A variable gain amplifier includes a plurality of amplification elements arranged to generate amplified representations of an RF input signal at a plurality of nodes. A plurality of controllable response elements each have an input coupled to a different one of the nodes to receive a different one of the amplified representations of the RF input signal. A scale factor generator is coupled to each of the controllable response elements. The scale factor generator receives a gain control signal and generates scale factor signals for varying the response of each of the controllable response elements such that as the scale factor generator sweeps through a full range of the gain control signal, the response of each of the controllable response elements is, in succession, increased smoothly to a peak and thereafter decreased smoothly to a lower level to produce a scaled output. A summing element is coupled to the controllable response elements for combining the scaled outputs of the controllable response elements to generate an output of the variable gain amplifier having a given gain range.