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

Los electrodos tisulares en electrocardiogramas (E-C-G) establecen una vía conductora para las corrientes eléctricas entre los tejidos y los electrodos de medición, lo que permite la observación de la actividad cardíaca.
La dinámica de la interfaz electrodo-tejido tiene un modelo de circuito que abarca la resistencia del electrodo, la capacitancia en la interfaz electrodo-tejido y la resistencia del tejido. La diferencia de potencial representa la diferencia de voltaje entre el electrodo y el tejido.
Aquí, la impedancia de entrada es igual a la resistencia del tejido. La impedancia de salida es la adición de la resistencia del tejido a la combinación paralela de resistencia y capacitancia en la interfaz electrodo-tejido.
La relación entre el fasor de salida y el fasor de entrada, calculada utilizando los valores conocidos de resistencia y capacitancia, es la función de transferencia.
Esto se puede aproximar a través de tres rangos de frecuencia distintos.
El gráfico de magnitud de Bode en un gráfico semilogarítmico representa la ganancia logarítmica calculada en decibelios frente a la frecuencia en radianes por segundo.
Las asíntotas de baja y alta frecuencia son líneas horizontales con una ganancia constante. En el rango de frecuencia intermedio, el gráfico de magnitud asintótica es lineal con una pendiente de 20 decibelios por década.

respuesta de frecuencia

Bode Plots Construction

El diagrama de Bode es una herramienta esencial en el análisis de sistemas de control, ya que mapea la respuesta de frecuencia de un sistema a través de un diagrama de magnitud y un diagrama de fase, ambos contra un eje de frecuencia logarítmico. Para construir un diagrama de Bode, considere la función de transferencia H(ω):
<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_1.svg" style="height: 32px;">
Tiene ganancia constante, ceros y polos. Después de normalizar la función de transferencia se escribe como:

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_2.svg" style="height: 32px;">
Cada término de esta función normalizada afecta claramente al diagrama de Bode. El término 10jω tiene una ganancia constante de 10 y cero en el origen jω. Cada término polar simple (1+jω/ωi) introduce un punto de interrupción o frecuencia de esquina ωi. La pendiente positiva del cero es evidente desde el origen, mientras que las pendientes negativas de los polos comienzan en sus frecuencias de esquina, ω=2 y ω=10 respectivamente.
<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;">
 Una vez identificada la contribución individual de cada término, se puede construir el diagrama de Bode general. Se trata de superponer las pendientes y cambios de fase de cada factor. En frecuencias bajas, el gráfico de magnitud comienza en 20 dB (ya que 20log_10(10) =20) y mantiene una respuesta plana hasta la primera frecuencia de esquina. El trazado de fase comienza en 90° debido al cero en el origen y comienza su descenso antes de la primera frecuencia de esquina.
La pendiente del gráfico de magnitud cambiará en cada frecuencia de esquina, disminuyendo en 20 dB/década en ω=2 y nuevamente en ω=10. En consecuencia, el gráfico de fase se inclinará hacia abajo, acercándose a -90° a una frecuencia mucho mayor que ω=10.
Finalmente, el diagrama de Bode asintótico, que consta de estas líneas rectas, se puede ajustar para aproximarse más a la respuesta de frecuencia real. Esto implica agregar una curva suave que intersecta el gráfico asintótico en cada frecuencia de esquina, lo que generalmente resulta en un ligero exceso cerca de las frecuencias de esquina, conocido como pico.

Respuesta de frecuencia

Los electrodos tisulares en electrocardiogramas (E-C-G) establecen una vía conductora para las corrientes eléctricas entre los tejidos y los electrodos de medición, ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Frequency Response

Respuesta en frecuencia

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

network function of a circuit

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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