Name: inductive circuit frequency response
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 20 s
Channel: JoVE

Consider an inductive circuit in the time domain. The equivalent frequency domain circuit is obtained by replacing the resistance and inductance with their impedances.
The circuit is connected to an input with variable frequency, and the output is taken across the inductance.
 The output-to-input voltage division determines the transfer function.
 The expression of the transfer function gives the magnitude and phase derived from it.
The ratio of inductance to resistance is equal to the time constant of the inductive circuit.
The magnitude and phase can be written in terms of the time constant.
As the frequency approaches zero, the transfer function approaches zero, and the phase shift approximates pi over two.
When the frequency equals the inverse of the time constant, the amplitude reaches about 0.707 times its maximum value, and the phase shift is pi over four.
Similarly, at higher frequencies, the transfer function approaches unity, and the phase shift tends to zero.
These points, among a few additional ones, depict the frequency response through amplitude or magnitude and phase response graphs.

frequency response of a circuit

Inductive circuits present intriguing challenges in electrical engineering, particularly during the transition from the time domain to the frequency domain. This transformation involves converting inductors into impedances and utilizing phasor representation.
The transfer function is pivotal in characterizing how these circuits react to various frequencies, facilitating a profound understanding of their behavior. An essential parameter is the time constant, signifying the inductance-to-resistance ratio in the circuit.
The magnitude of the transfer function is derived by integrating the inverse of the time constant into the transfer function equation. Furthermore, this approach allows for the calculation of phase shifts, illuminating differences in phase angles between output and input sinusoids.
<img alt="Low-pass filter formula \( H = \frac{1}{\sqrt{1 + (\omega / \omega_0)^2}} \), electrical diagram." src="/files/ftp_upload/15138/15138_Equation_1.svg" style="text-align: center; height: 32px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
<img alt="Phase angle equation &#966;=-tan&#8315;&#185;(&#969;/&#969;&#8320;) in oscillation analysis diagram." src="/files/ftp_upload/15138/15138_Equation_2.svg" style="text-align: center; height: 32px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
Graphing amplitude and phase responses visually represent the circuit's frequency characteristics, effectively conveying fundamental aspects of its performance. As the frequency spectrum is explored, distinctive trends emerge. The transfer function approaches zero at lower frequencies, accompanied by an approximate &#960;/2 phase shift. Conversely, the transfer function converges towards unity at higher frequencies while the phase shift approaches zero.
Of paramount importance is the identification of the half-power frequency, signifying the inverse of the time constant. At this specific frequency, an accurate assessment of the transfer function's magnitude and phase is attainable, offering a comprehensive understanding of the circuit's response characteristics.

Frequency Response of a Circuit

Consider an inductive circuit in the time domain. The equivalent frequency domain circuit is obtained by replacing the resistance and inductance with ...

Education

JoVE Core

Electrical Engineering

Unit 1

Frequency Response

KEY TERMS AND CONCEPTS

inductive circuit frequency response

Inductive circuit frequency response shows how a circuit with an inductor reacts to different frequencies. The analysis starts in the time domain and then moves into the frequency domain. In that step, the inductor is replaced by an impedance, and the circuit is written with phasors, which are sinusoidal signals shown with magnitude and phase.

The transfer function describes how the output changes compared with the input at each frequency. A key parameter is the time constant, which is the ratio of inductance to resistance in the circuit. The magnitude of the transfer function is found by using the inverse of the time constant in the transfer function equation.

This approach also gives the phase shift between the output and input sinusoids. The phase angle shows how far one signal leads or lags the other. Graphs of amplitude response and phase response help show the circuit’s frequency behavior in a clear way.

The response changes across the frequency spectrum. At low frequencies, the transfer function approaches zero, and the phase shift is about π/2. At high frequencies, the transfer function approaches unity, and the phase shift moves toward zero.

The half-power frequency is an important point in this behavior. It is the inverse of the time constant. At this frequency, the magnitude and phase of the transfer function can be determined accurately, giving a complete view of the circuit’s response.

Inductive Circuit Frequency Response

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...

Inductive circuit frequency response shows how a circuit with an inductor reacts to different frequencies. The analysis starts in the time domain and then moves into the frequency domain. In that step, the inductor is replaced by an impedance, and the circuit is written with phasors, which are sinusoidal signals shown with magnitude and phase. The transfer function describes how the output changes compared with the input at each frequency. A key parameter is the time constant, which is the...

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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...

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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...

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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

Series resonance in an RLC circuit happens when the inductive reactance and capacitive reactance are equal. An RLC circuit contains a resistor, an inductor, and a capacitor. The impedance of the circuit is the ratio of the supply voltage to the circuit current. At resonance, the imaginary part of the impedance becomes zero. The frequency at which this occurs is called the resonant frequency. It depends on the inductance (L) and capacitance (C) of the circuit. Mathematically, the resonant...

characteristics of series resonant circuit

characteristics-of-series-resonant-circuit

Series Resonance and RLC Filter Behavior

Series resonance in an RLC circuit happens when the inductor, capacitor, and resistor are connected in series. At the resonant frequency, the inductive reactance and capacitive reactance are equal in size but opposite in sign, so they cancel each other. As a result, the circuit impedance becomes very small and is mainly set by the resistance. The resonant frequency of a series RLC circuit can be calculated from its inductance and capacitance. At this frequency, the current reaches its maximum...

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Parallel RLC Tuning at Resonance

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key terms and concepts

Explore how inductive circuits change with frequency, using impedance, phasors, transfer functions, phase shift, and the half-power frequency.

Inductive Circuit Frequency Response | 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

Inductive Circuit Frequency Response

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