Name: circuit component scaling for filters
Uploaded: 2024-07-08T13:20:03.000Z
Duration: 1 min 26 s
Channel: JoVE

Büyüklük ve frekans ölçeklendirmesi, filtre yanıtlarını ve devre parametrelerini kullanılabilir aralıklara uyacak şekilde kalibre ederek filtre tasarımını basitleştirir.
Büyüklük ölçeklendirme, bir ağdaki tüm empedansların bir faktörle yükseltilmesini ve tutarlı frekans tepkilerinin sürdürülmesini içerir.
Ölçeklendirilmiş empedans ve frekans değerleri daha sonra ölçekleme faktörü kullanılarak ifade edilir.
Bu işlem devrenin rezonans frekansını, kalite faktörünü, bant genişliğini veya aktarım işlevlerini değiştirmez.
Frekans ölçeklendirme, empedansı değiştirmeden bırakırken bir ağın frekans yanıtını frekans ekseninde yukarı veya aşağı kaydırır. Frekansın bir ölçeklendirme faktörü ile çarpılmasıyla gerçekleştirilir.
Frekans ölçeklendirme, frekansa bağlı reaktif elemanların empedanslarını etkiler, ancak direnç etkilenmeden kalır.
Ölçekleme faktörü, rezonans frekansını ve bant genişliğini değiştirir, ancak kalite faktörü aynı kalır.
Empedans ve frekans ölçekleme için genel bir ifade, eşzamanlı büyüklük ve frekans ölçeklemesini barındırır.
Büyüklük ölçeklendirmenin uygulanmadığı durumlarda, büyüklük ölçekleme faktörü bir olarak ayarlanır. Benzer şekilde, frekans ölçeklendirme olmadan, frekans ölçekleme faktörü bir olarak ayarlanır.

frekans tepkisi  

Filtreleri, rezonans devrelerini veya genel olarak devre analizini tasarlarken ve analiz ederken, bu değerleri daha gerçekçi rakamlara ölçeklendirmeden önce 1 Ohm, 1 Henry veya 1 Farad gibi standart eleman değerleriyle çalışmak uygun olabilir. Bu yaklaşım, birçok örnek ve problemde gerçekçi eleman değerlerine yer verilmemesi nedeniyle yaygın olarak kullanılmaktadır; uygun bileşen değerleri aracılığıyla devre analizine hakim olmayı kolaylaştırır. Ölçeklendirme tekniklerinin daha sonra bu değerleri daha pratik seviyelere ayarlayabileceği anlayışıyla hesaplamaların karmaşıklığı azaltılır.

Bir devrenin ölçeklendirilmesi iki şekilde yapılabilir: büyüklük (veya empedans) ölçeklendirme ve frekans ölçeklendirme. Bu yöntemler devrenin bileşenlerini pratik aralıklarda çalışacak şekilde ayarlar. Büyüklük ölçeklendirme, devrenin farklı frekanslara nasıl tepki vereceğini etkilemeden bileşenlerin boyutunu değiştirir. Öte yandan frekans ölçeklendirme, devrenin tepkisini spektrumdaki daha yüksek veya daha düşük frekanslara kaydırır.

Büyüklük Ölçeklendirmesi:

Büyüklük ölçeklendirme, devre bileşenlerinin (dirençler, indüktörler ve kapasitörler gibi) boyutlarının belirli bir faktöre göre ayarlanmasını, ancak devrenin farklı frekanslara tepki verme şeklini değiştirmeyi içerir. Devrenin empedansları, devredeki dirençler (R), indüktörler (L) ve kapasitörler (C) cinsindendir. K_m büyüklük ölçeklendirmesi uygulandığında bu bileşenler aşağıdaki gibi dönüştürülür:

<img alt="Equation 1" src="/files/ftp_upload/15150/15150_Equation_1.svg" style="height: 12px;">

<img alt="Equation 2" src="/files/ftp_upload/15150/15150_Equation_2.svg" style="height: 36px;">

Frekans Ölçeklendirme:

Frekans ölçeklendirme, empedans seviyelerini değiştirmeden bir devrenin frekans tepkisini frekans ekseni boyunca yukarı veya aşağı kaydırır. Bu, frekansın K_f ile gösterilen bir ölçeklendirme faktörü ile çarpılmasıyla elde edilir. Endüktans ve kapasitansın yeni değerleri şu şekilde belirlenir:

<img alt="Equation 3" src="/files/ftp_upload/15150/15150_Equation_3.svg" style="height: 36px;">

<img alt="Equation 4" src="/files/ftp_upload/15150/15150_Equation_4.svg" style="height: 36px;">

Bir devre aynı anda hem büyüklük hem de frekans parametrelerine göre ölçeklendirilirse, o zaman:

<img alt="Equation 5" src="/files/ftp_upload/15150/15150_Equation_5.svg" style="height: 36px;">

<img alt="Equation 6" src="/files/ftp_upload/15150/15150_Equation_6.svg" style="height: 36px;">

Büyüklük ve frekans ölçeklendirme faktörleri eşitse, ne büyüklük ne de frekans ölçeklendirmesi gerçekleşmez.

Frekans Tepkisi  

Büyüklük ve frekans ölçeklendirmesi, filtre yanıtlarını ve devre parametrelerini kullanılabilir aralıklara uyacak şekilde kalibre ederek filtre tasarımını basitleştirir.
Büyüklük...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

Frequency Response

Frekans Tepkisi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

Scaling

circuit component scaling for filters

Circuit component scaling helps turn simple circuit values into practical ones for filter design and circuit analysis. Engineers often start with standard values like 1 ohm, 1 henry, or 1 farad because they make examples and problems easier to work through. Later, those values can be scaled to more realistic levels.

This method is useful in filters, resonant circuits, and many other circuit analysis problems. It reduces calculation complexity while keeping the circuit behavior easy to study. The idea is to learn the analysis first and then adjust the component values to fit real-world use.

There are two main ways to scale a circuit: magnitude scaling, also called impedance scaling, and frequency scaling. Magnitude scaling changes the size of the components without changing how the circuit responds to different frequencies. Frequency scaling shifts the circuit response higher or lower on the frequency axis without changing the impedance levels.

Magnitude scaling uses a factor called K m to change resistors, inductors, and capacitors. Frequency scaling uses a factor called K f to move the frequency response and to determine new inductance and capacitance values. When both magnitude and frequency scaling are applied together, the circuit can be adjusted in both size and response range. If the magnitude and frequency scaling factors are equal, neither type of scaling occurs.

Circuit Component Scaling for Filters

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transfer function and bode plots-ii

Bode Plot Slope and Phase Changes

Bode plots show how a transfer function changes with frequency. The standard form includes constant gain, poles and zeros at the origin, simple poles and zeros, and quadratic poles and zeros. Each part shapes the system response in a different way. A simple zero sets the magnitude trend first. The Bode magnitude plot stays flat at low frequencies, near 0 dB, and then rises at 20 dB per decade after the corner or break frequency, ω1. That corner frequency is where the straight-line...

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Reading Frequency Response with Bode Plots

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Series Resonance in RLC Circuits

Series resonance in an RLC circuit happens when the inductive reactance and capacitive reactance are equal. An RLC circuit contains a resistor, an inductor, and a capacitor. The impedance of the circuit is the ratio of the supply voltage to the circuit current. At resonance, the imaginary part of the impedance becomes zero. The frequency at which this occurs is called the resonant frequency. It depends on the inductance (L) and capacitance (C) of the circuit. Mathematically, the resonant...

characteristics of series resonant circuit

characteristics-of-series-resonant-circuit

Series Resonance and RLC Filter Behavior

Series resonance in an RLC circuit happens when the inductor, capacitor, and resistor are connected in series. At the resonant frequency, the inductive reactance and capacitive reactance are equal in size but opposite in sign, so they cancel each other. As a result, the circuit impedance becomes very small and is mainly set by the resistance. The resonant frequency of a series RLC circuit can be calculated from its inductance and capacitance. At this frequency, the current reaches its maximum...

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Parallel RLC Tuning at Resonance

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scaling

Circuit component scaling helps turn simple circuit values into practical ones for filter design and circuit analysis. Engineers often start with standard values like 1 ohm, 1 henry, or 1 farad because they make examples and problems easier to work through. Later, those values can be scaled to more realistic levels. This method is useful in filters, resonant circuits, and many other circuit analysis problems. It reduces calculation complexity while keeping the circuit behavior easy to study.

design example

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key terms and concepts

Learn how magnitude scaling and frequency scaling adjust resistors, inductors, capacitors, and circuit response for easier filter design and analysis.

Circuit Component Scaling for Filters | 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

Circuit Component Scaling for Filters

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