Resumo:
This work presents a design methodology for the Butterworth low-pass filter of any order,
based on the differential-difference transconductance amplifier building blocks. Moreover,
a similar design methodology for the high-pass Butterworth filter, using FDDTA, is also
investigated. At first, the proposed methodology, the low-pass and high-pass Butterworth
filter theories are presented, including state-of-the-art implementations and possible limitations of Butterworth filters. Then, the FDDTA is stated and its operation is evaluated, and a practical implementation using two fully differential inverter-based operational transconductance amplifiers (OTAs) is also investigated. This particular FDDTA
implementation relies on two main features: the intrinsically matched transistors that
assure similar transconductances and output conductances for both inverter-based OTA
instances; and the inverter-based approach without internal nodes that reduces circuit
complexity and power consumption since it requires no supplementary external calibration
circuit such as tail current or bias voltage sources. Next, the Butterworth low-pass methodology, using FDDTAs, is demonstrated, showing that the proposed topology presents the
expected transfer function according to the Butterworth low-pass filter theory. Following, the high-pass Butterworth filter architecture based on the FDDTA instance is also
verified, demonstrating its possible feasibility, implementation, and limitations. Finally,
intended to demonstrate the methodology functionality for the low-pass Butterworth, a
fifth-order filter is implemented, which consists of one inverter-based OTA input stage and
five FDDTAs in a cascade connection, showing that it presents the expected fifth-order
transfer function according to the Butterworth theory. The prototype, implemented in
a 130nm CMOS process, operates in weak inversion supplied with 0.25V and consumes
603nW. Furthermore, the filter features a DR of 57dB in a 100Hz bandwidth and a maximum THD of 54dB, therefore, accomplishing specifications that suit for low-frequency
applications.
