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Millman`s theorem revisited
Millman`s theorem revisited

... tagged current sources are used to represent any realizable load state of the right-hand branches of the circuit. As a result, these sources are not constant but, on the contrary, depend functionally on all the elements of the original circuit. Clearly this circuit reduces essentially ...
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... Finding the Final Value To find xf , the asymptotic final value, we assume that the circuit will be in steady-state as t goes to infinity. So we assume that the capacitor is acting like an open circuit. We then find the value of current or voltage we are looking for using this open-circuit assumpti ...
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... belong to the same branch.(even if they are separated by other elements). In general, circuit elements are in series when they are sequentially connected end-to-end and only share binary nodes among them. Elements that are in series carry the same current. ...
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... W. Yu, S. Sen and B. H. Leung, “Distortion Analysis of MOS Track-and-Hold Sampling Mixers Using TimeVarying Volterra Series”,IEEE Transactions on circuits and systems-II: Analog and Digital Signal Processing, vol. 46, No. 2, Feb.1999. In this paper time-varying theory of Volterra series is developed ...
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Ch 33 - A.C. Circuits

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RLC circuit



A RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit, where the sequence of the components may vary from RLC.The circuit forms a harmonic oscillator for current, and resonates in a similar way as an LC circuit. Introducing the resistor increases the decay of these oscillations, which is also known as damping. The resistor also reduces the peak resonant frequency. Some resistance is unavoidable in real circuits even if a resistor is not specifically included as a component. An ideal, pure LC circuit is an abstraction used in theoretical considerations.RLC circuits have many applications as oscillator circuits. Radio receivers and television sets use them for tuning to select a narrow frequency range from ambient radio waves. In this role the circuit is often referred to as a tuned circuit. An RLC circuit can be used as a band-pass filter, band-stop filter, low-pass filter or high-pass filter. The tuning application, for instance, is an example of band-pass filtering. The RLC filter is described as a second-order circuit, meaning that any voltage or current in the circuit can be described by a second-order differential equation in circuit analysis.The three circuit elements, R,L and C can be combined in a number of different topologies. All three elements in series or all three elements in parallel are the simplest in concept and the most straightforward to analyse. There are, however, other arrangements, some with practical importance in real circuits. One issue often encountered is the need to take into account inductor resistance. Inductors are typically constructed from coils of wire, the resistance of which is not usually desirable, but it often has a significant effect on the circuit.
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