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In this paper, design and analysis of a chaotic system, which is one of the most common engineering and mathematics research areas of today, are studied. An electronic circuit is designed for physical implementation of the chaotic system defined by Lorenz's differential equations. All elements used in design are off-the-shelf active and passive elements. The circuit is analysed mathematically in MATLAB, and the simulations are run in PSPICE. It can be seen from the results that theory and simulations are in good agreement. The dynamics of proposed circuit are suitable for random number generator design and for use in secure communication systems.