6.3
Fasores
Los fasores son una poderosa herramienta matemática que se utiliza para analizar circuitos de corriente alterna (CA). Proporcionan una representación…
Los fasores son representaciones complejas de las sinusoides donde la magnitud del fasor es igual a la amplitud y el ángulo es igual a la fase medida desde el eje x positivo.
Simplifican el análisis de los circuitos de CA al eliminar la dependencia temporal de la corriente y el voltaje, transformando el circuito en su forma de CC equivalente.
Los fasores se pueden representar en formas rectangulares, polares o exponenciales mediante el uso de la identidad de Euler.
Para obtener el fasor de una sinusoide en forma sinusoidal, primero conviértelo en forma de coseno y luego exprésalo como la parte real del número complejo.
El fasor de esta sinusoide es igual a la parte independiente del tiempo del número complejo.
Por el contrario, la sinusoide de un fasor dado se obtiene multiplicando el fasor por el factor tiempo y tomando su parte real.
Los fasores se pueden representar como vectores giratorios o sinores en sentido contrario a las agujas del reloj en un plano complejo con una frecuencia angular constante, y los diagramas que los representan se conocen como diagramas de fasor.
La proyección de los senos giratorios en el eje real representa los sinusoides.
View the full transcript and gain access to JoVE Core videos
Q1: What is a phasor and how does it simplify AC circuit analysis?
A phasor is a complex number representation of a sinusoid where the magnitude equals the amplitude and the angle represents the phase from the positive x-axis. Phasors simplify AC circuit analysis by eliminating time dependence, transforming the circuit into its equivalent DC form for easier calculations and analysis.
Q2: How do you convert a sinusoid in sine form to its phasor representation?
First convert the sine form sinusoid into cosine form, then express it as the real part of a complex number. The phasor equals the time-independent part of this complex number, removing the temporal component while preserving amplitude and phase information for circuit analysis.
Q3: What are the different forms used to represent phasors?
Phasors can be represented in rectangular, polar, or exponential forms using Euler's identity, which establishes the relationship between trigonometric and exponential functions. Each form offers distinct advantages for circuit analysis and mathematical manipulation depending on the specific application and calculation requirements.
Q4: How do you recover a sinusoid from a given phasor?
Multiply the phasor by a time factor and take the real part of the resulting complex number. This operation reintroduces the time dependence, converting the frequency-domain phasor representation back into the time-domain sinusoidal waveform for practical circuit applications and measurements.
Q5: What is a phasor diagram and what do the rotating vectors represent?
A phasor diagram depicts phasors as rotating vectors, or sinors, spinning counterclockwise on a complex plane at constant angular frequency. The projection of these rotating sinors onto the real axis represents the instantaneous values of the sinusoids they correspond to at any given moment.
Q6: How do phasors enable circuit analysis using phasor relationships?
Phasors transform AC circuit analysis by converting sinusoidal voltages and currents into complex numbers, allowing circuits to be analyzed using algebraic methods similar to DC analysis. Understanding phasor relationships for circuit elements enables engineers to apply Kirchhoff's laws and other circuit theorems directly to frequency-domain representations.
Q7: Why is Euler's identity important for phasor representation?
Euler's identity establishes the fundamental relationship between trigonometric and exponential functions, enabling phasors to be expressed in rectangular, polar, or exponential forms. This mathematical tool is essential for converting between different phasor representations and performing complex AC circuit calculations efficiently and accurately.