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

Tissue electrodes in electrocardiograms (E-C-G) establish a conductive pathway for electrical currents between the tissues and the measuring electrodes, enabling the observation of heart activity.
The electrode-tissue interface dynamics has a circuit model encompassing electrode resistance, the capacitance at the electrode-tissue interface, and tissue resistance. The potential difference represents the voltage difference between the electrode and the tissue.
Here, the input impedance equals the tissue resistance. The output impedance is the addition of the tissue resistance to the parallel combination of resistance and capacitance at the electrode-tissue interface.
The ratio of the output phasor to the input phasor, calculated using the known resistance and capacitance values is the transfer function.
This can be approximated across three distinct frequency ranges.
The Bode magnitude plot on a semilog graph depicts the calculated logarithmic gain in decibels against frequency in radians per second.
The low and high-frequency asymptotes are horizontal lines with a constant gain. In the intermediate frequency range, the asymptotic magnitude plot is linear with a 20-decibel-per-decade slope.

frequentierespons

Bode Plots Construction

De Bode-grafiek is een essentieel hulpmiddel bij de analyse van besturingssystemen, waarbij de frequentierespons van een systeem in kaart wordt gebracht via een magnitudegrafiek en een fasegrafiek, beide tegen een logaritmische frequentie-as. Om een Bode-diagram te construeren, moet je rekening houden met de overdrachtsfunctie H(ω):

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_1.svg" style="height: 32px;">

Het heeft constante versterking, nullen en polen. Na normalisatie wordt de overdrachtsfunctie geschreven als:

<img alt="Equation 2" src="/files/ftp_upload/15102/15102_Equation_2.svg" style="height: 32px;">

Elke term in deze genormaliseerde functie heeft een duidelijke invloed op de Bode-plot. De term 10jω heeft een constante versterking van 10 en nul bij oorsprong jω. Elke eenvoudige poolterm (1+jω/ωi) introduceert een breekpunt of hoekfrequentie ωi. De positieve helling van de nul is duidelijk zichtbaar vanaf de oorsprong, terwijl de negatieve hellingen van de polen beginnen bij hun hoekfrequenties, respectievelijk ω=2 en ω=10.

<img alt="Equation 3" src="/files/ftp_upload/15102/15102_Equation_3.svg" style="height: 36px;">

<img alt="Equation 4" src="/files/ftp_upload/15102/15102_Equation_4.svg" style="height: 28px;">

Zodra de individuele bijdrage van elke term is geïdentificeerd, kan de algehele Bode-plot worden geconstrueerd. Dit omvat het over elkaar heen leggen van de hellingen en faseveranderingen van elke factor. Bij lage frequenties begint de magnitudegrafiek bij 20 dB (aangezien 20log_10(10) =20) en handhaaft een vlakke respons tot aan de eerste hoekfrequentie. De fasegrafiek begint bij 90° vanwege de nul bij de oorsprong en begint te dalen vóór de eerste hoekfrequentie.

De helling van de magnitudegrafiek verandert bij elke hoekfrequentie en neemt af met 20 dB/decade bij ω=2 en opnieuw bij ω=10. Dienovereenkomstig zal het fasediagram naar beneden buigen en -90° benaderen met een frequentie die veel hoger is dan ω=10.

Ten slotte kan de asymptotische Bode-grafiek, die uit deze rechte lijnen bestaat, worden aangepast om de werkelijke frequentierespons beter te benaderen. Dit omvat het toevoegen van een vloeiende curve die de asymptotische grafiek bij elke hoekfrequentie doorsnijdt, wat doorgaans resulteert in een lichte overschrijding nabij de hoekfrequenties, ook wel peaking genoemd.

Tissue electrodes in electrocardiograms (E-C-G) establish a conductive pathway for electrical currents between the tissues and the measuring electrodes, ...

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

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bode plots construction

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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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