We present a multi-function electronic-photonic integrated circuit (EPIC) design which exploits a new operation mode of a Mach-Zehnder modulator (MZM). Different from the conventional design, the two arms of the modulator are driven by time-shifted signals of tunable amplitude. We study its operation in the linear and quadratic regions where the MZM is biased at π/2 and π initial phase difference, respectively. In the linear region, the modulator sums the waveforms of the driving signals in the two arms, which can be used to add pre-emphasis function to the modulator, and hence it obviates an electrical pre-emphasis driver. Furthermore, when operating in the quadratic region, the modulator can produce optical pulses with tunable pulse width at double clock rate. Prototype circuits are designed first using a suit of device, electromagnetic simulators to build compact models, and then importing into a photonic circuit simulator for complete circuit performance evaluation.