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

Süperpozisyon ilkesi, birden fazla bağımsız kaynağa sahip AC doğrusal devrelerin analizinde uygulama bulur.
İki direnç, bir indüktör ve farklı frekanslara sahip iki bağımsız sinüzoidal kaynaktan oluşan bir devre düşünün. Süperpozisyon teoremi, direnç üzerindeki voltaj düşüşünü belirlemek için kullanılabilir.
Süperpozisyon teoremine göre, birden fazla girişe sahip doğrusal bir devrenin toplam çıktısı, bağımsız olarak çalışan her girişten gelen bireysel çıkışların toplamına eşittir.
Böylece devre, her biri tek bir sinüzoidal girişe sahip birden fazla devreye bölünebilir. 
Empedans frekansa bağlı olduğundan, her frekans için farklı frekans alanı devreleri mevcuttur.
Her devrenin çıkış voltajını belirlemek için voltaj bölme kuralı ve Ohm yasası uygulanır.
Elde edilen voltajlar daha sonra zaman alanında ifade edilir.
Toplam çıkış voltajı, her bir kaynak tarafından ayrı ayrı üretilen voltajların toplamıdır.
Bu voltaj düşüşü grafiksel olarak çizildiğinde, tüm girişler sinüzoidal olmasına rağmen sinüzoidal olmayan bir çıkışla sonuçlanır.

ac devreler için süperpozisyon teoremi

Tüm girişlerinin sinüzoidal olduğu ancak hepsinin aynı frekansa sahip olmadığı, kararlı durumdaki bir devreyle karşılaştığınızı düşünün. Böyle bir devre, alternatif akım (AC) devresi olarak sınıflandırılmaz ve dolayısıyla akımları ve gerilimleri sinüzoidal davranış sergilemez. Ancak bu devre süperpozisyon prensibi kullanılarak analiz edilebilir.

Süperpozisyon ilkesi, birden fazla eşzamanlı girişe sahip bir doğrusal devrenin çıkışının, her giriş bağımsız olarak çalıştığında kümülatif çıkışlara eşdeğer olmasını şart koşar. Devrenin girişleri bağımsız gerilim kaynaklarından gelen gerilimler ve bağımsız akım kaynaklarından gelen akımlardır.

Biri hariç tüm girişler sıfıra ayarlandığında geri kalan girişler 0-V gerilim kaynağı ve 0-A akım kaynağı olur. 0-V gerilim kaynaklarının kısa devrelere, 0-A akım kaynaklarının ise açık devrelere karşılık geldiği göz önüne alındığında, diğer girişlere bağlanan kaynakların yerini açık veya kısa devreler alır. Geriye kalan, AC devresi olarak nitelendirilen ve fazörler ve empedanslar kullanılarak analiz edilen, tek sinüzoidal girişli bir kararlı durum devresidir.

Bu nedenle, süperpozisyon ilkesi, değişen frekanslarda birden fazla sinüzoidal girişe sahip bir devreyi, her biri tekil sinüzoidal girişe sahip birkaç ayrı devreye dönüştürmek için kullanılır. Bu AC devrelerinin her biri daha sonra sinüzoidal çıkışını belirlemek için fazörler ve empedanslar kullanılarak analiz edilir. Bu sinüzoidal çıkışların toplamı, başlangıç devresinin çıkışıyla çakışacaktır.

AC Devreler için Süperpozisyon Teoremi

Süperpozisyon ilkesi, birden fazla bağımsız kaynağa sahip AC doğrusal devrelerin analizinde uygulama bulur.
Aşağıdakilerden oluşan bir devre düşünün ...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

AC Circuit Analysis

AC Devre Analizi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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

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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 Elektrik Mühendisliği, devre analizi teknikleriyle birlikte elektrik devrelerinin temel kavramlarını kapsayan, anlaşılması kolay animasyonlu videolar sunar. Operasyonel amplifikatörler ve devre dönüşümü kavramlarını kullanarak birinci dereceden ve ikinci dereceden devreleri içerir. Pratik tasarım örneklerinin ve gerçek dünya uygulamalarının bilim insanlarınca hazırlanan videolar aracılığıyla dahil edilmesi, karmaşık kavramları erişilebilir hale getirerek önemli bir eğitim değeri katmaktadır.

electrical engineering

Analyzing Mixed-Frequency Linear Circuits

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