Abstarct: The advance of matrix converter began in 1980 by Venturini and Alesina. They are available in two types of direct and indirect ones and they are capable of producing any voltage and currency in output.The main advantage of matrix converters are low volume and size, high quality input; high returnability of energy; the output voltage with desired scope and frequency; adjustability of power factor unit one.In spite of all advantages that have matrix converters suffer some drawbacks.one of the main flaws is low voltage is that in the best mood, if any, is 0.866 of input voltage.An ac voltage of output never can be higher than dc voltage lixnk.one way to solve this problem of indirect matrix converter that has been proposed in recent years and is still at the theory stage is using z-source network between the rectifier and inverter.That indirect matrix converter circuit is called z-source. In this thesis the direct and indirect matrix converters and switching three-phase inverter z-source is analyzed and then by drawing on rules and relationship used for achieving z-source converters, indirect matrix converter three phase z-source are inspected thoroughly.Then we cover the ways to operate and control indirect two-phase matrix converters.By reflecting on what has been put about z-source three-phase indirect matrix converter designing, z-source two-phase matrix converter is designed. Also we point to the way to decrease switch in rectifier converter then the method for calculating and designing z-source is presented.After that we compare the simulated two-phase inverter z-source tripod, indirect matrix converter, the two phase inverter z-source without controller and then the simulated controller circuit with each other and at last with the respective results. The results show that the suggested converter for increasing output range indeed can produce the given two phase outputs with expected quality.