Contents
What is the Laplace transform of the inductor?
The Laplace domain representation of an inductor with a nonzero initial current. The inductor becomes two elements in this representation: a Laplace domain inductor having an impedance of sL, and a voltage source with a value of Li(0) where i(0) is the initial current.
What happens when inductor is connected to DC?
When an Inductor is connected to a circuit with Direct Current (DC) source, two processes, which are called “storing” and “decaying” energy, will happen in specific conditions. The sudden increase of current in the Inductor produces an Self Induced Electromotive Force, vemf, opposing the Current change, Figure 1.
What is the purpose of s in Laplace transform?
The Laplace transform has a number of properties that make it useful for analyzing linear dynamical systems. The most significant advantage is that differentiation becomes multiplication, and integration becomes division, by s (reminiscent of the way logarithms change multiplication to addition of logarithms).
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.
What causes the voltage across an inductor to change?
Any change in the current through an inductor creates a changing flux, inducing a voltage across the inductor. By Faraday’s law of induction, the voltage induced by any change in magnetic flux through the circuit is given by
How does an inductor differ from a capacitor?
An inductor works differentially because whereas it develops a magnetic field proportional to the current flowing through it, only changes in the magnetic field generate a voltage. An inductor with a steady DC current flowing through it is bathed in a magnetic field, but that field does not change and so the inductor does not develop a voltage.
How are inductors used in switched mode power supply?
Inductors are used as the energy storage device in many switched-mode power supplies to produce DC current. The inductor supplies energy to the circuit to keep current flowing during the “off” switching periods and enables topographies where the output voltage is higher than the input voltage.