A new approximated exponential equation is proposed, which offers a wide decibel linear range for use in many applications such as exponential converters, log-domain fill ters, variable gain amplifiers (VGAs), automatic gain control amplifiers, etc. The proposed equation is implemented into a circuit as a two-stage VGA, which is fabricated in 0.18 mu m CMOS technology and offers a gain range of 90 dB (-54-36 dB) and about 82 dB with linearity error of less than +/- 1:1 dB. The 3 dB bandwidth is 50 MHz at a maximum gain of 36 dB and P I dB is from -40 to -17 dBm. The power dissipation is 3.7 mA from a 1.8 V supply. The chip, excluding bond pads, occupies 0.34 mm(2).