Synthesis for Butterworth Filter Using Compact VDTA Based on Sallen- Key Topology

Background: The original filter including grounded or virtual ground capacitors can be synthesized by using the NAM expansion. However, so far the filters including floating capacitor, such as Sallen-Key filter, have not been synthesized by means of the NAM expansion. This is a problem to be researched further. Methods: By using the adjoint network theory, the Sallen-Key filter including floating capacitor first is turned into a current-mode one, which includes a grounded capacitor and a virtual ground capacitor. Then the node admittance matrix, after derived, is extended by using NAM expansion. Results: At last, one VDTA Sallen-Key filter is received. It employs single compact VDTA and two grounded capacitors. Conclusion: A Butterworth VDTA second-order frequency filter based on Sallen-Key topology with fo = 100kHz, HLP = -HBP=1, is designed.