Two-Tone Excited Hybrid-Coupler-Based Intermodulation Generator for High-Isolation Wireless Sensing Applications

An intermodulation generator is designed and presented with integration of a hybrid coupler and two identical Schottky diodes (i.e., D1 and D2). The connection polarities of D1 and D2 to the direct and coupled ports of hybrid coupler are opposite for its rapid realization of balanced intermodulation generation. Due to the superior coupling characteristics of hybrid coupler, it can distribute an incident two-tone signal to the direct and coupled ports evenly for D1 and D2, and deliver the balanced intermodulation generations to the isolation port highly insulated from its incident port. Two identical quarter-wavelength shorted stubs at the fundamental frequency are implemented by suppressing the second-order spectrums for an enhancement of the balanced intermodulation generations. Both theoretical analysis and experiments validate the presented intermodulation generator design, which can highly isolate its incidences (the two tones) and outputs (the intermodulation generations) for the future high-isolation wireless sensing applications.


I. INTRODUCTION
With an increased number of sensor nodes in the internet of thing (IoT), wireless sensing has been an insurmountable task to capture atmospheric physics, e.g., humidity, temperature, and pressure. Most of the time, a wireless sensing system with properties of high reliability, low cost, compactness, and lowpower consumption is preferred. Generally, a fully passive 2 nd -harmonic transponder can be an attractive candidate, and has been explored and developed since more than 50 years ago [1]. When a base station interrogates the harmonic transponder at the fundamental frequency (ω 0 ), the 2 nd harmonics (2ω 0 ) are accordingly generated and backscattered, which can then be captured and demodulated by the base station for atmospheric physics data retrieves. On account of its high robustness to the environmental clutter interference, The associate editor coordinating the review of this manuscript and approving it for publication was Theofanis P. Raptis . 2 nd -harmonic transponders have been successfully employed into various scenarios, e.g., the foraging range of bumblebees research [2], wood frogs tracking [3], avalanche victim searching [4], and cracked wall monitoring [5], and etc.
To preserve a possibility of further 2 nd harmonic recycling for a direct current (dc) current conversion enhancement (can be up to 25% of the fundamental incidences), an alternative 3 rd -harmonic generation from its high-efficiency rectification was recently exploited by implementing a hybrid coupler for the backscattering responses to align an antenna pair in a wireless power transfer (WPT) system [6], whose operation schematic is depicted in Fig.1. Because of the dual-mode characteristics of hybrid coupler, the fundamental interrogation (ω 0 ) and the 3 rd -harmonics (3ω 0 ) response can be highly isolated. However, it heavily requires dualband antenna pairs working at both the fundamental and 3 rd harmonic frequencies to establish both the power and data wireless link between the base station and the terminal, which VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ FIGURE 1. The schematic of the high-isolation wireless sensing system (The 3 rd harmonic/intermodulation generator is marked with a dash box successive to P 1 and P 4 ).
increases the complexity of circuit design and is not helpful for a compact system realization. Additionally, high-order harmonics (2 nd and 3 rd ) will bring about great free-space path loss [7] when penetrating through the air to degrade its operational distance range. Furthermore, to demodulate the backscattering 3 rd -hamronic carriers as shown in Fig.1, a local oscillator (LO) around 3ω 0 should be implemented [8], which increases the complexity and cost of overall system. Moreover, the spurious radiation from harmonic transponders can also be another problem to guarantee regulatory compliance [9]. In this research, an intermodulation generator is designed and presented with integration of hybrid coupler and two identical Schottky diodes (i.e., D 1 and D 2 ), whose operation schematic is similar to the proposed wireless sensing system from [6] as depicted in Fig. 1. It eliminates the worries on the penetration loss, LO frequency source, as well as spurious radiation from the harmonic transponders, however, still preserves very high robustness to the environmental clutter interference for the high-isolation wireless sensing system.
As shown in Fig. 1, to highly isolate the two-tone interrogation and backscattering intermodulation, two dual-polarized (DP) antenna pairs (DP 1 : TX 1 and RX 2 , DP 2 : TX 2 and RX 1 ) can be employed [10] by utilizing share-aperture antenna mechanism, which ensures a compact system by sharing the same antenna aperture for dual polarizations (i.e., VP and HP in Fig. 1). A transmitting antenna (TX 1 ) interrogates a vertically-polarized (VP) two-tone (ω 1 , ω 2 ) signal, which can be captured by a receiving antenna (RX 1 ) and distributed by the hybrid coupler for the balanced intermodulation generation from D 1 and D 2 [11]. Due to eliminations of the input matching networks, the intermodulation generator can be integrated compactly with other functional units. According to the coupling characteristic of hybrid coupler, the intermodulation generations (ω IM1 = 2ω 1 − ω 2 , ω IM2 = 2ω 2 − ω 1 ) can be completely delivered to the isolation port (P 4 ) for the backscattering link establishment between the two horizontally-polarized (HP) antennas (i.e., TX 2 and RX 2 ). Both simulated and measured results validate that the twotone excited intermodulation generator can produce and deliver the completed intermodulation to the isolation port highly isolated from the input port (P 1 ), which brings a prospect for the future high-isolation wireless sensing by adopting a shared-aperture dual-polarized antenna.

II. THEORY ANALYSIS AND OPERATION MECHANISM
The two-tone excited intermodulation generator is provided in the dash box of Fig. 1. The connection polarities of D 1 and D 2 to the direct and coupled ports of the hybrid coupler are opposite for its rapid realization of balanced intermodulation generation [11], which enables a compact system realization without considering any matching networks. To enhance the balanced intermodulation generations, two identical quarterwavelength shorted stubs at the fundamental frequency (ω 0 ) followed by P 2 and P 3 of the hybrid coupler are implemented by suppressing the second-order spectrums. Since frequency offsets between the intermodulation and ω 0 are insignificant (typically < 50 MHz), the hybrid coupler is thus capable of coupling and delivering both the two tones (ω 1 , ω 2 ) and the intermodulation (ω IM1 , ω IM2 ) generations within its effective frequency bandwidth simultaneously, whose S-parameters at the fundamental frequency (ω 0 ) can be expressed as follows.
To compare the intermodulation and the 3 rd -harmonic generators in Fig. 1, the dual modes of hybrid coupler are analyzed. According to its odd-even mode analysis, S-parameters at the 3 rd harmonic can thus be derived as given in (2). It should be noticed that the S-parameters at 3 rd harmonic are similar to ones at the fundamental frequency except the phase differences of S 21 (S 12 ) and S 43 (S 34 ). Consequently, the hybrid coupler can operate at both the fundamental and 3 rd harmonic frequencies.
To intuitively observe the properties of hybrid coupler, its S-parameters are simulated in the Advanced Design System (ADS), whose structure is realized with several ideal microstrips. Since the structure of hybrid coupler is symmetrical, only magnitudes of S 11 , S 21 , S 31 and S 41 , and phase differences of (S 11 -S 41 ) and (S 21 -S 31 ) of ADS simulation are given. The frequency is normalized from 0 to 4ω 0 , which fully covers the fundamental and 3 rd -harmonic frequencies ranges, as illustrated in Fig. 2.
It is firstly assumed that the power levels of the single and the two-tone incidences are identical, which can be expressed as V S at the input port (P 1 ) of the hybrid coupler. Based on the S-parameters as provided in (1), V S can be then distributed to the direct (P 2 ) and coupled (P 3 ) ports while its isolation port (P 4 ) maintains highly isolated. Therefore, the distributed signals at P 2 and P 3 can be calculated with where V S = √ 2V IN cosω 0 t and V S = V IN (cosω 1 t+cosω 2 t) for the single-tone and the two-tone incidences, respectively. It can be observed that V dir and V cou have even magnitudes (except their phase differences), which is important for the balanced intermodulation generations from the two identical diodes of D 1 and D 2 [11]. Typically, the nonlinear output response (Vo) of D 1 or D 2 can be expressed by the Taylor series in terms of its incident signal [6], for example, Vo generated from D 1 at P 2 with an excitation of V dir .
Only high-odd-order terms of a 3 V 3 dir and a 5 V 5 dir contribute to the 3 rd harmonic and intermodulation, whose corresponding voltages generated by D 1 and D 2 at direct (P 2 ) and coupled (P 3 ) ports can thus be calculated with where terms of = cos3ω 0 t and ξ = cosω IM1 t+cosω IM2 t for 3 rd harmonic and intermodulation, respectively. To analyze the above the delivery of 3 rd harmonic and intermodulation (6, 7) through the dual-mode hybrid coupler, the phase differences between V' dir and V' cou , and corresponding power magnitudes should be initially evaluated. Since it is not possible to know the phase and power magnitude info directly from (6) and (7), the harmonic balance (HB) simulation from advanced design system (ADS) is performed to evaluate the coefficients of a 3 and a 5 . The single-tone or the two-tone signal (V S ) is incident at the input (P 1 ) port of hybrid coupler. Then the mentioned phase differences and power magnitudes can be simulated respectively from Fig. 3. For the simple validation, the single tone incidence at frequency of ω 0 =2 GHz is selected without considering the authorized frequency band, such as the ISM, while the frequency space of the two tones diverse from the center frequency (ω 0 =2 GHz) with ω =0.02 GHz (20 MHz), whose detailed parameters in the ADS and the implemented diodes information are provided in the Table 1. HSMS2860 is firstly selected to evaluated power magnitudes and phase differences at the direct (P 2 ) and coupled (P 3 ) ports of hybrid coupler respectively. As indicated by the phase and power magnitudes simulation from Fig. 3a and Fig. 3b, it can be noticed that 3 rd harmonic generated from D 1 and D 2 at P 2 and P 3 respectively keeps equal, while its phase differences maintain approximately −90 • (−i). Henceforth, only the term of a 3 V 3 IN the term of 2a 5 V 5 IN in (6) and (7) can explain the equal power magnitudes and −90 • (−i) phase differences of the 3 rd harmonics at P 2 and P 3 of hybrid coupler. Similarly, the intermodulation generations from D 1 and D 2 can also be evaluated with an identical incident power, which is given in Fig. 3b. It indicates that within the power ranges of interest, the power magnitudes of P' cou and P' dir are closely equal. The differences in between are less than 2 dB even at an ultralow incident power level of −10 dBm. In the meantime, the power magnitude differences are continuously decreased (−10∼+10 dBm). Furthermore, with an increase of the incident power, the phase differences between the in t ermodulation of V' cou and V' dir decrease incessantly, whose trend approaches +90 • (+i). With comparison of (6) and (7), only a condition under the term of 12a 3 IN can explain such ADS simulation results in Fig. 3b. Therefore, the coefficient of a 5 contributes to almost all the intermodulation generation when the interrogating power ranger is over −10 to +10 dBm.
Hence, the 3 rd harmonic and intermodulation at the direct and coupled ports (V dir and V cou in (6) and (7)) of hybrid coupler can then be approximated to ones in (8) and (9). According to S-parameters provided in (1) and (2), V dir and V cou (both 3 rd harmonic and intermodulation) can be totally delivered through the hybrid coupler to the isolation port (P 4 ) with high isolation from the input port (P 1 ) as demonstrated by (10,11) as follows.
It is demonstrated that the 3 rd harmonic and intermodulation generations at the direct and coupled ports of hybrid coupler have same magnitudes and 90 • phase differences (−90 • (−i) for the 3 rd harmonic, while +90 • (+i) for the intermodulation) to maintain them be completely coupled to P 4 isolated from the incident port without any power reflection. Therefore, the signals generated from D 1 and D 2 are totally delivered to the isolated port of the dual-mode hybrid coupler, which can be calculated as shown below. The single-tone and two-tone signals as well as 3 rd harmonic and intermodulation spectrums delivering through the dualmode hybrid coupler can be observed in Fig. 4, which guides how to perform the experimental validation in next section. Furthermore, to evaluated the different diode influence of the balanced intermodulation generations, an SMS7630 diode is selected as a comparative simulation experiment for both the 3 rd harmonic and intermodulation through the hybrid coupler. The ADS parameters settings of SMS7630 are identical with ones of HSMS2860, which is detailed in the TABLE 1. The 3 rd harmonic and intermodulation generated from D 1 and D 2 for the diodes of SMS7630 and HSMS2860 are provided co-located in Fig. 3c and 3d. From the simulations, it is found that SMS7630 outperforms over the low power ranges for no matter the 3 rd harmonic (−10∼ −2 dBm) and intermodulation (−10∼−4 dBm), while the HSMS2860 outperforms over the mid power range for no matter the 3 rd harmonic (−2∼+10 dBm) and intermodulation (−4∼+10 dBm). Therefore, diodes can be carefully selected for its specific applications.

III. EXPERIMENTAL RESULT
The proposed intermodulation generator is designed at ω 0 = 2 GHz in ADS and fabricated on a low-loss 20-mil RO4350B substrate. Two categories of Schottky diodes SMS7630 and HSMS2860 are employed as D 1 and D 2 for high-efficiency balanced intermodulation generations.
As depicted in Fig. 5a, another 2-GHz hybrid coupler is used as a two-tone signal power combiner, whose coupled port is matched to a 50-terminal. A signal generator AV1441A and a vector network analyzer AV3656A (alternative signal generator) are utilized to generate the two tones at ω 1 = 1.98 GHz and ω 2 = 2.02 GHz, respectively, whose output ports are directly connected to the input (P 1 ) and isolated (P 4 ) ports of the two-tone power combiner (i.e., 2-GHz hybrid coupler).
Therefore, the two tones are generated at the direct (P 2 ) port. When two tones interrogate at the input (P 1 ) port, a spectrum analyzer is employed to readout the intermodulation at the isolation port (P 4 ) of hybrid coupler. Since intermodulation generations at ω IM1 and ω IM2 have equal power magnitudes, only the lower frequency (ω IM1 ) is considered and measured during the experiment. The intermodulation generation from different Schottky diodes of SMS7630 and HSMS2860 over the power range from  −10 dBm to +10 dBm can be observed in Fig. 6. Since the signal generator AV1441A and the vector network analyzer AV3656A cannot cover 3 rd harmonics (3ω 0 = 6 GHz), only the intermodulation from the isolation port (P 4 ) is measured by compared to the simulated 3 rd harmonics.
It is indicated that a good agreement between the simulated and measured results can be achieved from both the Schottky diodes of SMS7630 and HSMS2860. For the meantime, the intermodulation outperforms 3 rd harmonics (simulated) over low power range no matter the Schottky diode SMS7630 (−10∼0 dBm) or HSMS2860 (−10∼−3 dBm). However, for the diode of HSMS2860, the power level difference is very small, which demonstrations that the power conversion efficiency of both the intermodulation and 3 rd harmonics are kept with similar values. Therefore, for same power incidence (single or two tones), the intermodulation generator presented in this article can have absolutely superiority when transferring from the terminal to the base station.

IV. CONCLUSION
An intermodulation generator is designed and presented with integration of a dual-mode hybrid coupler and two identical diodes, whose connection polarities to the direct and coupled ports of the hybrid coupler are opposite for a rapid realization of balanced intermodulation generation. In consequence of the superior coupling characteristics of hybrid coupler, it can distribute incident tow tones to the direct and coupled ports evenly, and deliver the balanced intermodulation generations to the isolation port highly insulated from its incident port. To enhance the intermodulation generations, two identical quarter-wavelength shorted stubs at fundamental frequency are implemented by suppressing the second-order spectrums. Both theoretical analysis and experiments validate that the presented intermodulation generator can outperform the 3 rd harmonic generator, and highly isolate its incidences (the two tones) and outputs (the intermodulation generations) for its future high-isolation wireless sensing applications.