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

Zasada superpozycji znajduje zastosowanie w analizie obwodów liniowych prądu przemiennego z wieloma niezależnymi źródłami.
Rozważmy obwód składający się z dwóch rezystorów, cewki indukcyjnej i dwóch niezależnych źródeł sinusoidalnych o różnych częstotliwościach. Twierdzenie o superpozycji można wykorzystać do wyznaczenia spadku napięcia na rezystorze.
Zgodnie z twierdzeniem o superpozycji, całkowita moc wyjściowa obwodu liniowego z wieloma wejściami jest równa sumie poszczególnych wyjść z każdego wejścia działającego niezależnie.
Tak więc obwód można podzielić na wiele obwodów, z których każdy ma jedno wejście sinusoidalne. 
Ponieważ impedancja jest zależna od częstotliwości, dla każdej częstotliwości istnieją różne obwody w dziedzinie częstotliwości.
Reguła podziału napięcia i prawo Ohma są stosowane do określenia napięcia wyjściowego każdego obwodu.
Uzyskane napięcia są następnie wyrażane w dziedzinie czasu.
Całkowite napięcie wyjściowe to suma napięć wytwarzanych przez każde źródło z osobna.
Gdy ten spadek napięcia jest wykreślany graficznie, daje to wynik niesinusoidalny, mimo że wszystkie wejścia są sinusoidalne.

twierdzenie o superpozycji obwodów prądu przemiennego

Rozważmy obwód w stanie ustalonym, w którym wszystkie jego wejścia są sinusoidalne, ale nie wszystkie mają tę samą częstotliwość. Taki obwód nie jest klasyfikowany jako obwód prądu przemiennego (AC), w związku z czym jego prądy i napięcia nie będą wykazywać zachowania sinusoidalnego. Jednak obwód ten można analizować za pomocą zasady superpozycji.

Zasada superpozycji stanowi, że sygnał wyjściowy obwodu liniowego z kilkoma współbieżnymi wejściami jest równoważny skumulowanym wynikom, gdy każde wejście działa niezależnie. Wejściami do obwodu są napięcia z niezależnych źródeł napięcia i prądy z niezależnych źródeł prądu.

Gdy wszystkie wejścia oprócz jednego zostaną ustawione na zero, pozostałe wejścia staną się źródłami napięcia 0 V i źródłami prądu 0 A. Biorąc pod uwagę, że źródła napięcia 0 V odpowiadają zwarciom, a źródła prądu 0 A odpowiadają obwodom otwartym, źródła połączone z innymi wejściami są zastępowane przerwami lub zwarciami. Pozostaje obwód stanu ustalonego z pojedynczym wejściem sinusoidalnym, który kwalifikuje się jako obwód prądu przemiennego i jest analizowany za pomocą fazorów i impedancji.

Dlatego też zasada superpozycji jest stosowana w celu przekształcenia obwodu z wieloma sinusoidalnymi wejściami o różnych częstotliwościach w kilka oddzielnych obwodów, każdy z pojedynczym wejściem sinusoidalnym. Każdy z tych obwodów prądu przemiennego jest następnie analizowany przy użyciu wskazów i impedancji w celu określenia jego sinusoidalnej mocy wyjściowej. Suma tych sinusoidalnych wyjść będzie pokrywać się z mocą wyjściową obwodu początkowego.

Twierdzenie o superpozycji obwodów prądu przemiennego

Zasada superpozycji znajduje zastosowanie w analizie obwodów liniowych prądu przemiennego z wieloma niezależnymi źródłami.
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Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

AC Circuit Analysis

Analiza obwodów prądu przemiennego

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

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phasors

Phasors for AC Circuit Analysis

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AC Circuit Rules with Phasor Diagrams

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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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