There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Surface roughness of the conductor in transmission lines will introduce extra losses. The recently proposed Huray model is quite accurate for modeling these additional losses by changing R terms in RLGC models. However, only focusing on the loss modeling of the transmission line may lead to causality issues in time domain simulations. In this paper, the causality requirements of the RLGC models are theoretically analyzed firstly. Then, two solutions of the causality problems in Huray model-based transmission line with rough conductors modeling were proposed and compared. One of them is based on the numerical Hilbert transform, and the other one is analytically based on a complex-valued roughness factor. The causalities of those two solutions are validated by a time domain pulse through a transmission line. The results comparisons of the received pulse responses after the transfer functions show that both methods can improve the causality of the wave propagation term significantly, whereas the analytical solution has better performances and the numerical method has some limitations.

Causality Analyzing for Transmission Line with Surface Roughness

High-speed PCB design for signal integrity (SI) is about feasible material selection, trace geometry determination and optimization of discontinuities, where the accurate PCB material characterization is essential since incorrect material properties may lead to misleading results and wrong design descisions. The previous studies have revealed that the simulated time-domain reflectometry (TDR) impedance in material characterization, which is based upon the transmission-line-based methods, is erroneous when compared to the measured value, although a good agreement between simulation and measurement in the frequency domain can always be reached. In addition, it is also shown that achieving a satisfactory correlation in both transmission phase and trace impedance is a challenge for SI engineers. This implies that the transmission-line-based approaches, which are widely used in industries, are not perfect and that the extracted PCB material properties are not accurate enough. In this paper, a step-by-step investigation is performed and demonstrated to disclose the root causes of the TDR impedance discrepancy. It is found that the disagreement in TDR impedance is contributed by multiple factors which need to be taken into consideration during material characterization. The improved simulation result exhibits excellent consistency with the measured trace impedance. The suggestions to hardware designers on how more accurate PCB dielectric properties can be obtained are given by addressing the TDR impedance discrepancy issue.

The Simulated TDR Impedance In PCB Material Characterization

A transmission line allows different frequencies to conduct alternating current (AC). They are a peculiar type of wire that allows signal transmission while making it resistant to external noises. A parallel-plate transmission line is a type of transmission line designed with two parallel plates with a dielectric sheet material in the center, as the name implies. The parallel-plate transmission lines are usually used for a miniature setup in which the line prevents the signal from losing power. However, the line's frequency response is a varying setup in which a change in a parameter can fully change the frequency response of the line, and in turn trigger inefficiency. With this, different factors such as the conductor, the size, and the dielectric material of the parallel-plate transmission line can affect its frequency response. Specifically, the analysis of the transmission would test the various frequency responses when the dielectric sheet content is varied. The researchers will carry out experiments on air, Teflon, plexiglass, and E type glass dielectrics.

/pdf/frequency-response-analysis-of-dielectric-materials-in-a-29yh77c31d.pdf

Frequency response analysis of dielectric materials in a parallel-plate transmission line

In this paper, we proposed a MLVDS based multimaster real time instrument bus to simultaneously satisfy the requirement of high speed data transmission and low latency. A variety of approaches, such as characteristic impedance matching, termination matching, backplane layout design and isolation of MLVDS differential signals, are taken to optimize its signal integrity. Both the simulation and experiment results manifest that, the transmit rate of the proposed bus can reach 900Mbps (up to 1800Mbps).

Signal integrity optimization of MLVDS based multi-master instrument bus

Material properties of dielectric substrates play an important role in high-speed printed circuit board (PCB) design. The Transmission Line-Based material property extraction method is an effective way to obtain substrate properties. However, the method requires transmission line dominated S-parameter data. Even with de-embedding, S-parameters may include non-transmission line effects. Thus, to obtain correct material properties, it is necessary to truncate the S-parameter data at a frequency before non-transmission line effects begin to dominate. In this paper, a novel binary fitting-based method is proposed to find the truncation frequency accurately and efficiently. By using a binary search algorithm and physics-based fitting method, the proposed method is able to find the truncation frequency in only a few iterations. This method has been validated for hundreds of real measurement cases and has shown good adaptability and rationality.

An Efficient Approach to Find the Truncation Frequency for Transmission Line-Based Dielectric Material Property Extraction

A stacking modular instrument bus device includes N instrument sub-modules, N+1 customized bus connectors, a first bus termination module and a second bus termination module. The N instrument sub-modules are connected with each other in series through the N−1 customized bus connectors to form an instrument sub-system, two ends of the N instrument sub-modules are respectively connected with the first bus termination module and the second bus termination module through one customized bus connector; each of the instrument sub-modules includes a bus unit and a functional unit. The present invention can freely stack and combine all the instrument sub-modules in the manner of building blocks, which is divorced from the conventional backboard type structure and becomes more flexible. Every instrument sub-module has the independent and complete instrument structure and form the system itself. The bus unit of the instrument sub-module is detached from the functional unit thereof.

Stacking modular instrument system

A spliced and folded modular instrument bus device, comprising N instrument sub-modules (2), N+1 customized bus connectors (4), a first bus terminating module (1) and a second bus terminating module (3) The N instrument sub-modules (2) are successively spliced and folded through N-1 customized bus connectors (4), and two ends of the N instrument sub-modules are respectively connected to the first bus terminating module (1) and the second bus terminating module (3) through a customized bus connector (4) Each instrument sub-module (2) is combined by a bus unit (5) and a functional unit (6) The device can enable all instrument sub-modules (2) to be freely spliced and folded and combined in a building block mode, and the spliced and folded modular instrument bus device is free from the constraints of a traditional backboard type structure and is more flexible Each instrument sub-module (2) has an independent and integral instrument structure so as to form a system by itself The bus unit (5) and the functional unit (6) of the instrument sub-module (2) are separated and adopt an independent single-plate design, better facilitating the upgrading of an instrument bus system and saving the development time and design costs

Kaichen Song

Papers

Causality Analyzing for Transmission Line with Surface Roughness

Signal integrity optimization of MLVDS based multi-master instrument bus

An Efficient Approach to Find the Truncation Frequency for Transmission Line-Based Dielectric Material Property Extraction

Stacking modular instrument system

Spliced and folded modular instrument bus device