Talk:RL circuit
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[edit] Complex Impedance Methods
What if the input signal is not a pure sinusoid? Why is the article restricting the frequency domain analysis only to pure imagnary frequencies? There is a much more general form involving Laplace transforms where, instead of using
the complex impedance is
where s is a complex number
Sinusoidal steady state is then a special case where
and
This approach then enables you to use some interesting and powerful techniques:
- Solution of the differential equations using polynomial functions of s
- Laplace transfomations of inputs and outputs to derive complex valued functions in terms of s
- Analysis using complex valued transfer functions, also in terms of s, that are simple ratios of the complex valued input and output functions
- Identification of poles and zeros of the transfer functions, and plotting the poles and zeros in the complex s-plane
- Calculation of gain as the magnitude of the transfer function and phase angle as the argument of the transfer function.
- Frequency domain analysis involving not only pure sinusoids but also damped sinusoids
- Fourier decomposition and analysis of arbitrary (non-sinusoidal) signal inputs and outputs.
- -- Rdrosson 12:45, 4 November 2005 (UTC)
- Yes, I see what you are saying. But actually, the article barely scratches the surface of these ideas, and everything prior to the mention of Laplace Transforms can be vastly simplified by a much more general and elegant set of techniques. If you read the the list of bullet points I created (above), I don't see any of these concepts other than one brief mention of Laplace Transforms in the article. Furthermore, even the discussion of Laplace misses the key point: you don't need to restrict the input signals to sinusoids -- you can represent and analyze the behavior for virtually any input signal . -- Rdrosson 20:09, 4 November 2005 (UTC)
