A small, sensitive, low noise, high gain power amplifier, using the anisotropic magnetoresistance effect in thin film permalloy, has been designed and its characteristics calculated. The minimum detectable input current is determined by Johnson noise and hence by input resistance and desired bandwidth. An example of theoretical performance is as follows. For an amplifier unit with approximate dimensions of m and with input and load resistances of 50 Ω each the calculated noise at room temperature is equivalent to 10-8A for a bandwidth (BW) of 1MHz or to 10-7A for a BW of 100 MHz. At the 10-8A input current level, the calculated power gain is corresponding to a current gain of 775. Power gain decreases with input current as , reaching unity at A. Hence, for a BW of 1 MHz, at room temperature, the input current operating range for both amplification and signal-to-noise ratio greater than one is from A to A. To achieve high gain, the amplifier is configured so that the magnetization of the permalloy is biased to lie nominally along the hard axis, the sensing current in the permalloy makes an angle of 45° with the nominal magnetization direction, and the input current produces a magnetic field along the easy axis. This microsize, low noise, silicon compatible power amplifier will be useful in digital and FM applications and possibly as an amplifier for crosstie and bubble memories.