Safieddin Safavi-Naeini
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Research Interests
Safieddin Safavi-Naeini has a total of 121 co-authors. Here are the top co-authors by number of shared publications:
- George Shaker
University of Waterloo
11 shared publications - Ala Eldin Omer
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada
10 shared publications - Wael M. Abdel Wahab
Electrical and Computer Engineering, University of Waterloo, Canada
9 shared publications - Suren Gigoyan
MmSense Technologies Inc., Waterloo, ON, Canada
7 shared publications - Nasser Masoumi
Circuits and Systems and Test Laboratory (CST-Lab), School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran
6 shared publications - Ardeshir Palizban
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada
5 shared publications
Latest Publications
- 9 February 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 73 (00189456) , 1-13
An Online Calibration Method Using Hadamard–Fourier Clustering and Neural Network for Large-Scale Phased Arrays
This paper proposes a novel online calibration method based on clustering for large-scale phased array antennas. The proposed clustering method (called HaF clustering) leverages Hadamard and Fourier transform features, resulting in increased output power variation (suitable for large phased array calibration), noise robustness, and fewer measurements compared to traditional methods. Additionally, it eliminates the need for extra phase measurement instruments as it relies solely on power measurements. Analytical closed-forms are derived to demonstrate the effectiveness of HaF clustering. In this method, the mean phase error ( MPhE ) in each cluster is determined by a combination of Hadamard features and the extended rotational electrical vector field method (eREV). Using a trained multi-layer perceptron neural network and feeding it with each cluster’s MPhEs , the direction of arrival (DOA) error is determined. Subsequently, antenna phase errors are estimated based on the DOA error, and new calibration coefficients are applied to the array. To validate the proposed online calibration method, Monte-Carlo simulations, and experimental measurements were conducted on a 1024-element modular planar phased array receiver within the frequency range of 18 GHz – 21 GHz and an angle of elevation range between -70 to 70 degrees. The simulation and experimental results indicate a mean absolute error (MAE) value of approximately 6 degrees for phase error determination and a DOA estimation error of less than 0.1 degrees using the multi-layer perceptron (MLP). Furthermore, the array can be calibrated with a maximum calibration error of less than 0.1 degrees within a period of 3 milliseconds.
- 9 February 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 73 (00189456) , 1-13
An Online Calibration Method Using Hadamard–Fourier Clustering and Neural Network for Large-Scale Phased Arrays
This paper proposes a novel online calibration method based on clustering for large-scale phased array antennas. The proposed clustering method (called HaF clustering) leverages Hadamard and Fourier transform features, resulting in increased output power variation (suitable for large phased array calibration), noise robustness, and fewer measurements compared to traditional methods. Additionally, it eliminates the need for extra phase measurement instruments as it relies solely on power measurements. Analytical closed-forms are derived to demonstrate the effectiveness of HaF clustering. In this method, the mean phase error ( MPhE ) in each cluster is determined by a combination of Hadamard features and the extended rotational electrical vector field method (eREV). Using a trained multi-layer perceptron neural network and feeding it with each cluster’s MPhEs , the direction of arrival (DOA) error is determined. Subsequently, antenna phase errors are estimated based on the DOA error, and new calibration coefficients are applied to the array. To validate the proposed online calibration method, Monte-Carlo simulations, and experimental measurements were conducted on a 1024-element modular planar phased array receiver within the frequency range of 18 GHz – 21 GHz and an angle of elevation range between -70 to 70 degrees. The simulation and experimental results indicate a mean absolute error (MAE) value of approximately 6 degrees for phase error determination and a DOA estimation error of less than 0.1 degrees using the multi-layer perceptron (MLP). Furthermore, the array can be calibrated with a maximum calibration error of less than 0.1 degrees within a period of 3 milliseconds.
- 18 January 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Components, Packaging and Manufacturing Technology
- Vol. 14 (2) , 315-327
On the Use of an In-Package Dielectric Lens Antenna for Radar-Based Applications
Extensive research on millimeter-wave (mm-wave) chipset solutions has led to a reduction in size and cost while adding sensitivity and accuracy. Recent mm-wave chipset solutions using antenna-in package approaches were developed for various applications with wide beamwidth and low gain. However, for some applications, such as gait monitoring in a long corridor/hallway, there is a strong need to achieve a higher gain with narrower beamwidth. This will increase the signal-to-noise ratio (SNR) and the transmit/receive detection range of the system while mitigating reflections from the surrounding environment as well as reducing the multipath effects. An add-on dielectric lens is an appealing solution as it improves the system performance while using existing on-chip or on-PCB antenna solutions. Using a low-cost and rapid manufacturing 3D printing technology, an in-package 3D-printed hyperbola-based dielectric lens antenna for an mm-wave radar is designed, fabricated, and tested. This design leads to a low-cost, lightweight, easy-to-fabricate, and easy-to-integrate mm-wave radar system. Comprehensive parametric analyses of the effect of the lens dimensions, dielectric permittivity, and focal length on the radiation pattern are intensively investigated. All measurement results align with the theoretical analysis and simulation results. Compared with the radar system without the lens, the in-package 3D-printed dielectric lens antenna provides more than 14 dB gain improvement.
- 18 January 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Components, Packaging and Manufacturing Technology
- Vol. 14 (2) , 315-327
On the Use of an In-Package Dielectric Lens Antenna for Radar-Based Applications
Extensive research on millimeter-wave (mm-wave) chipset solutions has led to a reduction in size and cost while adding sensitivity and accuracy. Recent mm-wave chipset solutions using antenna-in package approaches were developed for various applications with wide beamwidth and low gain. However, for some applications, such as gait monitoring in a long corridor/hallway, there is a strong need to achieve a higher gain with narrower beamwidth. This will increase the signal-to-noise ratio (SNR) and the transmit/receive detection range of the system while mitigating reflections from the surrounding environment as well as reducing the multipath effects. An add-on dielectric lens is an appealing solution as it improves the system performance while using existing on-chip or on-PCB antenna solutions. Using a low-cost and rapid manufacturing 3D printing technology, an in-package 3D-printed hyperbola-based dielectric lens antenna for an mm-wave radar is designed, fabricated, and tested. This design leads to a low-cost, lightweight, easy-to-fabricate, and easy-to-integrate mm-wave radar system. Comprehensive parametric analyses of the effect of the lens dimensions, dielectric permittivity, and focal length on the radiation pattern are intensively investigated. All measurement results align with the theoretical analysis and simulation results. Compared with the radar system without the lens, the in-package 3D-printed dielectric lens antenna provides more than 14 dB gain improvement.
- Open Access
Millimeter-Wave Circular Synthetic Aperture Radar Imaging
In this paper, we present a high resolution microwave imaging technique using a compact and low cost single channel Frequency Modulated Continuous Wave (FMCW) radar based on Circular Synthetic Aperture Radar (CSAR) technique. We develop an algorithm to reconstruct the image from the raw data and analyse different aspects of the system analytically. Furthermore, we discuss the differences between the proposed systems in the literature and the one presented in this work. Finally, we apply the proposed approach to the experimental data collected from a single channel FMCW radar operating at $\rm 79 \;GHz$ and present the results.Open AccessMillimeter-Wave Circular Synthetic Aperture Radar Imaging
In this paper, we present a high resolution microwave imaging technique using a compact and low cost single channel Frequency Modulated Continuous Wave (FMCW) radar based on Circular Synthetic Aperture Radar (CSAR) technique. We develop an algorithm to reconstruct the image from the raw data and analyse different aspects of the system analytically. Furthermore, we discuss the differences between the proposed systems in the literature and the one presented in this work. Finally, we apply the proposed approach to the experimental data collected from a single channel FMCW radar operating at $\rm 79 \;GHz$ and present the results. - 1 December 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 71 (1) , 1093-1098
A Low-Profile 2D Passive Phased-Array Antenna-in-Package for Emerging Millimeter-Wave Applications
This article covers the implementation, calibration, and measurement aspects of a low-profile 4×4 passive phased-array Antenna-in-Package (AiP) employing the beamformer discussed in [9]. The antenna array comprises slot-coupled patch antennas with left-handed circularly-polarized (LHCP) radiation. MEMS-like tunable phase shifter functioning based on controlling the phase constant of a slow-wave microstrip line is employed for the phase tuning. Measurement results show the antenna’s main beam can be steered over an angular range of ±30° in both elevation and azimuth planes. The operating frequency bandwidth of the system ranges from 28-30 GHz. The peak directivity and the radiation efficiency of the antenna system are 18.48 dBic and 58 % at Boresight at 29 GHz, respectively. The efficiency drops 16% when the steering angle reaches the maximum.
- 1 December 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 71 (1) , 1093-1098
A Low-Profile 2D Passive Phased-Array Antenna-in-Package for Emerging Millimeter-Wave Applications
This article covers the implementation, calibration, and measurement aspects of a low-profile 4×4 passive phased-array Antenna-in-Package (AiP) employing the beamformer discussed in [9]. The antenna array comprises slot-coupled patch antennas with left-handed circularly-polarized (LHCP) radiation. MEMS-like tunable phase shifter functioning based on controlling the phase constant of a slow-wave microstrip line is employed for the phase tuning. Measurement results show the antenna’s main beam can be steered over an angular range of ±30° in both elevation and azimuth planes. The operating frequency bandwidth of the system ranges from 28-30 GHz. The peak directivity and the radiation efficiency of the antenna system are 18.48 dBic and 58 % at Boresight at 29 GHz, respectively. The efficiency drops 16% when the steering angle reaches the maximum.
- 30 September 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 70 (12) , 11595-11607
A 3D-Printed DRA Shared-Aperture Array for Low Cost Millimeter-Wave Applications
In this article, a K -/ K a -bands shared-aperture array with high isolation is proposed using 3D-printed dielectric resonator antennas (DRAs). The design procedure with DRAs enables flexibility while implementing shared-aperture arrays. Further, DRAs as non-metallic radiators are attractive for mm-wave applications due to the absence of ohmic loss. In addition, 3D-printing technology facilitates the design of complex shapes with high dimensional accuracy. The K - and K a -bands DRAs are orthogonally oriented to provide improved isolation and cross-polarization level. Meanwhile, the corresponding feeding networks are implemented using the substrate integrated coaxial line (SICL) and the substrate integrated waveguide (SIW), respectively. Thus, further isolation improvement is provided by using two different feeding mechanisms for the K - and K a -bands radiators. Moreover, the SICL network is shared with the SIW wall to efficiently utilize the feeding aperture. As a proof-of-concept, the 3D-printed shared DRAs are designed and fabricated. The standard printed circuit board (PCB) technology is used for the fabrication of the antenna boards. The measurement data agree with the simulations, realizing high isolation and cross-polarization level. The proposed array features low profile, ease of integration, wideband operation, which makes it viable candidate for mm-wave applications.
- 30 September 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 70 (12) , 11595-11607
A 3D-Printed DRA Shared-Aperture Array for Low Cost Millimeter-Wave Applications
In this article, a K -/ K a -bands shared-aperture array with high isolation is proposed using 3D-printed dielectric resonator antennas (DRAs). The design procedure with DRAs enables flexibility while implementing shared-aperture arrays. Further, DRAs as non-metallic radiators are attractive for mm-wave applications due to the absence of ohmic loss. In addition, 3D-printing technology facilitates the design of complex shapes with high dimensional accuracy. The K - and K a -bands DRAs are orthogonally oriented to provide improved isolation and cross-polarization level. Meanwhile, the corresponding feeding networks are implemented using the substrate integrated coaxial line (SICL) and the substrate integrated waveguide (SIW), respectively. Thus, further isolation improvement is provided by using two different feeding mechanisms for the K - and K a -bands radiators. Moreover, the SICL network is shared with the SIW wall to efficiently utilize the feeding aperture. As a proof-of-concept, the 3D-printed shared DRAs are designed and fabricated. The standard printed circuit board (PCB) technology is used for the fabrication of the antenna boards. The measurement data agree with the simulations, realizing high isolation and cross-polarization level. The proposed array features low profile, ease of integration, wideband operation, which makes it viable candidate for mm-wave applications.
- 1 September 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 70 (9) , 7378-7383
Guest Editorial Low-Cost Wide-Angle Beam-Scanning Antennas
One of the key antenna requirements in many modern wireless systems for communications and sensing is wide-angle beam-scanning [1] . The traditional method to achieve wide-angle beam-scanning is to employ mechanically controlled reflectors or lenses, which are bulky, heavy, and suffer from slow beam scanning speed. Other important limitations of mechanical scanning antennas include the lack of multi-beam scanning capability and the ability to conform with non-planar structures (conformal geometries), which are essential in a number of emerging systems requiring very low-profile antennas. An alternative technique is to employ electronically beam-scanning antennas using passive or active phased arrays [1] . Main disadvantages of phased arrays are high complexity, high power consumption, and high cost due to a large number of radio frequency (RF) or microwave phase shifters and T/R modules required. The problems worsen for phased arrays at millimeter-wave, sub-THz, and THz frequencies, due to significant losses in phase shifters and feed networks at higher frequencies combined with lower efficiency of power amplifiers [2] . The digital beamforming approach is even more costly and energy hungry due to the employment of large number of RF modules and digital devices [1] , [3] , [4] .
- 1 September 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 70 (9) , 7378-7383
Guest Editorial Low-Cost Wide-Angle Beam-Scanning Antennas
One of the key antenna requirements in many modern wireless systems for communications and sensing is wide-angle beam-scanning [1] . The traditional method to achieve wide-angle beam-scanning is to employ mechanically controlled reflectors or lenses, which are bulky, heavy, and suffer from slow beam scanning speed. Other important limitations of mechanical scanning antennas include the lack of multi-beam scanning capability and the ability to conform with non-planar structures (conformal geometries), which are essential in a number of emerging systems requiring very low-profile antennas. An alternative technique is to employ electronically beam-scanning antennas using passive or active phased arrays [1] . Main disadvantages of phased arrays are high complexity, high power consumption, and high cost due to a large number of radio frequency (RF) or microwave phase shifters and T/R modules required. The problems worsen for phased arrays at millimeter-wave, sub-THz, and THz frequencies, due to significant losses in phase shifters and feed networks at higher frequencies combined with lower efficiency of power amplifiers [2] . The digital beamforming approach is even more costly and energy hungry due to the employment of large number of RF modules and digital devices [1] , [3] , [4] .
- 8 June 2022
- Published by Springer Nature
- p. 113-124
An Overview of Vital Signs Monitoring Based on RADAR Technologies
- 8 June 2022
- Published by Springer Nature
- p. 113-124
An Overview of Vital Signs Monitoring Based on RADAR Technologies
- 30 May 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Microwave Theory and Techniques
- Vol. 70 (7) , 3741-3752
A Bidirectional MEMS-Like Passive Beamformer for Emerging Millimeter-Wave Applications
In this article, the design and implementation of a low-loss bidirectional microelectromechanical system (MEMS)-like passive beamformer for emerging millimeter-wave (mm-Wave) applications are illustrated. A 4$\times $ 4 phased-array antenna (PAA) is fabricated employing the proposed beamformer for demonstration. The phase shifter (PS) embedded in the beamformer operates based on the principle of loaded-transmission line (TL) PSs. Slow wave mechanism is employed to shrink the size of the PS. The PS measurement results show the average insertion loss (IL) of 1.3 dB in all the tuning states and the IL variation is 0.9 dB. The PS provides 380° of the phase tuning range in a compact footprint area of 2.4 mm$\times $ 3 mm. The antenna array incorporates slot-coupled patch antennas with left-handed circularly polarized (LHCP) radiation. The operating frequency bandwidth of the antenna system ranges from 28 to 30 GHz to provide co-pol/X-pol discrimination of more than 12 dB for all the steering angles. Measurement results show the beam steering angular range of ± 30° in both elevation and azimuth planes. The measurement results also show the peak directivity of 18.48 dBic and the radiation efficiency of 58% at boresight at the frequency of 29 GHz. The efficiency drops 16% when the steering angle reaches the maximum.- 30 May 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Microwave Theory and Techniques
- Vol. 70 (7) , 3741-3752
A Bidirectional MEMS-Like Passive Beamformer for Emerging Millimeter-Wave Applications
In this article, the design and implementation of a low-loss bidirectional microelectromechanical system (MEMS)-like passive beamformer for emerging millimeter-wave (mm-Wave) applications are illustrated. A 4$\times $ 4 phased-array antenna (PAA) is fabricated employing the proposed beamformer for demonstration. The phase shifter (PS) embedded in the beamformer operates based on the principle of loaded-transmission line (TL) PSs. Slow wave mechanism is employed to shrink the size of the PS. The PS measurement results show the average insertion loss (IL) of 1.3 dB in all the tuning states and the IL variation is 0.9 dB. The PS provides 380° of the phase tuning range in a compact footprint area of 2.4 mm$\times $ 3 mm. The antenna array incorporates slot-coupled patch antennas with left-handed circularly polarized (LHCP) radiation. The operating frequency bandwidth of the antenna system ranges from 28 to 30 GHz to provide co-pol/X-pol discrimination of more than 12 dB for all the steering angles. Measurement results show the beam steering angular range of ± 30° in both elevation and azimuth planes. The measurement results also show the peak directivity of 18.48 dBic and the radiation efficiency of 58% at boresight at the frequency of 29 GHz. The efficiency drops 16% when the steering angle reaches the maximum.- 18 May 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Microwave Theory and Techniques
- Vol. 70 (7) , 3629-3639
Dual-Mode Phase-Conjugating/Active Van Atta Array Design Based on Dual-Band Mixer/Reflection Amplifier
In this article, a dual-mode phase-conjugating/active Van Atta array using an integrated switchless phase-conjugating mixer/reflection amplifier is presented. The proposed array consists of N dual-band mixer/reflection amplifiers (DMRAs), N dual-mode hybrids, and 2N dual-band patch antennas. The novel integrated mixer/reflection amplifier comprises a single low-noise GaAs heterojunction field-effect transistor (HJ-FET) transistor with suitable input and output matching networks and identical power supply configuration at both modes. Switchless feature, not requiring external mixers, and improved backscatter communication are the main advantages of this component for the dual-mode retrodirective array design. Furthermore, to verify the proposed mixer/reflection amplifier, a DMRA is designed and fabricated at 3.55 and 5.8 GHz resulting in an acceptable performance in both modes. Meanwhile, the phase-conjugating/active Van Atta array microstrip prototype is fabricated. It is experimentally verified using the monostatic and bistatic radiation characteristics, which clearly shows the capability of the proposed architecture as a multimode retrodirective array.
- 18 May 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Microwave Theory and Techniques
- Vol. 70 (7) , 3629-3639
Dual-Mode Phase-Conjugating/Active Van Atta Array Design Based on Dual-Band Mixer/Reflection Amplifier
In this article, a dual-mode phase-conjugating/active Van Atta array using an integrated switchless phase-conjugating mixer/reflection amplifier is presented. The proposed array consists of N dual-band mixer/reflection amplifiers (DMRAs), N dual-mode hybrids, and 2N dual-band patch antennas. The novel integrated mixer/reflection amplifier comprises a single low-noise GaAs heterojunction field-effect transistor (HJ-FET) transistor with suitable input and output matching networks and identical power supply configuration at both modes. Switchless feature, not requiring external mixers, and improved backscatter communication are the main advantages of this component for the dual-mode retrodirective array design. Furthermore, to verify the proposed mixer/reflection amplifier, a DMRA is designed and fabricated at 3.55 and 5.8 GHz resulting in an acceptable performance in both modes. Meanwhile, the phase-conjugating/active Van Atta array microstrip prototype is fabricated. It is experimentally verified using the monostatic and bistatic radiation characteristics, which clearly shows the capability of the proposed architecture as a multimode retrodirective array.
- 25 February 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 71 (00189456) , 1-12
Non-Reciprocal Whispering-Gallery-Mode Resonator for Sensitive Blood Glucose Monitoring
In this article, a miniaturized low-cost microwave sensor of high sensitivity is proposed for noninvasive blood glucose monitoring. The traveling waves whispering gallery modes ( WGM ) are excited/launched on a ferrite-made ring resonator when placed nearby a microstrip line (MTL). The sensing structure is designed appropriately to support four distinct WGM modes with the desired coupling in the frequency range of 22–32 GHz. A disk of permanent magnet is incorporated beneath the MTL substrate to generate a bias magnetic field necessary to create a nonreciprocal effect in the resonator. This nonreciprocal behavior is demonstrated in the transmission responses $S_{12}$ and $S_{21}$ , where the WGM resonances of similar modes are triggered at different frequencies over a narrowband. A magneto-static analysis is performed to approximate the internal biasing fields inside the FRR at multiple longitudinal layers. The complex components of the permeability tensor are computed accordingly for each layer, and then integrated into HFSS to simulate the sensor scattering responses. The EM simulations are validated when compared with practical measurements of a magnetized FRR. The latter fabricated prototype is tested in different setups for monitoring the glucose in synthetic blood of concentrations related to diabetes conditions. The proposed sensor shows high detection sensitivity at WGM 600 and WGM 700 to small changes in the dielectric properties of glucose samples as demonstrated by the frequency and phase shifts (0.07 MHz and 0.17° per 1 mg/dL, respectively) of the measured $S_{21}$ and $S_{12}$ with repeatability error of about ±0.2 MHz and ± 0.5°.
- 25 February 2022
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 71 (00189456) , 1-12
Non-Reciprocal Whispering-Gallery-Mode Resonator for Sensitive Blood Glucose Monitoring
In this article, a miniaturized low-cost microwave sensor of high sensitivity is proposed for noninvasive blood glucose monitoring. The traveling waves whispering gallery modes ( WGM ) are excited/launched on a ferrite-made ring resonator when placed nearby a microstrip line (MTL). The sensing structure is designed appropriately to support four distinct WGM modes with the desired coupling in the frequency range of 22–32 GHz. A disk of permanent magnet is incorporated beneath the MTL substrate to generate a bias magnetic field necessary to create a nonreciprocal effect in the resonator. This nonreciprocal behavior is demonstrated in the transmission responses $S_{12}$ and $S_{21}$ , where the WGM resonances of similar modes are triggered at different frequencies over a narrowband. A magneto-static analysis is performed to approximate the internal biasing fields inside the FRR at multiple longitudinal layers. The complex components of the permeability tensor are computed accordingly for each layer, and then integrated into HFSS to simulate the sensor scattering responses. The EM simulations are validated when compared with practical measurements of a magnetized FRR. The latter fabricated prototype is tested in different setups for monitoring the glucose in synthetic blood of concentrations related to diabetes conditions. The proposed sensor shows high detection sensitivity at WGM 600 and WGM 700 to small changes in the dielectric properties of glucose samples as demonstrated by the frequency and phase shifts (0.07 MHz and 0.17° per 1 mg/dL, respectively) of the measured $S_{21}$ and $S_{12}$ with repeatability error of about ±0.2 MHz and ± 0.5°.