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AC circuit analysis - Iowa State University

EE 201AC the impedance way 1AC circuit analysisThe story so far: circuits that are driven by sinusoidal sources ( vs(t) = Vm cos( t) ), the voltages and currents are always sinusoids oscillating at the same frequency as the source and having distinct amplitudes. If there are capacitors and inductors in the circuit then the sinusoidal voltages and currents may also have phase shifts with respect to the source. These sinusoids, with the various amplitude and angles, are easy to see and measure in the lab. the amplitudes and phase angles using conventional differential-equation techniques is messy and may involve a lot of trigonometric gymnastics. we ignore transients effects and focus on the steady- State part of the solution, the math is made easier by leaving out half of the problem. This is known as sinusoidal steady- State analysis . we describe the sinusoids using complex exponentials (Vm ej t) instead of sines and cosines, the math needed to solve the differential equations is easier.

a complex exponential voltages to individual resistors, capacitors, and ... ratio of the of sinusoidal voltage to the sinusoidal current is a number. Of course, we expect this for resistors because they obey Ohm’s law, ... of manipulating and processing signals. (EE 230, EE 224) EE 201 AC — the impedance way – 9

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