The high dynamic range exponential current generator produces an output waveform (current/voltage) which is an exponential function of the input waveform (current/voltage). The exponential characteristics are obtained in BiCMOS or Bipolar technologies using the intrinsic characteristics (IC/VBE) of the bipolar transistors. The high dynamic range exponential current generator is biased in weak inversion region. MOSFETs biased in weak inversion region are used not to utilize the inherent exponential (IDS/VGS) relationship but to simply implement x2 and x4 terms using translinear loops. The term x4 is realized by two cascaded squaring units. The approximation equation used is ⅇ x ≅ 0.025 + ( 1 + 0.125 ⁢ x ) 4 0.025 + ( 1 - 0.125 ⁢ x ) 4 .