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 measurement noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the Monte Carlo analysis and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.

As many emerging technologies require the use of high-speed signals, the understanding of dielectric properties of materials used in manufacturing printed circuit boards (PCBs) is an essential aspect for accurate high-speed circuit designs, especially at millimeter-wave (mm-wave) frequencies. This work demonstrates a methodology for extracting complex relative permittivity of dielectric substrates covering mm-wave frequencies. For this purpose, low-temperature cofired ceramic (LTCC) substrate was measured up to 85 GHz and its complex relative permittivity was extracted. The approach used in this work is based on multiline thru–reflect–line (TRL) calibration for measuring the propagation constant and electromagnetic (EM) simulations to estimate the losses contributed by the conductor while accounting for surface roughness. An estimate of complex relative effective permittivity is obtained, from which the actual relative dielectric constant and the loss tangent of LTCC substrate are extracted. The estimated values for the relative dielectric constant and the loss tangent show an excellent agreement compared with the results obtained via split cavity resonator measurements.

Advances in memory IC technology for dynamic random access memory (DRAM) devices have come about from a reduction in individual cell thickness with a corresponding increase in cell depth in order to maintain the same stored capacitance value. As the memory size on DRAM devices rises, memory cells must get deeper making the process of measuring depth more difficult. In this article we describe a novel, nondestructive, noncontact metrology technique which utilizes both two-dimensional diffraction analysis and multivariate statistical methods to measure deep trench depth in the 6–9 μm range. We applied this technique to two DRAM product wafers and obtained a successful prediction of trench depth for both wafers with an accuracy of ±0.04 μm, or ±0.56% variation relative to scanning electron microscope measurements of the same samples.

This article 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 nonreciprocal 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 demonstrated the accuracy of the proposed method with measurements of coaxial standards using a commercial METAS traceable short-open-load-reciprocal (SOLR) calibration kit with verification standards. In addition, we presented a numerical Monte Carlo (MC) analysis considering various uncertainty factors. 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.

This paper proposes a modification to the traditional multiline thru-reflect-line (TRL) or line-reflect-line (LRL) calibration method used for vector network analyzers (VNAs). Our proposed method eliminates the need for a thru (or line) standard by using an arbitrary transmissive two-port device in combination with an additional reflect standard. This combination of standards allows us to arbitrarily set the location of the calibration plane using physical artifacts. In contrast to the standard multiline TRL method, the suggested approach avoids a post-processing step to shift the calibration plane if a line standard is used. We demonstrate our proposed method with measurements on a printed circuit board (PCB) and compare it to the multiline TRL method with a perfectly defined thru.

This study presents a new method for measuring the propagation constant of transmission lines using a single line standard and without prior calibration of a two-port vector network analyzer (VNA). The method provides accurate results by emulating multiple line standards of the multiline calibration method. Each line standard was realized by sweeping an unknown network along a transmission line. The network need not be symmetric or reciprocal, but must exhibit both transmission and reflection. We performed measurements using a slab coaxial airline and repeated the measurements on three different VNAs. The measured propagation constant of the slab coaxial airline from all VNAs was nearly identical. By avoiding disconnecting or moving the cables, the proposed method eliminates errors related to the repeatability of connectors, resulting in improved broadband traceability to SI units.