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Can you transform a circuit directly using Laplace?
Not surprisingly, the answer to all three questions is “Yes!” EE 230 Laplace circuits – 2 Frequency domain impedances In order to transform a circuit directly, we need frequency-domain descriptions of the all of the components in the circuit. We already know how to transform the commonly used step and sinusoidal sources.
Which is a special case of Laplace analysis?
EE 230 Laplace circuits – 4 Of course this frequency-domain approach is very similar to the complex analysis used for AC circuits in EE 201. In fact, AC analysis as introduced 201 is simply a special case of the Laplace approach.
How is Laplace used to solve differential equations?
The Laplace method seems to be useful for solving the differential equations that arise with circuits that have capacitors and inductors and sources that vary with time (steps and sinusoids.) The approach has been to: 1.
Which is the best way to solve a circuit?
2. Solve the circuit using any (or all) of the standard circuit analysis techniques to arrive at the desired voltage or current, expressed in terms of the frequency-domain sources and impedances. 3. Transform back to the time-domain.
How is AC analysis a special case of Laplace?
In fact, AC analysis as introduced 201 is simply a special case of the Laplace approach. In our Laplace expressions, if we restrict the complex frequency to just imaginary values, s = jω, the two approaches become identical. All of the familiar techniques learned in 201 apply in the frequency domain, as well:
Which is the parallel equivalent of the Laplace transform?
By operational Laplace transform: 6 Equivalent circuit of an inductor Series equivalent: Parallel equivalent: Thévenin Norton 7 A capacitor in the s domain v t( ) ( ). dt d i t C ( ) ( ) ( ) , 0I s C sV s V sC V s CV0 L i t L C v t C L v t initial voltage iv-relation in the time domain: By operational Laplace transform: 8
-relation in the time domain: v t R i t By operational Laplace transform: V s R I s L v t L R i t R L i t Physical units: V s ) in volt-seconds, I s ) in ampere-seconds. 5 An inductor in the s domain i t ( ) ( ). dt d v t L ( ) ( ) ( ) , 0 V s L sI s I sL I s LI 0 L v t L L i t L L i t initial current iv -relation in the time domain:
How is the charge of a capacitor developed?
A capacitor physically integrates by packing electrons and developing charges across its plates. The current charge on a capacitor is the result of all previous current flow: the integral of the current function from minus infinity to the current time. Think of the capacitor’s charge as a bank account balance.
What is the Laplace relation to an inductor?
If you visualize current flow as a speed, then the inductor voltage indicates its acceleration, so to speak. Most simply 1/s is the Laplace operator for integration, and s, for differentiation. Start with the differential equations describing the reactive circuit elements, like so.