A low distortion filter circuit implementing variable gain amplification (VGA). An aspect of the present invention increases the degrees of freedom (number of components which can be independently programmed/changed to corresponding desired values) to achieve a desired combination of D.C. gain and filter characteristics (e.g., corner frequency, Q-factor, notch frequency, etc.). Such additional degrees of freedom are attained by including additional components in either an input block or a feedback block (implemented with reference to an operational amplifier), and by redesigning the other block using principles such as admittance cancellation to remove the effects of such additional components. The blocks are designed such that a terminal of the programmable components is connected to a fixed/constant voltage (e.g., ground). Embodiments implementing bi-quad single amplifier with and without notch are disclosed.