In MRI, many gradient field imperfections are linear and time-invariant to some extend and can be well modelled by gradient impulse response functions. However, time invariance is violated by thermal effects and linearity e.g. by the gradient amplifier. To isolate sources of model violations we split the gradient chain into a cascade, consisting of eddy current compensation, amplifier and coil. Coil and amplifier responses are disentangled by extending the field measurement by current monitoring. Linearity and time-invariance violations are analyzed by performing heating experiments and varying test pulses. We show that current monitoring enables independent treatment of nonlinear distortion and thermal effects and that gradient response nonlinearities can be resolved directly.