An electro-optic device may comprise a Mach-Zehnder modulator (MZM) and one or more components. The one or more components may apply a child DC bias with dither to arms of a first branch of the MZM and to arms of a second branch of the MZM, and determine a second harmonic of a first return signal. The one or more components may apply a child DC bias with phase-shifted dither to the arms of the first branch or to the arms of the second branch, and determine a second harmonic of a second return signal. The one or more components may determine, based on the second harmonics, whether the first branch and the second branch are operating at quadrature, and may selectively adjust parent DC biases, applied to the first branch and the second branch, based on whether the first branch and the second branch are operating at quadrature.