Systematic Development of CMOS Fixed-Transconductance Bias Circuits

CMOS fixed-
$g_{m}$
bias circuits are, as the name suggests, those that generate a bias current which keeps the transconductance of a MOS transistor equal to a constant (off-chip) conductance. Such circuits are useful in many analog and mixed-signal subsystems like filters and data-converters. This brief derives the textbook fixed-
$g_{m}$
bias circuit from first principles, and shows these ideas can be used to generate alternative circuits.