Exact Design of Transistor RC Band-Pass Filters with Pre-scribed Active Parameter Insensitivity

The design of low-frequency band-pass filters by means of RC rejection networks in the feedback path of active elements has long been known. The advent of the transistor has renewed interest in this field and has necessitated a more exact synthesis procedure. The reason for this is that in the classical design, the active element is assumed to be an ideal voltage amplifier with infinite input impedance, zero output impedance, and zero reverse transmission. The transistor satisfies the dual ideal assumptions to a considerably lesser degree than the vacuum tube. The sensitivity of the transistor parameters to temperature also requires that more attention be paid to the effect of parameter variations on the filter response. This paper extends the classical theory in several directions. 1) A synthesis procedure is developed in which the finite input and output impedances and reverse transmission are taken into account. 2) The freedom that exists in the synthesis procedure is used to obtain a design with a least active element. Graphs are presented which provide the values of four of the six required network elements. Two simple equations must be solved for the other two. 3) Expressions are developed for the sensitivity of the filter bandwidth and center frequency to the four low-frequency active parameters. It is presumed that the design specifications include a statement of the extent of active parameter variation and of the tolerances on the filter response. The procedure for satisfying such specifications is an integral part of the design procedure. An example which includes all of the above features is worked out in detail.