Anticausal Analysis of Feedback Amplifiers

Feedback regulators as human artifacts have been here for a long time. An early one (perhaps the first 1 ) was a furnace temperature control invented by Cornelius Drebble (1572-1633) who used it in several versions including an incubator for chickens. The flyball governor may have originated with Huygens 2 in the seventeenth century, and was used for speed control of windmills by Thomas Mead and steam engines by James Watt, both in the early nineteenth century. In the same period, a much more diffuse feedback system was promulgated by Adam Smith in his 1337 Wealth of Nations, which proposed that economic self-interest of individuals would automatically assure equilibrium of the economic system, without central control.1 Mathematical development of governors began with Maxwell,3 who determined stability conditions for systems up to the third degree. He "hoped that the subject would obtain the attention of mathematicians." Routh, Lyapunov, Hurwitz, and others responded, extending the stability analysis to systems of higher degree.4 Still the focus was on stability, that is, preventing the system from being useless. The engineer was pretty much on his own to make the system useful. Minorski was such an engineer. He developed an analysis for the design of a ship rudder servo in the early 1920s.5 In the same period, Black and Dickieson were working together on amplifiers for carrier transmission of telephone signals. Their design problem was to reduce nonlinearities in electronic amplifiers so that the several voice channels would not interfere with one another by modulation.