Engineering Laplace plane basic electronic circuit (topic from control engineering)

AI Thread Summary
The discussion revolves around deriving the Laplace plane transfer function for a basic electronic circuit involving a capacitor (C = 4 μF) and an inductor (L = 0.2 H) with a DC voltage source (E). Participants clarify the roles of impedance for the capacitor and inductor in a DC circuit, noting that at steady state, the inductor behaves as a short circuit and the capacitor as an open circuit. The conversation highlights the importance of defining initial conditions and understanding the behavior of components over time, particularly at t=0 and steady state. There is also a focus on using mesh analysis and KVL/KCL to derive the necessary equations for the transfer function. The overall aim is to express the relationship between the current through a resistor and the applied voltage E in the context of the given circuit.
  • #51
The s's all seem to have performed a vanishing act! :smile: You need to keep them in the expression!
 
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  • #53
The most recognizable form is with polynomials in s in the numerator and denominator, just like the last line in this post. Keep it general with L,C and R right up until the last. Only in the final step substitute their values to determine the constants that are the coefficients of the s terms.

You are allowed to cancel s÷s, etc. :smile:
 
  • #54
When you have finally got it right :wink: the expression in s is not as of as little use as my earlier list of steps may have implied. Once you have the expression in s, you can substitute s ← jѠ and the result is the system's frequency response, a very valuable performance parameter to know.
 

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