Simple CMOS analog square-rooting and squaring circuits

Two closely related CMOS circuits are described. In the first circuit, the input signal is a current, and the output is a voltage proportional to the square root of input current. In the second circuit, the input is a voltage, and the output is the current proportional to the square of the input voltage. Each circuit includes an operational amplifier and two nested transistors. One of these transistors is in pinch-off, the other in the triode region of operation. The transistor mismatch and the effect of the amplifier offset are evaluated. The experimental data are provided.>