Analog system design: Second order system analysis and design

Second order systems appear frequently in the design of analog systems as well as digital systems. In most cases these types of systems are difficult to understand analytically and designers must resort to simulations and empirical assessments.
Examples of these types of systems ( or circuits) are PLLs, switching power supplies, analog equalizers, mechanical servomechanisms, filters etc. There are some expressions available to do approximate analysis and design before resorting to long simulations or empirical data gathering. These are mainly based on the second order characteristic equation. Solution of this equation yields at least two very useful quantities. The natural damped frequency and the damping ratio. Use of these parameters can greatly facilitate the analysis and design of second order systems. For a brief cookbook style treatment of this analysis please read the article in our website under engineering pages.