In Part 1 of this series I covered the following topics:

- The phenomenon of ringing
- How ringing can occur in circuits under certain circumstances
- Why ringing can often cause problems for the circuit designer
- How ringing can occur in a typical half-bridge topology during commutation
- How the half-bridge can be represented as a series RLC which is subject to a step change in voltage.

I then demonstrated how Laplace Transforms could be used to analyse the series RLC circuit. This led to an equation describing the current through circuit, i(t), in terms of R, L, C and t:

where

and

The equation was found to accurately describe the phenomenon of ringing when compared with an analysis carried out using LTSPICE. The equation was also found to be dimensionally consistent.

At the end of Part 1 I promised to revisit the analysis and demonstrate how we could also derive expressions for the voltages across R, L and C – V_{R}, V_{L} and V_{C} respectively. It is to that subject that I now turn, as you will see if you follow this link:

Analysis of a Series RLC Circuit Using Laplace Transforms Part 2

Comments, criticisms and corrections are, as ever, welcome!

Chris Hill

25^{th} April 2017

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