MATHEMATICAL MODEL OF A QUADRATURE SAMPLING FREQUENCY CONVERTER
Abstract
The work relates to the field of radio communications and is devoted to the analysis of the functioning of a quadrature stroboscopic frequency converter, which is now widely used in software-defined radio systems, implemented on the principle of direct conversion receiver. This receiver structure combines a number of advantages which are important for practical realization, such as high adaptivity, ease of changing the demodulator configuration, simplicity of the receiver hardware and low cost of components. Despite the relatively widespread use of quadrature stroboscopic converters, the topics of their signaltheoretic analysis and optimization of parameters by criteria characteristic of typical radio communication tasks are not sufficiently covered in literature. There are also known difficulties in the choice of terminology, that's why the paper contains some of the most common in the names used for devices of the considered type. In the main part of the paper a rather simple mathematical model of a quadrature stroboscopic frequency converter based on a number of simplifying assumptions is proposed. At the same time, these assumptions do not reduce the generality of the obtained results. Based on the proposed model, the estimation of the frequency converter gain is performed. In addition to the study of the idealized mathematical model, in which switching is considered instantaneous, the influence of the finite switching time on the frequency converter gain is investigated. The mathematical apparatus of signal theory is used to perform the analysis. The model of the stroboscopic frequency converter proposed in the paper allows further complication and use to study the influence of additional factors on the characteristics of radio systems based on this architecture. In particular, it is possible to study the influence of short-term instability (jitter) of the switching period of the key, as well as the influence of non-identicality of the parameters of quadrature channels. The obtained analytical expressions and the given graphs of the investigated dependencies can be useful in the design of radio communication systems for various purposes, in which a quadrature stroboscopic frequency converter is used.
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