversely, for the RF antenna, the pattern is directed toward the negative Z direction, with an FB ratio of 26.3 dB. The FB ratio, defined as the gain ratio between the positive and negative Z directions, exceeds 20 dB at both frequencies. This simulation theoretically verifies that the proposed LO and RF lens-antennas can function effectively in a quasi-optical mixer of back-to-back reception. Owing to the constant aperture size of the nylon lens, the half-power beam width diminishes from 33° at 85 GHz to 17° at 170 GHz. It's notable, however, that elevated levels are observed in the simulated radiation pattern within the E-plane, specifically from 240° to 270° for the LO and from 230° to 270° for the RF. This can be attributed to the spurious radiation of the feeding network on L6. Also, the perturbations of the patterns observed in the radiation pattern are due to the shielding effects of the finite ground planes.

 

Fig. 9. Simulated radiation patterns of LO and RF lens antennas at 85 GHz and 170 GHz, respectively. (a) E-Plane. (b) H-Plane.

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4. Mixer fabrication and measurement

4.1 Mixer implementation

The 170 GHz quasi-optical mixer was fabricated using HDI PCB technology. Figure 10(a) and (b) show the top and bottom views of the fabricated antenna-coupled mixer. The LO antenna was etched onto the top, while the RF antenna was positioned on the bottom. The Schottky diode, in close to the RF antenna, was mounted using a flip-chip method across the gap of the feedline on L6. The antenna-coupled mixer was subsequently packaged, and the photographs of the packaged mixer module are shown in Figs. 10(c) and (d). Dual 3D-printed lenses, with extended cuboids for enhanced mechanical stability, were placed on the top and bottom of the antenna-coupled mixer. A SMA connector was soldered onto the bottom of the mixer to facilitate the output of the IF signal.

 

Fig. 10. (a) Top and (b) bottom views of the proposed quasi-optical mixer. (c) Top and (d) bottom views of the packaged mixer.

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4.2 Experiment details

The antenna-coupled mixer packaged by back-to-back lenses was measured at the frequencies near 170 GHz in a sub-harmonic mixing mode. Figure 11. illustrates the schematic diagram of the mixing experimental setup to characterize the conversion loss and radiation patterns of the antenna-coupled mixer. The measurement setup consists of two signal generators AV 1487B and Agilent 8257D, a spectrum analyzer Agilent E4448A, a power meter Erickson PM5B, a plano-convex lens, a rotation stage controller, LO and RF output part. Two commercial solid-state sources (active multiplier-chains) were utilized to generate the LO and RF signals, respectively, which were transmitted by two standard horn antennas at the front and rear of the designed mixer. One frequency multiplier (×12), which can provide RF signal with maximum power level of 20 dBm at 170 GHz, is built up with the signal generator (13.3-15 GHz), an active 6×multiplier-chains GAMW6-10-8186P26 (80-90 GHz), and a doubler D175 (160-180 GHz). The other frequency multiplier (×6) was utilized to generate LO signal with maximum power level of 26.5 dBm at 85 GHz.

 

Fig. 11. The measurement setup of the quasi-optical sub-harmonic mixer.

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The RF radiation beam was directly coupled into the lens with an air cavity from the one side of the mixer module. In order to reduce LO power leakage and pump the diode effectively, a PTFE plano-convex lens with 50-mm focal length and 2-inch diameter was used. The LO radiation beam, after being collimated by the PTFE plano-convex lens, was coupled onto the lens from the other side, facilitating heterodyne mixing between the RF input signal and the second harmonic of the LO pumping signal. The down converted IF output signal was recorded using the Agilent E4448A spectrum analyzer. Moreover, the RF multiplier-chain module, followed by the RF transmitter horn antenna, was positioned at a distance (d = 0.4 m) from the mixer to satisfy far-field requirements based on the formula $ \textrm{2}{\textrm{D}^\textrm{2}}/\mathrm{\lambda }$, where D is the maximum physical aperture dimension of RF transmitter horn antenna with 15.4 mm × 10.6 mm, and λ is the free-space wavelength at the RF operating frequencies. For measuring the radiation pattern, the LO multiplier-chain module and plano-convex lens shared the rotating stage with the mixer and were moved together with it (as symbolized by the dashed box).

4.2.1 Conversion loss

The conversion loss of the quasi-optical mixer can be achieved according to the definition as (dB) [41]:

Figure 12 (a) plots the comparison between simulated and measured conversion loss versus frequency with the sub-harmonic mixing mode when the IF frequency is set to 1 GHz. It can be observed that the measured SSB conversion loss varies within the range between 11.3 and 15.4 dB at the RF operating band, and reached the minimum value of 11.3 dB at 178 GHz, and maximum value of 15.4 dB at 164 GHz, respectively. The value of the measured conversion loss increases by around 4 dB than the simulation, which may result from the variation of impedance matching condition within the RF operating frequency range as well as fabrication, assembly, and measurement errors. On the whole, the measured and simulated results agree reasonably well on the curve trends. Figure 12 (b) and (c) plots the simulated impedance Z_Diode of the Schottky diode versus LO and RF operating frequency with the LO pumping power of 6.4 dBm, that has an acceptable deviation from the 50 Ω impedance of the antenna.

 

Fig. 12. (a) Comparison between simulated and measured conversion loss. (b) and (c) Simulated impedance Z_Diode of the Schottky diode

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4.2.2 Radiation patterns

Due to the RF antenna is integrated with the Schottky diode, it is generally quite difficult to directly measure the radiation patterns of the RF antenna. It can be demonstrated in terms of the IF output power-level recorded from the spectrum analyzer by controlling the rotation stage. Figure 13 shows the normalized radiating patterns of the RF antenna on the E- and H-planes at 170 GHz. It can be found that a good agreement is achieved between the measurement and simulation on the pattern main lobes. The high level of measured co-polarization in the E-plane from 90° to 135° and the H-plane from 90° to 135° is mainly due to the reflection caused by the assembly and measurement errors. Since the power level in the backside and cross-polarized direction is quite weak, only radiation patterns in the co-polarized direction are measured, where the azimuth angle θ is from 90° to 270°.

 

Fig. 13. Simulated and measured radiation patterns of the quasi-optical sub-harmonic mixer at 170 GHz. (a) E-plane. (b) H-plane.

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4.3 Comparison and discussion

Table 1 shows the comparison of the performance of the proposed mixer and other state-of-the art ones using Schottky diodes. It can be found that the waveguide-based mixers exhibit the best performance, yet they are both challenging and expensive to manufacture good quality waveguide structures duo to the reduced feature size with the increasing frequency at THz band. In comparison, the quasi-optical mixers make a good compromise between device performance and system cost. The reason for this is that the lack of effective modeling and optimization methods poses obstacles to optimize the performance of quasi-optical mixers which integrate planar antennas and nonlinear device. Additionally, accounting for the Schottky diodes with parasitic reactance, it is challenging to design the optimal antenna and impedance matching network, while achieving a high coupling efficiency and isolation for RF, LO and IF signals. With the Ref. to [17] and [18], the Schottky diode is simply integrated at the antenna center without any impedance matching or coupling circuits, resulting in poor conversion performance.

Table 1. Comparison Performance of The Proposed Quasi-optical Mixers with Others

View Table

The best value of conversion loss for our designed quasi-optical is 11.3 dB that is a great progress closer to the performance of waveguide mixers at similar frequencies. The achievement mainly benefits from the configuration of our presented quasi-optical coupling RF/LO signals by back-to-back antennas as well as good matching / isolation network. Finally, it should be emphasized that the proposed quasi-optical mixer is a good solution to scale the number of pixels into a 2-D array, facilitating low-cost sensing and imaging applications.

5. Conclusion

In this paper, a quasi-optical 170 GHz sub-harmonic mixer packaged by 3D-printed back-to-back lens is proposed using HDI technology. The LO and RF antenna elements integrate a compact matching/isolation network with a low-loss quasi-optical via transition structure to achieve high-efficiency radiation coupling at two frequency bands. In order to enhance the gain, dual 3D-printed back-to-back dielectric lenses are loaded on LO and RF antenna elements, respectively. Additionally, in the multilayer build-up substrate configuration, the buried plane reflectors realize the LO and RF radiation isolation in the free space. Based on the integrated antenna elements, a quasi-optical mixer is fabricated and experimentally characterized operating in the sub-harmonic mixing mode. The measured results exhibit the best value of the conversion loss is 11.3 dB. The presented configuration of the mixer offers a good compromise between performance and cost, thus will have huge potential in the sub-THz sensing and imaging applications.