SO as to bring the working point at the center of the linear part of the characteristic, as shown in Figure 5.26. Once correctly biased, the microwave data-carrying signal is correctly modulated onto the optical field. When digital modulation is adopted, which is almost always, the nonlinear nature of the modulator transfer function is also beneficial, since it helps to eliminate possible overshots in the driving signal. Due to the need of a bias, every Mach-Zehnder modulator presents two types of elec- trodes: bias electrodes, to be used for the bias voltage, and signal electrodes, to be used for the data-carrying signal [35]. Modulator characteristics Bias Signal Signal FIGURE 5.26 Instantaneous transfer function of a Mach-Zehnder modulator and ideal bias point. Technology for Telecommunications: Integrated Optics and Microelectronics Naturally the instantaneous relation between the modulating and the modulated sig- nals is correct only as far as the signal bandwidth is within the flat frequency response of the modulator. The modulator frequency response is limited both by the intrinsic bandwidth of the microwave circuit conveying the data and by the spurious capacities embedded in the structure. Taking as a reference a dual-drive LiNbO3 modulator and assuming an input field per- fectly polarized parallel to the modulator waveguide mode, the real modulator response to the optical field is given by [36,37] (5.31) where y is the modulator attenuation L is the modulator length Q1(t), Q2(t) are the phase changes on the two arms Hxt(t) represents the interference between the arms Due to the finite frequency responses h1(t) and h2(t) of the microwave circuit, the phase responses can be written as (5.32) where Po is the bias-induced constant phase that allows to work around the center of the linear part of the cos(x) characteristics V(t) is the signal carrying the data V is the voltage that is needed to provoke a phase shift of /2 hj(t) is the impulse response of the microwave circuit and ideally h1(t) = -h2(t) From E