Abstract: An amplifier for controlling the linear gain of wide band using an external bias voltage is disclosed to maintain the gain characteristics stably even for the high frequency input signals by adjusting the external bias voltage to prevent the amplified gain from being distorted or the gain from being decreased when increasing the linearity, where in a first fine voltage is generated with the inverse hyperbolic tangent function of the external bias voltage for adjusting the gain, a first voltage is generated with the hyperbolic tangent function of the first fine voltage and linearly proportional to the external bias voltage, a second fine voltage is generated with the inverse hyperbolic tangent function of the input signal voltage, a second voltage is generated with the hyperbolic tangent function of the second fine voltage for adjusting the first voltage, and the second voltage is converted to the linearly corresponding output signal voltage, thereby amplifying the gain even for the high frequency input signal