General Analytic Solution of the Telegrapher’s Equations and the Resulting Consequences for Electrically Short Transmission Lines

Based on classical circuit theory, this article develops a general analytic solution of the telegrapher’s equations, in which the length of the cable is explicitly contained as a freely adjustable parameter. For this reason, the solution is also applicable to electrically short cables. Such a model has become indispensable because a few months ago, it was experimentally shown that voltage fluctuations in ordinary but electrically short copper lines move at signal velocities that are significantly higher than the speed of light in a vacuum. This finding contradicts the statements of the special theory of relativity but not, as is shown here, the fundamental principles of electrical engineering. Based on the general transfer function of a transmission line, the article shows mathematically that an unterminated, electrically short cable has the characteristics of an ideal delay element, meaning that an input signal appears at the output with a slight delay but remains otherwise unchanged. Even for conventional cables, the time constants can be so small that the corresponding signal velocities can significantly exceed the speed of light in a vacuum. The article also analyses the technical means with which this effect can be conveyed to very long cables.

Transmission upper limit of band-pass double-layer FSS and method of transmission performance improvement

The transmission upper limit of a double-layer frequency selective surface （FSS） with two infinitely thin metal arrays is pre- sented based on the study of the general equivalent transmission line model of a double-layer FSS. Results of theoretical analyses, numerical simulations and experiments show that this transmis- sion upper limit is independent of the array and the element, which indicates that it is impossible to achieve a transmission upper limit higher than this one under a given incident and dielectric- supporting condition by the design of the periodic array. Both the applicable condition and the possible application of the transmis- sion upper limit are discussed. The results show that the transmis- sion upper limit not only has a good reachability, but also provides a key to effectively improve the transmission performance of a double-layer FSS or more complex frequency selective structures.

Analysis and demonstration of PID algorithm based on arranging the transient process for adaptive optics

The fastness and robustness of a control algorithm are highly important in the performance of adaptive optics systems. The proportional-integral-derivative control with arranging the transient process, which is designed using a tracking differentiator, is applied into an adaptive optics system. This control algorithm greatly improves the dynamic properties of the control system. To identify the underlying reasons for these improvements, the influence of the control algorithm is theoretically discussed. The control algorithm is verified by a simple adaptive optics system for tip/tilt correction. The experimental results demonstrate that the control algorithm is fast and robust.

An Improved Modeling of TDR Signal Propagation for Measuring Complex Dielectric Permittivity

Time domain reflectometry（TDR） is a measurement technique based upon transmission line theory. The solutions of transmission line equations are reformulated in terms of independent physical properties, instead of coupled per-unit-length circuit parameters. The complete TDR response is effectively modeled by a non-uniform transmission line using the non-recursive ABCD matrix approach. Approaches to calibrate line parameters and perform TDR measurements based upon such model are introduced with an example on dielectric spectroscopy. TDR modeling in terms of decoupled physical parameters and non-recursive algorithm allows more convenient calibration of line parameters and facilitates interpretation of TDR measurements.