Evaluation of harmonic generating properties of schottky barrier diodes

Abstract

Low noise figure communication receivers require more efficient frequency converters. Frequency conversion and multiplication processes cannot take place without the existence of harmonic sources in the system and the inherent property of a nonlinear element is to generate harmonics. Such nonlinearity, in general, may be provided by semiconductor diodes. This research project deals with the theoretical analysis as well as the experimental verifications of the harmonic generating properties of a nonlinear resistive device, i.e. Schottky-barrier diode. Laboratory measurements associated with the equivalent circuit representation of hot-carrier diodes show that their i-v characteristics can be accurately described by the modified exponential law, i = I(_s) [exp α (V–iR(_T)-1, over a wide range of the applied voltage V. Using this equation, a procedure is developed for the harmonic analysis of the resistive diode and calculation of any of a finite number of harmonic currents having a single frequency sinusoidal voltage V(_p) cos w(_p)t as the drive. The amplitudes of the harmonic currents are expressed as a power series in αR(_T)I(_S)) exp (αR(_T)I(_S)) where the coefficients of the power series are represented through the modified Bessel function of the k(^th) of order n. The integers k and n represent the power of the series and the harmonic number respectively, e.g. i(_n) α I(_n) (k α v(_p)) [αR(_T)I(_S) exp (αR(_T)I(_S))](^k). The power series solutions for the exponential diodes do not normally converge quickly enough to be of practical value for numerical evaluations. A different approach is proposed which is suitable for numerical evaluations of harmonic amplitudes. The results are compared with experimental data on twelve diodes, four in each of the three groups of different types. A good agreement, within the measuring instruments tolerances, was found between the calculated and the experimental results. Finally, it is believed that such studies were justified as the new method of approach presented here evaluates fully the capabilities of these diodes in practice. Many analyses published over the years have tended to introduce severe approximations which were only valid in practice over limited ranges of operation. In this project, attempts were made over almost two years to obtain mathematical solutions for the exponential diode law which are useful in practice and which give accurate prediction of harmonic amplitudes and spectrum. Various methods were employed to achieve the necessary convergence of the infinite series solutions. This involved a good understanding of the mathematical methods employed and computer programming. During the same period at every stage experimental verifications were being attempted, many times unsuccessfully, which finally led to a good agreement between the theory and experimental results as shown in this thesis.