A 200–240 GHz Sub-Harmonic Mixer Based on Half-Subdivision and Half-Global Design Method

For the terahertz harmonic mixer, a design model based on Half-Subdivision and Half-Global Design Method (HS-HGDM) with a single functional unit is proposed. The single functional unit circuit of the mixer, such as LO or IF Low Pass Filter (LPF), is designed by Subdivision Design Method (SDM), and the rest circuits of the mixer are designed by Global Design Method (GDM). The harmonic mixer based on this model is characterized by simple circuit structure, low conversion loss, small circuit size and high stability. In this paper, an improved Compact Suspended Micro-strip Resonators (CSMRs) filter is developed for the IF part of sub-harmonic mixer. The remaining circuits consist of some basic transmission units, such as the High-Z Low-Z impedance Transmission Lines (H-Z L-Z TLs) applied for main circuit, and full/reduced height WR4.3/WR8 applied for providing RF/LO signal. In RF frequency range 200–240 GHz, a Single Sideband (SSB) conversion loss of 7.36±0.76 dB operating at IF frequency 1.8 GHz, and a Double Sideband (DSB) noise temperature below 1034 K with the LO power of 2–5 mW and the LO frequency of 107 GHz were achieved. This broadband sub-harmonic mixer operates at room temperature, which makes it applicable to sub-millimeter wave or terahertz wireless communication systems and imaging inspection systems.


I. INTRODUCTION
At present, the solid-state sub-millimeter wave and terahertz technologies, such as frequency multiplication, detection, mixing, power amplification and combiner based on various types of diodes and transistors [1]- [6], are moving toward higher operating frequency bands, higher output power and newer materials [7], [8]. Due to the lack of high power and stable radiation sources operating at higher frequency, the mixing technology has received rising popularity for the design of sub-millimeter wave or terahertz system. For example, the harmonic mixers with Schottky Barrier Diodes (SBDs) [9]- [11], Hot Electron Bolometer [12], [13] and Super-conductor Insulator Super-conductor [14], [15] have been extensively applied in the conversion of high frequency to relatively low frequency for the purpose of signal amplification and measurement. Especially when the RF operating The associate editor coordinating the review of this manuscript and approving it for publication was Yuhao Liu. frequency band of the mixer reaches in excess of 1 THz, high order harmonics are usually involved to facilitate the LO signal, the related measurement and application conditions to be realized [16]- [18]. At present, harmonic mixers based on the SDM, the GDM and the HS-HGDM have been commonly applied to the sub-millimeter wave or terahertz wireless communication systems and imaging inspection systems [19]- [23].
Among those methods, the terahertz harmonic mixer based on the SDM is known as the most common one, as shown in Fig. 1. At first, it requires the design of some passive functional units, such as LO LPF, IF LPF and the likes [24]- [28]. In addition, those passive functional units can be directly applied for other sub-terahertz circuits. Then, the completed RF part (the blue box) and the completed LO part (the green box) are designed to achieve their specific performance, respectively. At last, the RF part, diode and the LO part are connected and matched through a number of Suspended Micro-Strips (SMS). At this time, the impedance matching variables of the whole circuit are reliant on the numbers of SMS. It would make the circuit structure complicated and cause the circuit size to increase. Therefore, the operating frequency band of the mixer based on the SDM is narrow in most cases. Moreover, once the expected performances of the mixer fail to be achieved, there is a necessity for all of the functional units and the RF part and the LO part to be redesigned. For example, [26] presented a 211-226 GHz subharmonic mixer using a high-low impedance filter applied for LO LPF and a CSMRs filter applied for IF LPF. The SSB conversion loss is 5.9-12 dB for the mixer, which has a 14 GHz operation bandwidth and a 8.908 mm circuit size. Also, this mixer has a narrow frequency band and poor flatness. In [27], a 290-310 GHz sub-harmonic mixer with the RF waveguide filter, the LO filter and the IF filter is reported. The measured SSB conversion loss is 9-10 dB, and the DSB noise temperature is 1000-1500 K with the operation bandwidth of merely 20 GHz. The mixer shows a complex structure, and a further improvement is necessary for the effective operating frequency band.
In addition to the mixer designed by the SDM with functional unit circuits, another approach to the design of the harmonic mixer is the GDM, consisting of some basic circuit units and treating the SSB conversion loss as the optimization goal. Those basic circuit units mainly include H-Z L-Z TLs, full/reduced height rectangular waveguides and others, as described in our previous work [29]- [31]. The simple model of sub-terahertz harmonic mixer based on the GDM is illustrated in Fig. 2. As there are a large number of optimization variables and massive optimization space, such mixers demonstrate such characteristics as simple structure, small size and wide working frequency band. Nevertheless, the GDM requires repeated iterations by performing field simulation and circuit simulation until the desired results are achieved, which is time consuming in the design process and leads to a poor stability in actual operation. Though the GDM can be used commonly, the specific design circuit for every mixer is unique and incapable to be applied to other circuits straightaway. For example, [30] referred to a 220 GHz subharmonic mixer based on the GDM. In the RF frequency 198-238 GHz, this mixer has achieved a SSB conversion loss of 6.35-10 dB operating at 110 GHz and a substrate size of 5.365 mm. The problem lies in a large flatness shown by that measured SSB conversion losses, and a deviation from the simulation results with LO non-central frequencies.  Due to the addition of functional units, the performance of harmonic mixer designed by the HS-HGDM is consistent when compared with that of GDM. With similar LO LPF and IF LPF structures to [26], [32] introduced a 220 GHz sub-harmonic mixer premised on the HS-HGDM with double LPFs. This mixer achieved a SSB conversion loss of 9 dB and a DSB noise temperature of 500-1500 K at 208-229 GHz.
In this paper, a model for designing terahertz harmonic mixers based on the HS-HGDM with a single functional unit is introduced in section II. In section III, a 200-240 GHz sub-harmonic mixer based on this method proposed by us is designed, and an improved CSMRs is applied for IF part. In section IV, the results of sub-harmonic mixer are presented, including simulated and measured SSB conversion loss, DSB noise temperature, the linearity and S11. In section V, the analysis of 220 GHz sub-harmonic mixers is conducted by applying different methods. The conclusion is drawn in Section VI.

II. METHOD
In general, the harmonic mixer with specific performances is obtained by combining the circuit model designed by 33462 VOLUME 8, 2020 Advanced Design System and the field model designed by High Frequency Structure Simulator. According to the harmonic mixers designed by the SDM, the GDM and the HS-HGDM with double function units [19]- [32], it can be found out that the HS-HGDM with a single function unit is able to be realized. The design process of the mixer can be referenced in [30].
A simple model for the design of terahertz harmonic mixer by the HS-HGDM with a single functional unit is illustrated in Fig. 3. The IF output part is very important to the whole mixer. Therefore, a LPF filter intended to pass the IF signal is applied to the IF part of the harmonic mixer. The remaining circuits of the mixer, including RF part and LO part, consist of some basic transmission units, such as H-Z L-Z TLs and full/reduced height waveguide.

III. DESIGN A. THE 200-240 GHZ SUB-HARMONIC MIXER BASED ON THE HS-HGDM WITH A SINGLE LPF
In order for further introduction and validation of the model, a sub-terahertz sub-harmonic mixer is designed based on Fig.  3, which covers the range from 200 to 240 GHz. The circuit model and the field model of this sub-harmonic mixer are shown in Fig. 4 and Fig. 5, respectively. The mixer is comprised of the continuous basic circuit units and the discontinuous basic circuit units. The former includes the suspended micro-strip transmission line, micro-strip transmission line and full/reduced height WR4.3/WR8. The latter includes a DC grounded in RF port, the RF/LO probe transition, the RF/LO reduced waveguide transition, the shorted circuit end of RF/LO reduced waveguide, SBDs flipped on quartglass substrate, suspended micro-strip high-low impedance step structure, micro-strip high-low impedance step structure, an improved CSMRs filter and IF output. The details about the diode and the basic circuit units can refer to [30], [31]. The full height WR4.3 and a reduced height WR4.3 coupled to a quartz suspended micro-strip probe are applied to generate the RF signal. The full height WR8 and a reduced height WR8 coupled to a quartz micro-strip probe are involved to generate the LO signal. The CSMRs filter is intended for IF part with the performances of passing the IF signal and blocking the RF/LO signal. The K connector is employed to output the IF signal, and the IF port is terminated in 50 .
In addition to the improved CSMRs filter (specific stated in B), 220 GHz sub-harmonic mixer involves 12 variables, as shown in Fig. 5. Based on the field model of 220 GHz broadband sub-harmonic mixer, its corresponding circuit model is designed as illustrated in Fig. 4. After repeated design and simulation of the mixer field model and circuit model, the mixer 3-D illustration and dimensions are finalized as shown in Fig. 6 and Table 1, respectively.  Initially, in order to validate the effectiveness of the HS-HGDM with a single functional unit, two sub-terahertz subharmonic mixers with different RF grounded structures are designed, both of which achieve an excellent performance. For one mixer, the RF end of the substrate and the cavity are connected by three gold wires. For the other mixer, the holes are punched at the RF end of the substrate and are filled with the silver epoxy. In comparison to the former, the latter minimizes manual assembly errors and avoids the additional losses. However, due to the small circuit size of the terahertz band and the brittleness of the quartz substrate, it is challenging to ensure the integrity of the substrate in the process of fabricating the holes. Therefore, the former mixer structure with jumping gold wires at the end of the RF ends up being chosen.

B. THE IF LPF
Concerning 220 GHz sub-harmonic mixer, the IF LPF based on quartz micro-strip is applied to pass the IF signal (0-50 GHz), and to block the LO signal (100-120 GHz) and RF signal (200-240 GHz) propagation into the IF channel. In this work, a symmetrical improved CSMRs is proposed, as illustrated in Fig. 7. The performance and dimension of the CSMRs are indicated in Fig. 8 and Table 2, respectively. The S21 of the CSMRs is better than −0.25 dB from frequency between 0 and 50 GHz, and the S11 is greater than −20 dB. The out-of-band suppression of the CSMRs is below −19 dB  from frequency 92 GHz to 248 GHz. It is worth noting that the improved CSMRs exhibits such characteristics as low passband insertion loss, high stop-band rejection, wide stop-band and small size. It is capable of enabling the IF signal to pass and the RF/LO signal to block.

C. THE OTHER PARTS
In addition to the structures of 220 GHz sub-harmonic mixer referred to above, more details on other parts, such as RF probe-to-waveguide, LO probe-to-waveguide and the highlow impedance transition of LO part, are presented in Fig. 9. The two ends of the RF probe-to-waveguide and H-Z L-Z TLs of LO part adopt suspended micro-strip structure. In respect of the LO probe-to-waveguide, the suspended micro-strip structure is applied to one end of connection with H-Z L-Z TLs, while the micro-strip structure is adopted for the other end close to the IF part.

D. THE FABRICATION
With regard to the main circuit of the sub-harmonic mixer, a quartz substrate with the length of 5.33 mm is designed.  A gold conductor is electroplated on the surface of the quartz substrate. Fig. 10 illustrates the fabricated and the assembled cavities of 220 GHz sub-harmonic mixer.

IV. MEASUREMENT AND RESULTS
In order to validate the accuracy of the HS-HGDM with the single functional unit, the performances of 220 GHz subharmonic mixer are subject to assessment with consideration given to the simulated and measured SSB conversion loss, DSB noise temperature,linearity and S11. The similar mixer measurement process is detailed in [31]. Furthermore, a comparison is performed between this 220 GHz sub-harmonic mixer and other 220 GHz sub-harmonic mixers designed by taking different methods.

A. THE SSB CONVERSION LOSSES WITH FIXED LO FREQUENCIES
The simulated and measured SSB conversion losses of the mixer are obtained by sweeping the RF frequency to maintain the LO frequencies (104 GHz, 111 GHz and 115 GHz), as illustrated in Fig. 11. When the LO frequency is maintained at 111 GHz with the LO driven power of 3 mW and the RF power of 0.15 mW, the conversion loss was simulated to be 7.9±0.76 dB and measured to be 8±1.38 dB across the RF frequency range from 201 to 238 GHz.
The summary of the SSB conversion losses with LO frequencies is indicated in Table 3, and it can be discovered that the measured results are consistent with the simulation ones. The difference of average value between the simulated and measured SSB conversion loss is lower than 0.83 dB. The fluctuation of the measured SSB conversion loss is insignificant, and the max fluctuation is less than ±1.38 dB.

B. THE SSB CONVERSION LOSSES WITH FIXED IF FREQUENCIES
The simulated and measured SSB conversion losses of the 220 GHz sub-harmonic mixer are determined by sweeping the RF frequency at multiple fixed IF frequencies, which are 1.8 GHz, 3.6 GHz and 5.2 GHz, respectively. Those data are plotted in Fig. 12, and the measured results conform to the simulated ones. As for the RF frequency ranging from 200 to 240 GHz, the simulated SSB conversion loss is 6.88-7.86 dB, and the measured results with IF frequencies are lower than 8.6 dB overall. It can be noticed that the IF output of the mixer is consistent in the low frequency range. The summary made of those conversion losses is indicated in Table 4.

C. THE DSB NOISE TEMPERATURE OF MIXER VERSUE THE LO POWERS, FIXED IF FREQUENCIES
In respect of the LO frequency fixed at 107 GHz, the measured DSB noise temperatures of the measurement system VOLUME 8, 2020 and mixer versus the LO powers are indicated in Fig. 13. When the sub-harmonic mixer operates at the fixed IF frequencies (1.83 GHz and 2.75 GHz), the DSB noise temperature of the measurement system ranges from 763 K to 1137 K, and the DSB noise temperature of the mixer is lower than 1034 K with the LO power of 2-5 mW. The minimum DSB noise temperature is 688 K at the IF frequency 1.83 GHz, with the LO power being 2 mW.

D. THE IF OUTPUT POWER VERSUS THE RF INPUT POWER
In order to describe the linearity of the 220 GHz subharmonic mixer, the measured IF output power versus the RF input power is illustrated in Fig. 14. The LO frequency is maintained at 110 GHz with the LO power of 3 mW and the RF frequency of 217 GHz. The P 1dB of the IF output power is −9.1 dBm with the RF input power of −0.6 dBm. When the RF input power rises to 3 dBm, the IF output power is saturated at −8.1 dBm.

E. THE S11 OF THE SUB-HARMONIC MIXER
In the RF frequency range from 192 to 249 GHz, the simulated S11 of the 220 GHz sub-harmonic mixer is lower than −13.8 dB and the measured S11 is lower than −10 dB, as indicated by Fig. 15. This sub-harmonic mixer achieves an excellent return loss in the RF port.

V. ANALYSIS
The 220 GHz sub-harmonic mixer based on the HS-HGDM with a single functional unit has demonstrated an excellent performance in terms of SSB conversion loss, DSB noise  temperature, linearity and S11. In [31], it has demonstrated that a 220 GHz sub-harmonic mixer designed by the GDM achieves a superior performance on the circuit size, conversion loss and DSB noise temperature of the mixer compared to the mixers designed by the SDM. Therefore, in this paper, just some of the details about the comparison between the HS-HGDM and the GDM are shown in Fig. 16.
When LO frequencies are maintained at non-central frequencies, 104 GHz and 115 GHz, the problems of the mixer designed by the GDM [31] include a deviation of the measured SSB conversion loss from the simulation results, and a relatively large flatness. The sub-harmonic mixer designed by the HS-HGDM with a single functional unit has achieved an excellent consistency in the simulation and measurement of the SSB conversion loss. Meanwhile, the fluctuation is significant.
As revealed by a further analysis, the core of the mixer designed by the GDM is that all transmission lines and rectangular waveguides with varying impedances are taken as the optimization variables, and the SSB conversion loss is treated as the final optimization goal. Despite the mixer based on the GDM that possesses a simple structure and demonstrates a superior performance to the SDM, it discounts the VOLUME 8, 2020  performance of some internal circuits. In addition, the mixer operates at terahertz frequencies, which causes the gap to be widened between simulation and measurement results. The comparison performed of the 220 GHz sub-harmonic mixers based on the HS-HGDM with single LPF/double LPFs, the GDM and the SDM is indicated in Table 5.
In comparison to the 220 GHz sub-harmonic mixers designed by the SDM [25]- [27], the mixer designed by the HS-HGDM exhibits such advantages as simple circuit structure, low conversion loss and low DSB noise temperature. And relative to the 220 GHz sub-harmonic mixers designed by the GDM [31], the mixer designed by the HS-HGDM with a single LPF is effective in reducing the flatness of SSB conversion loss.

VI. CONCLUSION
In this paper, the design, fabrication, measurement and analysis of the 200-240 GHz sub-harmonic mixer using the HS-HGDM with a single functional unit are discussed in detail. It consists of an improved CSMRs filter and variety of basic transmission units, such as the H-Z L-Z TLs and full/reduced height WR4.3/WR8. This 220 GHz sub-harmonic mixer is characterized by SSB conversion loss, DSB noise temperature, linearity and S11, all of which indicates an excellent performance. When IF frequency is maintained at 1.8 GHz, the measured SSB conversion loss is measured to be 6.61-8.12 dB across the RF frequency range from 200 to 240 GHz. In comparison to the harmonic mixers designed by the SDM, the GDM and HS-HGDM with double LPFs, the harmonic mixer based on the HS-HGDM with a single LPF demonstrates various advantages, including simple circuit structure, low conversion loss, small circuit size and high stability.