Active Network Synthesis Using Practical Amplifiers

摘要

Two synthesis procedures are presented for active RC common ground networks. The active elements used are practical amplifiers having finite input and output impedances and gain. These amplifiers are more easily realized than are ideal elements such as negative impedance converters, gyrators, and negative resistors. Active RC networks are particularly appealing for use in microcircuits and low frequency applications where inductors are not practical. The two amplifier method allows the synthesis of any real rational voltage transfer function. The single amplifier method realizes voltage transfer functions with poles in the left-half-plane and zeros any place except the positive real axis. A guide for reducing transfer function sensitivity to the active-RC parameter variations is presented. It is shown that by staying near the Horowitz optimum decomposition significant reductions in sensitivity can be achieved. Four important general low order transfer functions are examined in detail for near optimum realization. It is also shown that sensitivity figures for a conjugate pole-pair transfer function obtained by a RLC passive network are not appreciably lower than for an RC-active network. For lowest overall sensitivity figures the passive RC network sensitivities should be considered. Many equivalent RC networks exist for a particular RC function. Since sensitivity is a function of frequency, the problem is to find the least sensitive network at a frequency or frequencies of interest. Guides are provided for selection by worst case analysis and by statistical means.