Received May 17, 2020, accepted June 1, 2020, date of current version June 30, 2020. Digital Object Identifier 10.1109/ACCESS.2020.3002501 A Method for Accurately Characterizing Single Overmoded Circular TM01-TE11 Mode Converter JUNKAI YAN1, JIANGUO WANG 1,2, WENXI HAO1, XINHONG CUI 1, YINGJUN LIU1, XIAOXIN ZHU1, AND ZHIQIANG ZHANG1 1Northwest Institute of Nuclear Technology, Xi'an 710024, China 2School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China Corresponding author: Jianguo Wang ([email protected]) This work was supported by the National Natural Science Foundation of China under Grant 61231003. ABSTRACT In the case of characterizing waveguide mode converter, the widely applied back-to-back method can only extract two mode converters' joint S-parameters, the accuracy of the far-field radiation pattern method is limited. This paper experimentally demonstrates a method for accurately characterizing single circular TM01-TE11 mode converter, which consists of extracting the asymmetric two-port TM01 and TE11 mode generator test fixtures' S-parameters and de-embedding them from the 'TM01 mode generator + TM01-TE11 mode Converter + TE11 mode generator' cascade measurement results. The peak problem occurring in measuring overmoded circular waveguide devices with VNA is analyzed and settled with an offset waveguide based peak-shifting tactic plus the Loess smoothing method. Fairly good agreement between the simulated and finally extracted complex S-parameter matrix of a TM01-TE11 mode converter throughout the device's working frequency span validates the proposed method's merits over traditional methods. INDEX TERMS Asymmetric fixture, de-embedding, mode generator, overmoded mode converter, offset waveguide, S-parameter, thru-reflect-line (TRL) calibration. I. INTRODUCTION In some RF systems, such as high-power microwave (HPM), plasma heating systems, millimeter wave and terahertz wave systems [1]-[7], the overmoded circular waveguide mode converters are widely used to convert the produced mode in a radiation source to the mode needed for specific tasks, and mitigate the possibility of breakdown [8]-[10]. As the two ports of mode converter are electrically asymmetric with different mode patterns, it is not possible to measure a mode converter's S-parameters directly with VNA usually calibrated to two symmetric arm ports [11], [12]. Literatures relating to mode converter design generally adopt two methods for testing the developed mode converters and verifying the design. The first and most widely applied method is the so called back-to-back method [4], [13]-[18], which requires two identical mode converters A and B connected back-to-back to form a symmetric two-port device, as shown in Fig. 1 with our circular TM01-TE11 mode converter under test for example. The TE11A and TE11B in Fig. 1 are two circular TE11 mode generators, which can excite pure circular TE11 mode from standard R140 rectangular waveguide TE10 mode or in reverse with a classical rectangular to circular waveguide transition structure. A standard thru-reflect-line (TRL) calibration process is conducted in advance and computed inside VNA to move the measurement planes to the pair of TE11 mode generators' circular ports, as shown in Fig. 2. In this way, the joint S-parameters of the two back-to-back connected TM01-TE11 mode converters are measured. The limitation of the back-to-back method is obvious. While single target mode converter with known parameters is required for use in RF systems, the method can only get joint complex S-parameters of the two mode converters. FIGURE 2. The standard TRL calibration process for setting the VNA's measurement planes to the TE11 mode generators' circular ports. FIGURE 3. Measured |S21| curve of our TM01-TE11 mode converters with the back-to-back method. Most literatures had to compare the measured |S21| curve with the back-to-back simulation results for design verification [13]-[17]. The single device's transmission phase parameters as well as reflection parameters cannot be measured, which are critical in some applications like power combination. Another difficulty with the back-to-back method for measuring overmoded circular waveguide mode converter is that there may exist many peaks in the measured S-parameter curves [4], [15], as shown in Fig. 3. These peaks may become so dense in some cases [16]-[18] that it is hard to judge the device's conversion efficiency and meet the test precision requirement of some high performance mode converters, whose required mode conversion efficiency is often higher than 95% and port voltage reflection ratio less than 10% [13]. Wang et al. [17] simply explain that these peaks are caused by weak resonators existing between the identical converters, but provide no further tackling way. The other method used in some literatures [1]-[3], [5] is to measure the device's far-field E or H plane radiation pattern. This method can verify the device's output mode, but cannot provide precise conversion efficiency. This study aims at developing a method to characterize a high-performance dual-bend overmoded circular TM01-TE11 mode converter. The device under test (DUT) is designed to achieve 1GW peak power handling capacity and 98.5% power conversion efficiency within 14.6 ~ 15.4GHz, which measures 20cm long by 3cm inner waveguide diameter with an overmoded ratio of about 1.5. To characterize single target mode converter, our idea is to employ a TM01 mode generator A and a TE11 mode generator B to conduct a 'TM01A + Mode Converter + TE11B' measurement [19], as shown in Fig. 4, then to remove the TM01A and TE11B mode generators' influence from the composite measurement results through de-embedding calculation [20] for the net S-parameters of the target TM01-TE11 mode converter. To do this, a pair of circular TE11 mode generators and a pair of circular TM01 mode generators are fabricated. The TM01 mode generators' structure is similar to the ones introduced in [21] but working at Ku band. The TE11 mode generators have classical rectangular to circular waveguide transition structure. All two kinds of mode generators feature high mode purity. FIGURE 4. Schematic (a) and hardware setup (b) of the 'TM01A + Mode Converter + TE11B' measurement for extracting single TM01-TE11 mode converter's S-parameters. The remainder of this paper is organized as follows. Section II describes the VNA measurement and solution method for extracting TM01A mode generator's S-parameters. In Section III, the origin of the peaks in the extracted TM01A's S-parameters is explored and an offset waveguides based method is proposed to get the TM01A and TE11B mode generators' intrinsic S-parameters without peaks. The 'TM01A + Mode Converter + TE11B' measurement and mode generator de-embedding calculation are finished in Section IV. Section V provides some measurement uncertainty estimation results and conclusions. Next, all the measurements are made using an Agilent N5244A vector network analyzer, whose two arms connect R140 rectangular waveguide-coaxial transitions respectively. An Agilent P11644A waveguide calibration kit is used to conduct a standard TRL calibration and set the VNA's measurement planes to the waveguide-coaxial transitions' R140 waveguide ports. For unity, the TM01A and TE11B mode generators' rectangular waveguide ports are numbered 1, the circular waveguide ports are numbered 2, the mode converter's TM01 and TE11 ports are numbered 1 and 2 respectively. The corresponding signal flow diagram and S-parameter variables are shown in Fig. 5. FIGURE 5. Signal flow diagram of the 'TM01A + Mode Converter + TE11B' measurement configuration. II. BASIC TRL MEASUREMENTS AND SOLUTION FOR EXTRACTING TM01A MODE GENERATOR'S S-PARAMETERS As TM01A and TE11B mode generators are asymmetric two-port devices (both mechanically and electrically, as indicated in Fig. 4) and its S-parameters cannot be measured directly with VNA, we have to find a way to extract the TM01A and TE11B mode generators' respective S-parameter matrix firstly. The TRL calibration technique [11], [22]-[24] is a classical method for extracting asymmetric fixtures' S-parameters, such as transitions from coaxial port to microstrip, substrate-integrated waveguide (SIW) [25], and so on. In Fig. 1, the two TE11 mode generator fixtures' S-parameters are actually extracted through the TRL calibration process and saved in VNA's calibration file [26], but it is encrypted and cannot be accessed for de-embedding calculation. Thus, we can solve the matrix equations relating to the TRL measurement results manually and determine the TM01A and TE11B mode generators' complex S-parameter matrix for the fixture de-embedding calculation in Fig. 4. To extract the two fixtures' S-parameters with TRL method, a blind flange reflection standard and a circuit waveguide line standard (Phi = 30mm, L = 5mm) are fabricated with aluminum. The standard line length is about one quarter of the central frequency's (15GHz) waveguide wavelength. All two standard devices have bolted flange for proper connection. A. TRL CALIBRATION SOLUTION The kernel TRL calibration solution for getting individual fixture's S-parameters is as follows [22]-[24]. Let the S-parameter matrixes of TM01 mode generators A and B be denoted by Sa and Sb respectively, whose cascading matrix conversion Ra and Rb can be written as Ra = r22 * [a, b; c, 1] (1) Rb = rho22 * [alpha, beta; gamma, 1] (2) The equations for yielding the unknown quantities a, b, c, alpha, beta, gamma, r22 and rho22 from the thru calibration measurement ST (whose cascading matrix conversion is denoted by Rt), the reflection S11R, S22R, and the line (delay) SD (whose cascading matrix conversion is denoted by Rd) are detailed in [22]. FIGURE 6. The TRL measurement configurations of the TM01 mode generators. FIGURE 7. The TRL measurement results plus the calculated S-parameters for the two TM01 mode generators. (a) |S21T|. (b) |SR|. (c) |S21D|. (d) |S21a| and |S21b|. Now, the TM01 mode generators A and B's individual cascading matrix Ra and Rb can be extracted from the TRL measurement ST, S11R, S22R, and SD. TM01A's cascading matrix Ra can be used directly for de-embedding calculation of the 'TM01A + Mode Converter + TE11B' measurement result. Ra and Rb can also be converted back to the S-parameter matrixes Sa, Sb. B. CALCULATION RESULTS AND DISCUSSION The two TM01 mode generators are connected with standards VNA and measured in three TRL steps, as shown in Fig. 6. Fig. 7 presents the measured |S21T|, |S11R|, |S22R|, |S21D|, and the calculated |S21a| and |S21b|. Obviously, the |S21a| and |S21b| curves show gain at some peak frequencies, which are non-physical. To check the accuracy of the extracted Ra and Rb, inverse matrixes Ra^-1 and Rb^-1 are multiplied to the measured Rt or Rd and converted back to S-parameter matrixes according to (3) or (4) [27]. Theoretically, these de-embedding calculations should yield the fictitious 0 mm long waveguide's S-parameter matrixes S0mm and the 5mm long waveguide line standard's S-parameter matrixes S5mm [20], [26]. FIGURE 8. De-embedding calculation results of S21T and S21D. (a) |S21-0mm|. (b) phase S21-0mm. (c) |S21-5mm|. (d) phase S21-5mm. Fig. 8 indicates that the de-embedded S0mm and S5mm basically agree with theoretical expectation, implying that the extracted Sa and Sb are precise, except at some frequencies, which coincide with the peaks in the |S21a| and |S21b| curves. Further investigation shows that the peaks in the extracted |S21a| and |S21b| curves occur at the frequencies where the measured ST, SR or SD have peaks (see Fig. 7). So, it can be concluded that the extracted Sa and Sb are precise, except at the frequencies where the measured ST, SR, or SD have peaks. S0mm = S(Ra^-1 * Rt * Rb^-1) = S(Ra^-1 * Ra * Rb * Rb^-1) (3) S5mm = S(Ra^-1 * Rd * Rb^-1) = S(Ra^-1 * Ra * RL * Rb * Rb^-1) (4) The peaks in the measured |S11R| (decayed echo) obviously indicate that some resonances happen and part of the injected microwave energy is saved inside the structures' cavity rather than completely reflected. So we suspect that the peaks in |ST| and |SD| curves are also caused by resonances occurred at resonant frequencies of the measurement cavity. To verify this, the right-side rectangular waveguide port of the connected TM01 mode generators (Meas. Plane 2 in Fig. 7) is shorted with a reflect device in P11644A calibration kit to measure the reflection coefficient S11T-R from Meas. Plane 1. As compared in Fig. 9, |S21T| and |S11T-R|'s peaks occur at same frequency points. Similar peculiarity also exists between the |S21D| and |S11D-R| curves of line counterpart. Thus, it is verified that the peaks in |ST|, |SR| and |SD| curves occur at the resonant frequencies of measurement cavity where non-propagation modes are excited and invalidate the TRL method [28]. FIGURE 9. Comparison of the |S21T| and |S11T-R| curves. III. EXTRACTING S-PARAMETERS OF TM01A AND TE11B MODE GENERATORS WITH OFFSET WAVEGUIDES The excitation of cavity's resonant modes during TRL calibration is a deviant but incidental phenomenon to overmoded circular waveguides. Most literatures about TRL method [25], [28]-[31], take substrate-integrated waveguide (SIW), coplanar-waveguide (CPW) or coaxial transmission line for application demonstration, where non-propagation modes are not easy to be excited, so the peak problem is not well addressed. Here, we have to find a reasonable way to tackle this special problem. As the invalid values are caused by the excitation of resonant modes inside the TRL measurement structure's inner cavity, a straightforward mending idea might be to connect an attenuator to the mode generator and take the two devices together as a mode generator. However, a verification measurement, by using a 30cm long aluminum circular waveguide (approximating the TM01-TE11 mode converter's length) with TM01A and TM01B mode generators (whose circular waveguide ports connect a 10 dB circular waveguide attenuator respectively) through the TRL calibration and de-embedding process, indicates that while the waveguide attenuators can eliminate the resonant modes and the peaks, it also degrades the extracted Sa+10dB's precision to an unacceptable level for the 30cm long straight waveguide device with quite low transmission loss and reflection coefficient, because of VNA's dynamic accuracy characteristics [32]. An alternative way is to connect offset circular waveguides with different lengths to the mode generator to change the measurement cavity structure and shift the peaks to higher or lower frequencies. Then, the invalid values in Fig. 7 can be replaced with correct ones. This method can keep the VNA to measure S-parameters near its best dynamic accuracy region and meet measurement precision requirement. Two pairs of offset circular waveguides fabricated for this task are listed in Table 1. Their length is selected as just about one-third or half of the circular waveguide wavelength, so while the offset devices can make notable peak shift, their insertion losses are negligible. Using the TRL method described in Section II, S-parameters of the TM01A mode generator cascaded with offset waveguide are extracted and shown in Fig. 11, where the reciprocal S12 is omitted for brevity. It can be seen that all the two groups of S-parameters' amplitude curves superpose to the original ones within +/-1%, except the shifted peaks. The phase curves of S21, and S22 deviate from the original ones because of the offset waveguide's phase shift effect. Using the basic assumption of no reflecting and absorption characteristics for line standard [21], offset waveguide's TABLE 1. Offset circular waveguide parameters. Pair | Length of each segment | Phase shift at 15GHz TM01 mode | Phase shift at 15GHz TE11 mode l1 | 0 mm | 0 deg | 0 deg l2 | 8 mm | 123.9 deg | 132.7 deg l3 | 12 mm | 185.9 deg | 199 deg FIGURE 10. Schematic of the TM01 mode generators with offset circular waveguides cascaded. FIGURE 11. Calculated S-parameters for the TM01A mode generator cascaded with offset waveguide of three different lengths. (similar to the line standard) inverse cascading matrix R_l^-1 can be written as R_l^-1 = [exp(-gamma*l), 0; 0, exp(gamma*l)]^-1 = [exp(gamma*l), 0; 0, exp(-gamma*l)] (5) where gamma = alpha + j*beta is the waveguide's propagation constant, alpha approximates 0, beta can be calculated according to offset waveguide's length l [20]. Thus, the offset waveguide's phase shift effect can be removed from the results in Fig. 11 with a de-embedding calculation of (6) and (7) to get TM01A's net S-parameters, as shown in Fig. 12. In (6) and (7), Ra+li denotes the extracted cascading matrix for TM01A together with offset waveguide li, Rai represents the de-embedded result for TM01A only. As expected, all the three groups of S-parameters' phase curves in Fig. 12 superpose to each other. The curves' peaks are shifted to higher or lower frequencies, so at least one group of values are valid (no peak happens) at most frequency points. Rai = Ra+li * R_li^-1 (i = 1, 2, 3) (6) Rbi = R_li^-1 * Rb+li (i = 1, 2, 3) (7) FIGURE 12. Calculated S-parameters for the TM01A mode generator with offset waveguide's phase shift effect de-embedded. FIGURE 13. The Loess smoothing result of |S21a|. (a) |S21a| and the smoothing counterpart. (b) |Delta S21a|. To detect the frequency points fij (i=1...3, j=1...6401) with valid S-parameter values, we adopt a Loess smoothing method resistant to outliers [33] to get the smooth curve, shown in Fig. 13(a), from the original S21a amplitude curve in Fig. 12, and calculate the difference |Delta S21a| (see Fig. 13(b)) between the smooth and original curves. All the frequency points fij with |Delta S21a| < 0.2% are picked out as the frequency points with valid values and given in Fig. 14. Then, the precise S-parameters of the TM01A are obtained by averaging all the three groups of S-parameters with valid values, and presented in Fig. 15. FIGURE 14. The detected frequency points with valid value in the three groups of S-parameters. FIGURE 15. TM01A's precise S-parameters by averaging all the three groups of S-parameters with valid values. FIGURE 16. Calculated S-parameters for the TE11B mode generator with offset waveguide's phase shift effect de-embedded. FIGURE 17. TE11B mode generator's precise S-parameters by averaging all the three groups of S-parameters with valid values. The precise S-parameters of TE11B mode generator can be extracted in similar process, as shown in Figs. 16 and 17. The rectangular-to-circular waveguide transition device's transmission loss and reflection coefficient are quite low throughout its working frequency span. IV. EXTRACTING S-PARAMETERS OF THE TM01-TE11 MODE CONVERTER With the precise S-parameters of TM01A and TE11B mode generators well extracted, the 'TM01A + Mode Converter + TE11B' measurement and the de-embedding calculation process can be conducted to get the S-parameters of the target TM01-TE11 mode converter. Similar to the measured S-parameters of the TM01-TE11 mode converter with the back-to-back method, there are also many peaks in the measured S-parameter curves with the 'TM01A + Mode Converter + TE11B' configuration. To tackle this problem, three pairs of offset circular waveguides (listed in Table 1) are connected to the TM01-TE11 mode converter's two ports (see Fig. 18) respectively to shift the peaks. Fig. 19 presents the three groups of S-parameters measured with VNA from the 'TM01A + offset waveguide + TM01-TE11 Mode Converter + offset waveguide + TE11B' configuration. FIGURE 18. Schematic of the TM01-TE11 mode converter with offset circular waveguides cascaded. FIGURE 19. Three groups of S-parameters measured from the 'TM01A + offset waveguide + Mode Converter + offset waveguide + TE11B' configuration. FIGURE 20. S-parameters for the TM01-TE11 mode converter with mode generators' and offset waveguides' effect de-embedded from the measured S-parameters. FIGURE 21. The valid values of the three groups of S-parameters for the TM01-TE11 mode converter. The effects of the TM01A and TE11B mode generators' fixture effects (or S-parameters shown in Figs. 15 and 17) and the offset waveguide's phase shift effects are removed from the composite measurement results through de-embedding calculations to get the target TM01-TE11 mode converter's net S-parameters, as shown in Fig. 20. Then, we adopt the Loess smoothing method to get smooth curve from the measured S21 amplitude curve in Fig. 20 and find the frequency points fij (i = 1...3, j = 1:6401) with valid values in all the three groups of S-parameters, as shown in Fig. 21. The average results of the three groups of S-parameters with valid values are taken as the finally extracted S-parameters of the target TM01-TE11 mode converter, which are compared with the simulated S-parameters of the mode converter in Fig. 22. As shown in Fig. 22, the finally extracted S-parameter curves agree well with the simulated counterparts. FIGURE 22. The average results of the three groups of S-parameters with valid values for the TM01-TE11 mode converter and the simulated counterparts. The two S21 amplitude curves' difference is within 2% throughout the frequency span, and the two S21 phase curves' difference is within 3 deg. The extracted S11 and S22 amplitude curves are a bit higher than the simulated counterparts, but also fit the device's weak reflection ratio characteristic. The S11 and S22 phase curves generally agree with the simulated counterparts. V. UNCERTAINTY ANALYSIS AND CONCLUSION A Monte Carlo calculation with 10000 iterations are conducted in the fixture S-parameter extracting and de-embedding processes to evaluate the measurement uncertainty of S-parameters of the final TM01-TE11 mode converter [34]. All the direct measurement quantities' uncertainty as Monte Carlo calculation's input are estimated according to N5244A's data sheet [32] and listed in Table 2. Table 3 presents the estimated uncertainty of the TM01-TE11 mode converter's S-parameters at 15GHz. The comparison with simulation result and uncertainty analysis proves that the fixture S-parameter extracting and de-embedding processes is feasible for characterizing single high performance overmoded circular TM01-TE11 mode converter or other asymmetric two-port overmoded circular waveguide devices and overcome the limitations of the back-to-back method or radiation pattern method. 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Arz, 'Monte-Carlo analysis of measurement uncertainties for on-wafer thru-reflect-line calibrations,' in Proc. 71st ARFTG Microw. Meas. Conf., Atlanta, GA, USA, Jun. 2008, pp. 1-4. AUTHOR BIOGRAPHIES JUNKAI YAN was born in Gansu, China, in October 1982. He received the B.S. degree in electrical engineering from Xi'an Jiaotong University, in 2004, the M.S. degree in physical electronics from National Defense Science and Technology University, in 2007, and the Ph.D. degree in nuclear science and technology from Tsinghua University, in 2018. He is currently with the Northwest Institute of Nuclear Technology (NINT), China, as a Senior Engineer. His main research interests include transient electromagnetics, HPEM susceptibility test, and effects diagnostics. JIANGUO WANG was born in Jiangsu, China, in December 1965. He received the B.S. degree in physics from Nanjing University, in 1987, the M.S. degree in physics from the Northwest Institute of Nuclear Technology (NINT), in 1990, and the Ph.D. degree in electromagnetic theory and microwave techniques from Xidian University, in 1997. From 1998 to 2000, he conducted his Postdoctoral Research with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, USA. He is currently a Professor with NINT. His main research interests include transient electromagnetics, numerical electromagnetic methods, antenna designs, and plasma physics. WENXI HAO received the B.S. degree in computer science and technology from Second Artillery Engineering University, China, in 2003. She is currently a Senior Laboratory Assistant with the Northwest Institute of Nuclear Technology (NINT). Her research interests include microwave component measurements and HPEM susceptibility test. XINHONG CUI received the B.S. degree in electrical information engineering from Northwestern Polytechnical University, in 2007, and the M.S. degree in electronic and information science and technology from the University of Electronic Science and Technology of China (UESTC), in 2012. She is currently a Senior Engineer with the Northwest Institute of Nuclear Technology (NINT). Her main research interests include microwave radiation field measurement technique, microwave directional coupler, microwave mode converter design, and measurement technique. YINGJUN LIU received the B.S. degree in electrical information engineering from Xidian University, in 2005, and the M.S. degree in electromagnetic field and microwave technology from the Northwest Institute of Nuclear Technology (NINT), in 2011. She is currently a Senior Laboratory Assistant with NINT. Her main research interests include microwave component measurement and uncertainty estimation. XIAOXIN ZHU received the B.S. degree in applied physics and the M.S. degree in optical engineering from National Defense Science and Technology University (NUTD), in 1999 and 2002, respectively. She is currently a Senior Engineer with the Northwest Institute of Nuclear Technology (NINT). Her main research interests include high-power microwave transmission and emission technology. ZHIQIANG ZHANG was born in Jilin, China, in 1978. He received the B.S. degree in electromagnetic field and microwave technology from Xidian University, in 2001, the M.S. degree in electromagnetic field and microwave technology from the Northwest Institute of Nuclear Technology (NINT), in 2004, and the Ph.D. degree in electromagnetic theory and microwave techniques from Xidian University, in 2014. He has been with NINT, since 2001. His current research interests include high-power microwave antenna and passive waveguide components.