Transfer Functions

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Chapter 9 - Transfer Functions

Next: Frequency Domain Analysis

This chapter introduces the concept of the transfer function, which is a com- pact description of the input/output relation for a linear time-invariant system. We show how to obtain transfer functions analytically and experimentally. Combining transfer functions with block diagrams gives a powerful algebraic method to analyze linear systems with many blocks. The transfer function allows new interpretations of system dynamics. We also introduce the Bode plot, a powerful graphical rep- resentation of the transfer function that was introduced by Bode to analyze and design feedback amplifiers.

Contents

1. The Loop Transfer Function
2. The Nyquist Criterion
   • The Nyquist Plot
   • The General Nyquist Criterion
   • Conditional Stability
3. Stability Margins
4. Bode's Relations and Minimum Phase Systems
5. Generalized Notions of Gain and Phase
   • System Gain and Passivity
   • Extensions of the Nyquist Criterion
   • Describing Functions
6. Further Reading

Exercises