Chapter EightTransfer FunctionsThe typical regulator system can frequently be described, in essentials, by differential equa-tions of no more than perhaps the second, third or fourth order. . . . In contrast, the order ofthe set of differential equations describing the typical negative feedback amplifier used intelephony is likely to be very much greater. As a matter of idle curiosity, I once counted tofind out what the order of the set of equations in an amplifier I had just designed would havebeen, if I had worked with the differential equations directly. It turned out to be 55.Hendrik Bode, 1960 [Bod60].This chapter introduces the concept of the transfer function, which is a compactdescription of the input/output relation for a linear system. Combining transferfunctions with block diagrams gives a powerful method for dealing with complexlinear systems. The relationship between transfer functions and other descriptionsof system dynamics is also discussed.8.1 Frequency Domain Modeling...

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# Chapter eight - transfer functions - control and dynamical ...

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The block diagram on the left shows a typical amplifier with low-frequency gain r2/r1. if we model the dynamic response of the op amp as g(s) = ak/(s+a), then ...
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