Name: bode plot slope and phase changes
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 23 s
Channel: JoVE

Transfer fonksiyonunu standart formunda, kutuplar ve sıfırlar ile düşünün
Basit sıfırlı bir transfer fonksiyonu için, küçük frekans değerlerinde büyüklük kazancı sıfır eğimli düz bir çizgidir ve faz sıfıra yaklaşır.
Köşe frekansında, asimptotik büyüklük sıfır eğim çizgisinden sapar ve faz 45 dereceye yaklaşır.
Daha yüksek frekanslarda, büyüklük grafiği +20 dB/on yıllık bir çizgi oluşturur ve faz 90 derecedir.
Basit bir kutup, basit bir sıfırın tersidir. Bu, kutup tabanlı Bode grafiklerinin, yatay eksen etrafında yansıtılan basit sıfır grafiğini yansıttığı anlamına gelir.
İkinci dereceden bir kutup transfer fonksiyonu düşünün.
Daha düşük frekanslarda, kazanç ve faz açısı sıfıra yaklaşır.
Köşe frekansında, asimptotik büyüklük sapması sönümleme faktörüne bağlıdır ve faz açısı yaklaşık -90 derecedir.
Daha yüksek frekanslarda, büyüklük grafiği -40 dB/on yıllık bir eğim ve -180 derecelik bir faz ile düz bir çizgi oluşturur.
Birden fazla ikinci dereceden kutup için, doğrunun eğimi ve faz kayması kutup sayısı ile çarpılır.

frekans tepkisi

Standart formda, transfer fonksiyonu sabit kazanç, başlangıç ​​noktasındaki kutuplar/sıfırlar, basit kutuplar/sıfırlar ve ikinci dereceden kutuplar/sıfırlarla gösterilir; her biri sistemin genel tepkisine benzersiz bir şekilde katkıda bulunur. Terim basit sıfırın büyüklüğünü temsil eder:

<img alt="Equation 1" src="/files/ftp_upload/15142/15142_Equation_1.svg" style="height: 36px;">

Bode büyüklüğü grafiği düşük frekanslarda (0 dB'ye yaklaşan) düz kalır ve köşe veya kırılma frekansı (ω_1) olarak bilinen belirli bir frekanstan sonra 20 dB/dekad yılda yükselmeye başlar. Bu, büyüklük grafiğinin eğiminin değiştiği ve gerçek tepkinin düz çizgi yaklaşımından sapmaya başladığı frekanstır. Bu sapma ω=ω_1'de 3 dB olarak ölçülür.

Faz açısı ϕ şu şekilde ifade edilir:

<img alt="Equation 2" src="/files/ftp_upload/15142/15142_Equation_2.svg" style="height: 60px;">

Faz açısı 0°'den başlar ve frekans arttıkça asimptotik olarak 90°'ye yaklaşır. Köşe frekansından (ω≪ω_1) çok daha düşük frekanslar için jω/ω_1 terimi çok küçüktür, dolayısıyla büyüklük ihmal edilebilir ve faz esasen sıfırdır. Frekans ω1'e yaklaştıkça, büyüklük olarak -3 dB noktasına ve 45°'lik bir faz açısına yol açar. ω_1'den (ω≫ω_1) çok daha yüksek frekanslar için, büyüklüğün eğimi 20 dB/dekad olarak değişir ve faz 90°'ye ulaşır.

<img alt="Figure 1" src="/files/ftp_upload/15142/15142_Figure_1.svg" style="height: 160px;">

İkinci dereceden kutup/sıfır:

İkinci dereceden bir kutbun büyüklüğü ve faz açısı:

<img alt="Equation 3" src="/files/ftp_upload/15142/15142_Equation_3.svg" style="height: 42px;">

<img alt="Equation 4" src="/files/ftp_upload/15142/15142_Equation_4.svg" style="height: 60px;">

İkinci dereceden bir kutup için genlik grafiği iki bölümden oluşur: doğal frekans ω_n'nin altında düz bir yanıt ve ω_n'nin üzerinde -40 dB/on yıllık bir eğim, gerçek grafiğin tepe noktası sönümleme faktörü ζ_2 ile değişir. İkinci dereceden bir kutup için faz grafiği, sönümleme faktörü ζ_2'den etkilenerek, doğal frekansın onda birinden başlayıp on katında biten, on yılda -90°'lik bir eğimle doğrusal olarak azalır.

Frekans Tepkisi

Transfer fonksiyonunu standart formunda, kutuplar ve sıfırlar ile düşünün
Basit sıfırlı bir transfer fonksiyonu için, küçük büyüklük kazancı ...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

Frequency Response

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 approximation starts to differ from the actual curve, and the error is 3 dB at ω = ω1.

The phase angle for a simple zero also changes with frequency. It starts at 0° and rises toward 90° as frequency increases. When ω is much smaller than ω1, the term jω/ω1 is very small, so the magnitude is negligible and the phase is close to zero. At ω = ω1, the magnitude is at the -3 dB point and the phase is 45°. When ω is much larger than ω1, the magnitude slope is 20 dB per decade and the phase settles near 90°.

Quadratic poles have a different shape on Bode plots. Their magnitude is flat below the natural frequency, ωn, and drops at -40 dB per decade above ωn. The actual peak depends on the damping factor, ζ2. Their phase plot decreases linearly at -90° per decade from one-tenth of ωn to ten times ωn, and that shape is also affected by ζ2.

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electrical engineering

Bode Plot Slope and Phase Changes

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