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Related Concept Videos

Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
Transfer Function in Control Systems01:21

Transfer Function in Control Systems

The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
Network Function of a Circuit01:25

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
Phase-lead and Phase-lag Controllers01:22

Phase-lead and Phase-lag Controllers

Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass filters, manage...
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
Transfer Function to State Space01:23

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...

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Related Experiment Video

Updated: Jul 7, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Optical transfer function design by use of a phase-only coherent transfer function.

Z Zalevsky, D Mendlovic, G Shabtay

    Applied Optics
    |February 10, 1997
    PubMed
    Summary
    This summary is machine-generated.

    Researchers developed an optimal phase-only filter for approximating desired optical transfer functions (OTFs). This high-efficiency filter has applications in beam shaping and optical signal processing.

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    Area of Science:

    • Optics and Photonics
    • Optical Engineering

    Background:

    • Designing optical transfer functions (OTFs) is crucial for various optical applications.
    • Existing methods may face limitations in efficiency or approximation accuracy.

    Purpose of the Study:

    • To derive a mathematical expression for an optimal phase-only filter.
    • To achieve a minimal mean square error approximation to a desired OTF.

    Main Methods:

    • Mathematical derivation of a phase-only filter.
    • Integration of the filter with an imaging lens.

    Main Results:

    • An optimal phase-only filter was mathematically derived.
    • The filter provides an optimal approximation to the desired OTF in the minimal mean square error sense.
    • High efficiency is achieved due to the phase-only nature of the filter.

    Conclusions:

    • The derived phase-only filter offers an efficient and accurate solution for approximating desired optical transfer functions.
    • This approach has potential applications in beam shaping and optical signal processing.