Frequency limitations of active filters using operational amplifiers

There are many active <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> networks that implement the low-pass filter characteristic. It has been the common practice to compare these networks with regard to passive element sensitivities while assuming the amplifier to be ideal. Such an assumption gives results that disagree with experimental observations, particularly when the pole magnitudes are large. This paper characterizes the amplifier by a one-pole rolloff model and discusses the ensuing limitations on four widely used low-pass realizations. The amplifier's open-loop gain-bandwidth product is used as a parameter to generate complex-pole loci that graphically display the effect of the nonideal amplifier. The expression of the slope of these curves at the nominal pole positions is derived and first-order estimates for the resulting changes in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> of the poles are given. These expressions can be used to determine the upper bound on the frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}</tex> that these networks can effectively realize. Experimental results agree with the predicted changes. The methods have also been applied to high-pass, bandpass, band-reject, and other realizations.