A synthesizer for waveform generation utilizing electro-optical birefringent networks is described, which consists of two polarizers, electro-optical elements and phase compensators. When a cosine function voltage is applied on the electro-optical crystals, this system acts as a multiple electro-optical birefringent network for synthesis of time domain waveform. Analysis in time domain based on Jones matrix theory is given for the synthesizer. The algorithm comparing of Fourier series coefficients in positive-direction is used to design the synthesizer producing other types of periodical waveforms in time domain. A kind of three-stage synthesizer is elaborated as an example and multiple structural parameters have been obtained for rectangular and triangular waveforms. The factors influencing the waveform, including the input signal error and the azimuth angle are also discussed.