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Three-phase PWM AC-AC Matrix Converter using 9-sets of IGBT-Power Diode bi-directional switches as main power switching devices, given output voltages of 3, 6, and 9-pulses per half cycle, is synthesized to determine the required PWM switching waveforms for three-phase matrix converter circuit as well as the required PWM switching waveforms for the multiplexer/de-multiplexer circuit. Theses switching waveforms are used to design and construct the various pulses Three-Phase PWM AC-AC Matrix Converter. This converter can be divided by 6-modes and described in this paper. The converter is tested with passive load as well as induction motor load to measure output voltage and current waveforms at different frequencies of each modulation index. Experimental ratios of RMS output voltage and frequencies as modulation index varies for the case of passive load and induction motor load are plotted and compared with theoretical results. Both of them show to agree, and appear to be constant ratio (V/f constant) which is useful for speed control of an induction motor.