Name: transfer function gain and origin effects
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 19 s
Channel: JoVE

標準形式で表されるシステムの伝達関数を考えてみましょう。
伝達関数には、一定のゲイン、原点のゼロと極、単純なゼロ、単純な極、二次極、および二次ゼロがあります。
個々の因子のボード線図は、別々にプロットされ、グラフィカルに結合されます。
正の定数ゲイン項の場合、マグニチュード ゲインは一定で、位相角はゼロで周波数に依存しません。
負の定数ゲイン項の場合、マグニチュードゲインは同じままで、位相角は±180°です。
原点がゼロの伝達関数の場合、マグニチュードプロットは20dB/ディケードの正の傾きを持つ直線を表します。位相プロットは、90°の一定の位相角を示しています。
原点の極の場合、マグニチュードプロットの傾きは-20dB/ディケードで、位相シフトは-90°です。
原点に複数の極またはゼロがある場合、マグニチュードプロットと位相シフトの傾きは、原点に存在するポールまたはゼロの数で乗算されます。

周波数応答

標準形式で表された伝達関数は、要素の定数ゲイン、原点のゼロと極、単純なゼロと極、および 2 次極とゼロを統合します。伝達関数は、H(ω) と記述できます。
<img alt="Equation 1" src="/files/ftp_upload/15141/15141_Equation_1.svg" style="height: 40px;">
標準形式で表現されることが多い伝達関数 H(ω) は、伝達関数の多項式係数を正規化することによって導出されます。極 (jω) とゼロ (jω) は、システムの出力の振幅と位相が大幅に変化する重要な周波数です。
ゲイン、K:
伝達関数には定数項 K があり、K の値が正の場合、振幅は 20 log_10K、位相角は 0° です。振幅と位相はどちらも周波数に対して一定です。Kが負の場合、振幅は変化しませんが、位相は ±180° です。ゲイン K =1 の場合、振幅は位相角とともにゼロになります。ボード線図では、振幅はデシベル (dB) で 20log_10K として表され、位相は K の符号に応じて 0∘ または 180∘ のままです。
原点の極/ゼロ:
原点の極またはゼロは、線図に決定的な影響を与えます。原点のゼロ (jω)^+1 の振幅は 20 log10 ω で、位相は 90° です。振幅線図の傾きは 20dB/decade で、位相は周波数に対して一定です。
原点の極 (jω)^-1 の場合、振幅は -20dB/decade で、位相は -90° です。一般に、(jω)^N (N は整数) の場合、振幅線図の傾きは -20NdB/decade で、位相は 90N° です。
振幅 K が一定で、原点の極/ゼロの位相角は周波数によって変化しません。零点/極の場合、原点での極/零点の数が変わると位相角も変わります。

標準形式で表されるシステムの伝達関数を考えてみましょう。
伝達関数には一定のゲインがあり、原点にゼロと極があり、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Frequency Response

周波数特性

KEY TERMS AND CONCEPTS

主要用語および概念

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 is 0° when K is positive. If K is negative, the magnitude stays the same, but the phase becomes ±180°. When K = 1, the magnitude is 0 dB and the phase angle is 0°.

A zero at the origin has a strong effect on the Bode plot. For a zero at the origin, the magnitude is 20 log 10 ω, and the phase is 90°. The magnitude rises with a slope of 20 dB/decade, and the phase stays constant as frequency changes. A pole at the origin acts in the opposite way. Its magnitude slope is -20 dB/decade, and its phase is -90°.

More generally, a factor of (jω)^N changes the plot by an integer amount. For a zero at the origin, the magnitude slope becomes 20N dB/decade and the phase is 90N°. For a pole at the origin, the magnitude slope becomes -20N dB/decade, and the phase is also 90N°. In both cases, the constant gain K and the poles or zeros at the origin keep a phase angle that does not change with frequency. The phase changes when the number of poles or zeros at the origin changes.

Transfer Function Gain and Origin Effects

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transfer function and bode plots-i

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...

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Reading Frequency Response with Bode Plots

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Series Resonance and RLC Filter Behavior

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key terms and concepts

Explore how constant gain, poles, and zeros at the origin affect transfer functions and Bode plots, including dB slope and phase changes.

Transfer Function Gain and Origin Effects | JoVE K12

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electrical engineering

Transfer Function Gain and Origin Effects

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