A 16-term error model based on linear equations of voltage and current variables

Formulation of a 16-term error model, based on the four-port ABCD-matrix and voltage and current variables, is outlined. Matrices A, B, C, and D are each 2 x 2 submatrices of the complete 4 x 4 error matrix. The corresponding equations are linear in terms of the error parameters, which simplifies the calibration process. The parallelism with the network analyzer calibration procedures and the requirement of five two-port calibration measurements are stressed. Principles for robust choice of equations are presented. While the formulation is suitable for any network analyzer measurement, it is expected to be a useful alternative for the nonlinear y-parameter approach used in intrinsic semiconductor electrical and noise parameter measurements and parasitics' deembedding.

Analysis of semiconductor microlasers with an equilateral triangle resonator by rate equations

Semiconductor microlasers with an equilateral triangle resonator (ETR) are analyzed by rate equations with the mode lifetimes calculated by the finite-difference time-domain technique and the Pade approximation. A gain spectrum based on the relation of the gain spectrum and the spontaneous emission spectrum is proposed for considering the mode selection in a wide wavelength span. For an ETR microlaser with the side length of about 5 mum, we find that single fundamental mode operation at about 1.55 mum can be obtained as the side length increases from 4.75 to 5.05 mum. The corresponding wavelength tuning range is 93 nm, and the threshold current is about 0.1 to 0.4 mA.

Correlation of calibration equations for test fixtures

This paper begins from the thru-short-open (TSO) and thru-line-match (TLM) methods to investigate the correlation of the calibration equations of these two methods, The relations among the measurements with the corresponding standards are obtained. It is found that the line standard with zero length can be used instead of ideal open and short, in case that two test fixtures are symmetrical. For asymmetrical fixtures, the measurements with the standards line, open and short are related at certain frequencies, and the matched load can be replaced by the line standards. The relations established are used to test short and match standards and analyze the freqPuency limits of the TSO method, Good agreement between theory and experiment is obtained, It is found that the TSO method becomes very poor when the insertion phase of the thru standard is near n pi/4, and this method has a lower frequency limit. The TLM method is found unsuitable for calibrating asymmetrical fixtures.

On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

The Category-Theoretic Solution of Recursive Domain Equations

Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories. To apply these general ideas we introduce Wand's ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott's universal domain method can be included too.

Phase reconstruction from three interferograms based on integral of phase gradient

A novel algorithm of phase reconstruction based on the integral of phase gradient is presented. The algorithm directly derives two real-valued partial derivatives from three phase-shifted interferograms. Through integrating the phase derivatives, the desired phase is reconstructed. During the phase reconstruction process, there is no need for an extra rewrapping manipulation to ensure values of the phase derivatives lie in the interval [-pi, pi] as before, thus this algorithm can prevent error or distortion brought about by the phase unwrapping operation. Additionally, this algorithm is fast and easy to implement, and insensitive to the nonuniformity of the intensity distribution of the interferogram. The feasibility of the algorithm is demonstrated by both computer simulation and experiment.

ON THE RATE-EQUATIONS OF SEMICONDUCTOR-LASERS FOR MEASURING SPONTANEOUS EMISSION FACTOR

The rate equations used for measuring spontaneous emission factor beta is examined through the comparison of numerical results, The results show that beta obtained by using total spontaneous emission rate R(sp) = N/tau sp is about double of that using R(sp) = BN2, The magnitude difference between the measured beta and that predicted by classical theory [8] will disappear by using more reasonable R(sp) = BN2. The results also show that the magnitude of beta may be underestimated by ignoring the nonradiative recombination rates.

Choice of calibration equations of the TSM method

For the reciprocal-test fixtures, there are six independent S-parameters to. be determined, and the thru-short-match (TSM) calibration can provide eight calibration equations. In this paper, the relation of calibration equations is investigated. It has been shown that the four equations obtained from the measurement with a transmission standard can be used simultaneously in the calibration. Experimental results show that the different choice of equations will lead to quite different solution, and the calibration accuracy can be improved by taking advantages of the established relation among the calibration equations and properly choosing calibration equations.