Full-Wave De-embedding:Principles And Applications

The continuing development of microwave measurement techniques has enabled various advanced instruments,making comprehensive,accurate and fast device characterization possible.In many cases,however,the device under test(DUT)cannot be connected to the instrument directly,and a physical intervening structure,also known as a fixture,must be inserted between the DUT and instrument to make any measurement viable.The measured results therefore contain both the characteristics of the DUT and the fixture,or in other words,the DUT is embedded into the fixture.In this circumstance,a process of removing the effects of fixture as well as establishing desired reference planes will be necessary to extract the pure electrical properties of the DUT.Such a process is termed de-embedding and it is crucial for accurate characterization of microwave components and devices.In recent years,a new de-embedding technique named full-wave de-embedding has received more and more attention.Different from the traditional methods,in this approach,the electrical properties of the fixture used to de-embed the DUT are obtained from full-wave electromagnetic(EM)simulation instead of by measuring known standards alone.It has the advantage that less or no standards are necessary,and thereby the number of measurements as well as the measurement errors can be largely reduced.Besides,the fixture can be easily modeled as a general multi-port network by the EM simulator,which can handle the distributed effects better especially at higher frequencies.Finally,the parasitic effects introduced by the internal port of an EM simulator during the EM/circuit co-simulation process can be better handled if full-wave de-embedding is used to characterize the lumped components involved,which helps to provide more accurate co-simulation results and shorten the trial-and-error procedure in the development of microwave circuits.Unfortunately,there is still a lack of comprehensive research on this technique and some important aspects regarding its principles,realization and applications have not been well-understood.In view of the above,this thesis provides an in-depth study of full-wave de-embedding,aiming to contribute to the efforts of building a solid theoretical foundation for this method and to demonstrate its usefulness in microwave circuit analysis and design.The major contributions of this thesis are summarized as follows.1.Vectorization is introduced and used for the first time to study the fundamental equation of fullwave de-embedding,namely,the embedding equation.The vectorized embedding equation reduces to a system of typical non-linear multivariate equations that contain only vector variables,and thereby classical multivariate calculus,multiple regression analysis,uncertainty analysis and various optimization algorithms can be applied directly to its quantitative studies.This significantly simplifies the mathematical treatment of full-wave de-embedding,and as a consequence,vectorization turns out to be one of the most important keys to the development and improvement of this technique.2.An improved multifixture full-wave de-embedding method is proposed for one-port DUTs,where multiple redundant fixtures with mutually complementary properties are used to minimize the effects of random errors.The embedding equations obtained with different fixtures are combined and solved in a generalized least-square sense.This can reduce the impact of random errors on the de-embedded results,and thus improve the overall de-embedding accuracy.To obtain complementarity,each fixture should yield minimum de-embedding uncertainty within a different frequency range or/and under a different operating state of the DUT,which can be difficult to achieve in practice.To resolve the problem,a simple design methodology is proposed where complementarity is produced by adopting series-and shunt-type connection topologies for different fixtures.Numerical and experimental results show that the multifixture method can evenly and efficiently reduce the effects of random errors over a broad frequency range,and this improvement is nearly independent of the DUT's operating states.As a result,the new approach is very suitable for broad-band characterization of reconfigurable devices,such as diodes.3.An improved hybrid full-wave de-embedding method,which can reduce the impact of systematic errors on the de-embedded results,is proposed and experimentally verified.Different from the traditional techniques and the original full-wave de-embedding,in the hybrid approach,the fixture is characterized through a combination of EM simulation and measurement.The main idea is to first obtain the general multiport Sparameters of the fixture from EM simulations,and then correct these results according to the measurement of one or more arbitrary standards based on a least-norm correction algorithm.This can reduce the systematic errors generated during the un-terminating process,and thus enhance the overall de-embedding performance.Experimental results confirm that the hybrid approach can achieve higher de-embedding accuracy than the original full-wave de-embedding method at the cost of measuring only a small amount of standards,due to a successful reduction of systematic errors.In addition,the hybrid approach can provide significantly improved accuracy using the same standards as compared with the open-short method,or it can achieve similar or even better performance using less than half of the standards as compared with the four-port method.4.An EM/circuit co-simulation strategy based on full-wave de-embedding is proposed for the design and analysis of microwave circuits.The main idea is to ensure that the internal port configurations remain unchanged from when a fixture is characterized in the full-wave de-embedding process to when a circuit layout is simulated in the co-simulation process.This can avoid the case in which a portion of the parasitic effects introduced by the internal ports of an EM simulator are calculated twice or handled incorrectly,and thereby enable higher co-simulation accuracy to be achieved.The new strategy is demonstrated through the simulations and measurements of two surface-mount capacitor loaded circuits,an X-band single-pole singlethrow switch and a Ku-band low-noise amplifier.A significantly improved agreement between the measured and co-simulation results has been observed when the new strategy is applied,indicating that the trial-anderror process in the development of microwave circuits may be shorten and the cost can be reduced.