Name: analyzing mixed-frequency linear circuits
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 13 s
Channel: JoVE

El principio de superposición se aplica en el análisis de circuitos lineales de CA con múltiples fuentes independientes.
Considere un circuito que consta de dos resistencias, un inductor y dos fuentes sinusoidales independientes con diferentes frecuencias. El teorema de superposición se puede utilizar para determinar la caída de voltaje a través de la resistencia.
De acuerdo con el teorema de superposición, la salida total de un circuito lineal con múltiples entradas es igual a la suma de las salidas individuales de cada entrada que funcionan de forma independiente.
Por lo tanto, el circuito se puede dividir en varios circuitos, cada uno con una sola entrada sinusoidal. 
Dado que la impedancia depende de la frecuencia, existen diferentes circuitos de dominio de frecuencia para cada frecuencia.
La regla de división de voltaje y la ley de Ohm se aplican para determinar el voltaje de salida de cada circuito.
Los voltajes obtenidos se expresan en el dominio del tiempo.
El voltaje de salida total es la suma de los voltajes producidos por cada fuente individualmente.
Cuando esta caída de voltaje se traza gráficamente, da como resultado una salida no sinusoidal, aunque todas las entradas sean sinusoidales.

teorema de superposición para circuitos de ca

Considere encontrar un circuito en estado estacionario donde todas sus entradas son sinusoidales, pero no todas poseen la misma frecuencia. Un circuito de este tipo no está clasificado como circuito de corriente alterna (CA) y, en consecuencia, sus corrientes y voltajes no exhibirán un comportamiento sinusoidal. Sin embargo, este circuito se puede analizar utilizando el principio de superposición. El principio de superposición estipula que la salida de un circuito lineal con varias entradas concurrentes es equivalente a las salidas acumuladas cuando cada entrada opera de forma independiente. Las entradas al circuito son los voltajes de las fuentes de voltaje independientes y las corrientes de las fuentes de corriente independientes. Cuando todas las entradas excepto una se establecen en cero, las entradas restantes se convierten en fuentes de voltaje de 0 V y fuentes de corriente de 0 A. Dado que las fuentes de voltaje de 0 V equivalen a cortocircuitos y las fuentes de corriente de 0 A corresponden a circuitos abiertos, las fuentes vinculadas a las otras entradas se reemplazan por circuitos abiertos o cortocircuitos. Lo que queda es un circuito de estado estacionario con una única entrada sinusoidal, que califica como un circuito de CA y se analiza mediante fasores e impedancias. Por lo tanto, el principio de superposición se emplea para transformar un circuito con múltiples entradas sinusoidales a frecuencias variables en varios circuitos separados, cada uno con una entrada sinusoidal singular. Luego, cada uno de estos circuitos de CA se analiza utilizando fasores e impedancias para determinar su salida sinusoidal. El agregado de estas salidas sinusoidales coincidirá con la salida del circuito inicial.

Teorema de superposición para circuitos de CA

El principio de superposición se aplica en el análisis de circuitos lineales de CA con múltiples fuentes independientes.
Considere un circuito que consta de ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

AC Circuit Analysis

Análisis de circuitos de corriente alterna (CA)

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Superposition Theorem for AC Circuits

analyzing mixed-frequency linear circuits

Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources.

When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This leaves a steady-state circuit with only one sinusoidal input.

That single-input circuit can then be treated as an AC circuit. It is analyzed with phasors, which represent sinusoidal signals, and impedances, which describe how circuit parts oppose current in AC. The same process is repeated for each source in the original circuit.

The final result is found by adding the separate sinusoidal outputs together. This sum matches the output of the full circuit with multiple sinusoidal inputs at different frequencies. In this way, superposition turns one mixed-input circuit into several simpler AC circuits.

Analyzing Mixed-Frequency Linear Circuits

analyzing-mixed-frequency-linear-circuits

sinusoidal sources

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graphical and analytic representation of sinusoids

graphical-and-analytic-representation-of-sinusoids

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phasors

Phasors for AC Circuit Analysis

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AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier. For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction. An inductor works differently because its voltage depends on the rate of change of current. The...

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Series and Parallel Impedance Rules

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Norton Current in AC Circuit Analysis

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superposition theorem for ac circuits

Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources. When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This...

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key terms and concepts

Learn how superposition breaks a linear circuit with multiple sinusoidal sources into simpler AC circuits, then combines the results into one output.

Analyzing Mixed-Frequency Linear Circuits | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Analyzing Mixed-Frequency Linear Circuits

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