Symmetric-Reciprocal-Match Method for Vector Network Analyzer Calibration

This paper proposes a new approach, the symmetric-reciprocal-match (SRM) method, for calibrating vector network analyzers (VNAs). The method involves using multiple symmetric one-port loads, a two-port reciprocal device, and a matched load. The load standards consist of two-port symmetric one-port devices, and at least three unique loads are used. However, the specific impedances of the loads are not specified. The reciprocal device can be any transmissive device, although a non-reciprocal device can also be used if only the one-port error boxes are of interest. The matched load is fully defined and can be asymmetric. We numerically demonstrated the proposed method's accuracy with synthetic data and with measurements of coaxial standards using a commercial short-open-load-reciprocal (SOLR) calibration kit with verification standards. An advantage of the proposed method is that only the match standard is defined, whereas the remaining standards are partially defined, either through symmetry or reciprocity.Comment: GitHub: https://github.com/ZiadHatab/srm-calibratio

Indirect Measurement of Switch Terms of a Vector Network Analyzer with Reciprocal Devices

This paper presents an indirect method for measuring the switch terms of a vector network analyzer (VNA) using at least three reciprocal devices, which do not need to be characterized beforehand. This method is particularly suitable for VNAs that use a three-sampler architecture, which allows for applying first-tier calibration methods based on the error box model. The proposed method was experimentally verified by comparing directly and indirectly measured switch terms and performing a multiline thru-reflect-line (TRL) calibration.Comment: GitHub: https://github.com/ZiadHatab/vna-switch-term

Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers. The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo analysis using a combination of measured and synthetic data to model various uncertainties, such as additive noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the Monte Carlo method and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.Comment: GitHub: https://github.com/ZiadHatab/uncertainty-multiline-trl-calibratio

An Impedance Transition Method to Verify the Reference Impedance of Multiline TRL Calibration

In this paper, we present a new technique for assessing the validity of the reference impedance in multiline thru-reflect-line (mTRL) calibration. When performing an mTRL calibration, it is assumed that all transmission line standards exhibit the same characteristic impedance. As a result, the reference impedance after calibration is set to the characteristic impedance of the transmission line standards used in the calibration. However, because of imperfections, these assumptions are prone to errors. The purpose of this paper is to assess the validity of the reference impedance after an mTRL calibration. The method we propose uses the reflection coefficient of an impedance transition segment as a verification metric. The verification is achieved by performing two mTRL calibrations. The first mTRL calibration is the one we desire to validate, while the second mTRL calibration is based on step impedance lines that create the impedance transition. We conclude that the mTRL calibration is valid if the resulting reflection coefficient falls within the expected 95% confidence interval. We demonstrate our proposed method with printed circuit board (PCB) measurements of microstrip lines up to 150 GHz. The advantage of our approach is that the reflection coefficient of an impedance transition is almost constant with respect to frequency for many types of transmission line, which makes this validation metric easy to interpret when errors are present.Comment: Code on github: https://github.com/ZiadHatab/verification-multiline-trl-calibratio

Heuristic algorithms for power amplifier behavioral modeling

This letter presents the use of two heuristic search algorithms, named simulated annealing and genetic algorithms, for the extraction of power amplifier (PA) behavioral model parameters. Their application in this letter consists in determining the memory length and the most significant delays of the considered model structure. Two PA behavioral models have been considered: an augmented nonlinear moving average model and a nonlinear auto-regressive moving average model. By using WCDMA signals measured from a three-stage LDMOS class AB PA, both PA models were extracted. Finally, results presenting the advantages of using these heuristic search algorithms are provided.Peer Reviewe

Validation of the Decomposition Method for Fast MIMO Over-the-Air Measurements

Over-the-air (OTA) throughput tests of wireless Multiple-Input Multiple-Output (MIMO) devices are an important tool for network operators and manufacturers. The user equipment (UE) is placed in an anechoic chamber and a random fading process is emulated by a base-station emulator (BSE). The antenna characteristic of the UE is taken into account by sampling the sphere around the UE with the BSE test antenna at a large number of positions. For low-variance throughput results, long measurement intervals over many fading realizations are required, leading to long and expensive measurement periods in an anechoic chamber. To speed up the OTA test, we analyze the Decomposition Method (DM). The DM splits the throughput measurement into two parts: (1) a receiver algorithm performance tests taking the fading process into account and (2) an antenna performance test without fading process emulation. Both results are combined into a single throughput estimate. The DM allows for a measurement time reduction of more than one order of magnitude. We provide an analytic and numerical analysis as well as measurements. Our detailed results show the validity of the DM in all practical settings

Virtuelle Realität für Radargeräte in Autos

Car manufacturers spend quite a lot on the development of driver assistance systems and subsequently on autonomous driving functionality. To ensure the safety and reliability of these functions meet industrial standards it is necessary to verify and validate their functionality. While tests on the road are still the ultimate evidence of correct operation they are associated with huge efforts and risks. Therefore, they have to be complemented by other means like simulations and tests on specialised testbeds. For the latter the car’s sensors have to be stimulated in a way that they perceive a desired – but only virtual – environment. An important type of sensor in cars is the radar due to its various advantages. This article describes the development of a stimulator generating virtual radar targets in order to enable the testing of autonomous driving functions. Document type: Articl