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

ضع في اعتبارك وظيفة النقل في شكلها القياسي ، مع الأعمدة والأصفار
بالنسبة لدالة النقل ذات الصفر البسيط ، فإن كسب الحجم عند قيم التردد الصغيرة هو خط مستقيم بميل صفري ، ويقترب الطور من الصفر.
عند تردد الزاوية ، ينحرف الحجم المقارب عن خط المنحدر الصفري ، وتقترب المرحلة من 45 درجة.
عند الترددات الأعلى ، يشكل مخطط الحجم خط +20 ديسيبل / عقد ، والمرحلة 90 درجة.
القطب البسيط هو مقلوب الصفر البسيط. هذا يعني أن مخططات Bode القائمة على القطب تعكس مخطط الصفر البسيط ، المنعكس حول المحور الأفقي.
ضع في اعتبارك دالة نقل القطب التربيعي.
عند الترددات المنخفضة ، تقترب زاوية الكسب والطور من الصفر.
عند تردد الزاوية ، يعتمد انحراف الحجم المقارب على عامل التخميد ، وزاوية الطور تقارب -90 درجة.
وعند الترددات الأعلى، يشكل مخطط الحجم خطا مستقيما بميل قدره -40 ديسيبل/عقد وطور -180 درجة.
بالنسبة لأكثر من قطب تربيعي واحد ، يتم ضرب ميل الخط وتحول الطور في عدد الأقطاب.

الاستجابة الترددية

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في النموذج القياسي، تظهر دالة النقل في الكسب الثابت، والأقطاب/الأصفار عند الأصل، والأقطاب البسيطة/الأصفار، والأقطاب التربيعية/الأصفار؛ يساهم كل منها بشكل فريد في الاستجابة الشاملة للنظام. يمثل المصطلح حجم الصفر البسيط:


<img alt="Equation 1" src="/files/ftp_upload/15142/15142_Equation_1.svg" style="height: 36px;">

يظل مخطط حجم Bode ثابتًا عند الترددات المنخفضة (تقترب من 0 ديسيبل) ويبدأ في الصعود عند 20 ديسيبل / عقد بعد تردد محدد يُعرف باسم تردد الزاوية أو الكسر، ω_1. هذا هو التردد الذي يتغير فيه ميل مخطط الحجم وتبدأ الاستجابة الفعلية في الانحراف عن تقريب الخط المستقيم. يتم قياس هذا الانحراف بمقدار 3 ديسيبل عند ω = ω_1.

زاوية الطور ϕ، معبراً عنها بالصيغة التالية:


<img alt="Equation 2" src="/files/ftp_upload/15142/15142_Equation_2.svg" style="height: 60px;">

تبدأ زاوية الطور عند 0 درجة وتقترب من 90 درجة بشكل مقارب مع زيادة التردد. بالنسبة للترددات الأقل بكثير من تردد الزاوية (ω≪ω_1)، يكون المصطلح jω/ω_1 صغيرًا جدًا، وبالتالي فإن الحجم لا يكاد يذكر، والطور هو صفر بشكل أساسي. عندما يقترب التردد من ω_1، مما يؤدي إلى نقطة بمقدار -3 ديسيبل وزاوية طور قدرها 45 درجة. بالنسبة للترددات الأعلى بكثير من ω_1 (ω≫ω_1)، يتغير ميل الحجم إلى 20 ديسيبل/عقد، ويستقر الطور عند 90 درجة.


<img alt="Figure 1" src="/files/ftp_upload/15142/15142_Figure_1.svg" style="height: 160px;">

القطب التربيعي/صفر:

مقدار وزاوية الطور للقطب التربيعي هي:


<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;">

يتكون مخطط السعة للقطب التربيعي من جزأين: استجابة مسطحة تحت التردد الطبيعي ωn، ومنحدر -40 ديسيبل/عقد أعلى من ωn، مع اختلاف ذروة المخطط الفعلي مع عامل التخميد ζ_2. يتناقص مخطط الطور للقطب التربيعي خطيًا بميل قدره -90 درجة لكل عقد، بدءًا من عُشر التردد الطبيعي وينتهي بعشرة أضعاف ذلك، متأثرًا بعامل التخميد ζ_2.


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ضع في اعتبارك وظيفة النقل في شكلها القياسي ، مع الأعمدة والأصفار
بالنسبة لوظيفة النقل ذات الصفر البسيط ، فإن كسب الحجم عند ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Frequency Response

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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.

Bode Plot Slope and Phase Changes

network function of a circuit

How Transfer Functions Shape Circuit Response

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Circuit gain and phase shift describe how a linear circuit changes a sinusoidal input voltage or current. These properties matter in circuits with reactive elements, because the response depends on the input frequency. As the frequency changes, the gain and phase shift also change. Gain compares the size of the output sinusoid to the size of the input sinusoid. If Vin is the input and Vout is the output, the gain K is the ratio of the output amplitude to the input amplitude. A gain greater...

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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 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

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...

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Series Resonance in RLC Circuits

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characteristics-of-series-resonant-circuit

Series Resonance and RLC Filter Behavior

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Parallel RLC Tuning at Resonance

A parallel RLC circuit uses a resistor, inductor, and capacitor connected to the same nodes. Because they share the same voltage, the circuit is analyzed with admittance, which describes how easily current can flow. In a parallel RLC circuit, admittance helps show how the circuit responds as the frequency changes. Resonance happens when the net reactance is zero. At that point, the capacitive and inductive effects cancel each other out. The resonant frequency is found from this condition. At...

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Op Amp Gain and Bode Plot Basics

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key terms and concepts

Learn how simple zeros and quadratic poles shape Bode plot magnitude and phase, including corner frequency, 3 dB shift, and damping effects.

Bode Plot Slope and Phase Changes | 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

Bode Plot Slope and Phase Changes

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