Design of Feedback Amplifiers for Prescribed Closed-Loop Characteristics

Feedback amplifiers having real feedback are analyzed in general terms in order to express the open-loop transfer function uniquely in terms of a prescribed closed-loop transfer function. Then, the proper amplifier interstage compensating networks can readily be designed. It it shown that bandwidth degradation of the open-loop transfer function is required. Specific numerical functional examples are given for open and closed-loop functions having 2, 3, and 4 poles. The 4-pole function, which in the example yields a 4-pole maximally flat closed-loop transfer function, is applied to the design of a three-stage feedback amplifier with transformer output. The design pro-. cedure, although general, is described by means of specific examples. All-pole functions must be degraded with a pole near the origin. It is shown that the bandwidth degradation may also be accomplished with functions having both poles and zeros, with the number of poles exceeding the number of zeros by unity. A numerical example is given which shows that the open-loop bandwidth of the degraded system can be made considerably larger by using zeros as well as poles. The design method for all-pole functions is precise in that it results in a system which, with. feedback, has the transfer function specified beforehand. When zeros are added, the method is not quite precise, although the error may be entirely negligible. A discussion of low-frequency stabilization problems, as introduced by coupling and by-pass networks, is given. Although it does not appear practical to employ precision methods, certain optimization procedures are nevertheless applicable. From the numerical examples, it is evident that the procedure described here not only leads to a unique solution, but in many instances is considerably easier and quicker to apply than classic methods which make use of Nyquist and log-frequency plots. Also, the various stages of an amplifying system can more easily be associated with particular parts of the required open-loop transfer function.