Name: reading frequency response with bode plots
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 24 s
Channel: JoVE

Elektrokardiyogramlardaki doku elektrotları (E-C-G), dokular ve ölçüm elektrotları arasında elektrik akımları için iletken bir yol oluşturarak kalp aktivitesinin gözlemlenmesini sağlar.
Elektrot-doku arayüz dinamiği, elektrot direncini, elektrot-doku arayüzündeki kapasitansı ve doku direncini kapsayan bir devre modeline sahiptir. Potansiyel fark, elektrot ve doku arasındaki voltaj farkını temsil eder.
Burada giriş empedansı doku direncine eşittir. Çıkış empedansı, elektrot-doku arayüzündeki paralel direnç ve kapasitans kombinasyonuna doku direncinin eklenmesidir.
Bilinen direnç ve kapasitans değerleri kullanılarak hesaplanan çıkış fazörünün giriş fazörüne oranı transfer fonksiyonudur.
Bu, üç farklı frekans aralığında yaklaşık olarak hesaplanabilir.
Semilog bir grafik üzerindeki Bode büyüklüğü grafiği, saniyede radyan cinsinden frekansa karşı desibel cinsinden hesaplanan logaritmik kazancı gösterir.
Düşük ve yüksek frekanslı asimptotlar, sabit bir kazancı olan yatay çizgilerdir. Ara frekans aralığında, asimptotik büyüklük grafiği, on yılda 20 desibel eğimle doğrusaldır.

frekans tepkisi

Bode Plots Construction

Bode grafiği, kontrol sistemi analizinde önemli bir araçtır; bir sistemin frekans tepkisini, her ikisi de logaritmik bir frekans eksenine karşı bir büyüklük grafiği ve bir faz grafiği aracılığıyla ilişkilendirir. Bir Bode grafiği oluşturmak için H(ω) transfer fonksiyonunu dikkate alalım:

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_1.svg" style="height: 32px;">

Sabit bir kazanç, sıfırlar ve kutuplara sahiptir. Normalizasyon işleminden sonra transfer fonksiyonu şu şekilde yazılır:

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_2.svg" style="height: 32px;">

Bu normalize edilmiş fonksiyondaki her bir terim Bode grafiğini farklı şekilde etkiler. 10jω terimi 10'luk sabit bir kazanca sahiptir ve jω orijininde sıfırdır. Her basit kutup terimi (1+jω/ω_i) bir kesme noktası veya köşe frekansı ω_i ortaya çıkarır. Sıfırın pozitif eğimi orijinden itibaren belirginleşirken, kutupların negatif eğimleri sırasıyla ω=2 ve ω=10 olan köşe frekanslarında başlar.

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_3.svg" style="height: 36px;">

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_4.svg" style="height: 28px;">

Her bir terimin yaptığı katkı belirlendikten sonra genel Bode grafiği oluşturulabilir. Bu, her bir faktörün eğimlerinin ve faz değişikliklerinin üst üste eklenmesini içerir. Düşük frekanslarda, büyüklük grafiği 20 dB'de başlar (20log_10(10) =20 olduğundan) ve ilk köşe frekansına kadar düz bir yanıt sağlar. Faz grafiği orijindeki sıfır nedeniyle 90°'de başlar ve ilk köşe frekansından önce düşüşe geçer.

Büyüklük grafiğinin eğimi her köşe frekansında değişecek, ω=2'de ve ω=10'da tekrar 20 dB/ons azalacaktır. Buna bağlı olarak faz grafiği, ω=10'dan çok daha yüksek bir frekansta -90°'ye yaklaşarak aşağı doğru bükülecektir.

Son olarak, bu düz çizgilerden oluşan asimptotik Bode grafiği, gerçek frekans tepkisine daha yakın olacak şekilde ayarlanabilir. Bu, her köşe frekansında asimptotik grafiği kesen düzgün bir eğrinin eklenmesini içerir; bu, tipik olarak köşe frekanslarının yakınında tepe noktası olarak bilinen hafif bir aşmaya neden olur.

Frekans Tepkisi

Elektrokardiyogramlardaki doku elektrotları (ECG), dokular ve ölçüm elektrotları arasında elektrik akımları için iletken bir yol oluşturur, ...

Education

JoVE Core

Electrical Engineering

Unit 1

Frequency Response

KEY TERMS AND CONCEPTS

reading frequency response with bode plots

Bode plots show the frequency response of a system with a magnitude plot and a phase plot. Both plots use a logarithmic frequency axis. In control system analysis, this makes it easier to see how a transfer function changes with frequency.

To build a Bode plot, start with the transfer function H(ω). After normalization, the function includes constant gain, zeros, and poles. Each term affects the plot in a different way.

A constant gain of 10 gives a starting magnitude of 20 dB, since 20 log10(10) = 20. The term 10jω also creates a zero at the origin, so the magnitude has a positive slope from the start. Each simple pole term, such as 1 + jω/ωi, adds a breakpoint or corner frequency ωi.

The zero at the origin gives the phase plot an initial value of 90°. The phase then begins to fall before the first corner frequency. The poles at ω = 2 and ω = 10 add negative slope changes to the magnitude plot, each reducing the slope by 20 dB per decade at its corner frequency.

The full Bode plot comes from adding the effects of each factor together. At low frequencies, the magnitude stays flat until the first corner frequency. The phase curve bends downward and approaches -90° at a frequency much higher than ω = 10.

The first result is an asymptotic Bode plot made of straight-line segments. A smoother curve can then be added to match the actual frequency response more closely. This adjustment often crosses the asymptotic lines near each corner frequency and can show a small peak, called peaking.

Reading Frequency Response with Bode Plots

reading-frequency-response-with-bode-plots

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How Transfer Functions Shape Circuit Response

Transfer functions show how a circuit responds as signal frequency changes. They describe the link between input and output in frequency response analysis. This makes them useful for studying how circuits behave in electronics and engineering. A transfer function is a mathematical tool that relates phasor output to phasor input. It can be written as voltage gain, current gain, transfer impedance, or transfer admittance. The poles and zeros are the most important parts of the function. Zeros...

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Reading Frequency Response on Bode Plots

Bode plots show how a circuit or system responds across frequency. They use a logarithmic frequency scale on the x-axis and gain in decibels on the y-axis. This format makes it easier to display a wide range of frequencies and to see how circuit parts affect behavior over that range. A network function gives the ratio of output to input for a system. Its complex form provides both magnitude and phase angle. The logarithmic gain on a Bode plot comes from the magnitude, calculated by multiplying...

transfer function and bode plots-i

Transfer Function Gain and Origin Effects

Transfer function gain and poles or zeros at the origin shape a system's Bode plot. The transfer function is often written in standard form after the polynomial coefficients are normalized. In that form, the constant gain, zeros, poles, and quadratic terms all appear clearly. The poles and zeros mark critical frequencies where the output magnitude and phase change noticeably. The constant gain K creates a fixed magnitude and phase term. Its magnitude is 20 log 10 K in decibels, and its phase...

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...

bode plots construction

Bode plots show the frequency response of a system with a magnitude plot and a phase plot. Both plots use a logarithmic frequency axis. In control system analysis, this makes it easier to see how a transfer function changes with frequency. To build a Bode plot, start with the transfer function H(ω). After normalization, the function includes constant gain, zeros, and poles. Each term affects the plot in a different way. A constant gain of 10 gives a starting magnitude of 20 dB, since 20...

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Series Resonance and RLC Filter Behavior

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Op Amp Gain and Bode Plot Basics

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key terms and concepts

Learn how Bode plots track magnitude and phase on a log frequency axis, including gain, zeros, poles, corner frequencies, and peaking.

Reading Frequency Response with Bode Plots | 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

Reading Frequency Response with Bode Plots

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