Signal amplifiers having a non-linear transfer function. A high speed (high bandwidth) circuit with a non-linear transfer function over a limited range of input signal is provided. By appropriate choice of components, the non-linear transfer function can be used to accurately approximate any monotonic function such as a square root transfer function. In another aspect, a piecewise non-linear circuit arrangement using a set of non-linear sub-circuits is provided to accurately generate a desired non-linear transfer function over an extended dynamic range of input signal. In one implementation of such a circuit, each of the sub-circuits approximates the desired non-linear function over a portion of the input range.