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Related Concept Videos

Cascaded Op Amps01:16

Cascaded Op Amps

Operational amplifiers (op-amps) are versatile electronic components that can be interconnected in a cascade - one after another in a linear sequence. This cascading is possible due to their infinite input resistance and zero output resistance, allowing them to maintain their input-output relationships even when connected in series.
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...
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,...
Gain01:15

Gain

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
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...
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...
Small-Signal Analysis of MOSFET Amplifiers01:23

Small-Signal Analysis of MOSFET Amplifiers

In small-signal analysis, a MOSFET transistor amplifier acts as a linear amplifier when operating in its saturation region. The gate-to-source voltage (VGS) of the MOSFET is the sum of the DC biasing voltage and the small time-varying input signal. This combination sets up the operating point and modulates the drain current (ID) that flows from the drain to the source. When a small AC signal is superimposed on the DC bias voltage at the gate, the instantaneous drain current comprises three...

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Updated: Jun 20, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Published on: May 30, 2014

Phase noise in photonic communications systems using linear amplifiers.

J P Gordon, L F Mollenauer

    Optics Letters
    |September 23, 2009
    PubMed
    Summary

    Spontaneous emission noise limits photonic communication systems. Optimal phase detection is achieved with a nonlinear phase shift of about 1 radian, but this still restricts system range.

    Area of Science:

    • Photonics
    • Optical Communications
    • Nonlinear Optics

    Background:

    • Spontaneous emission noise degrades performance in linear optical amplifier-based photonic systems.
    • Amplitude-to-phase noise conversion, driven by the nonlinear Kerr effect, is a key challenge.
    • Current phase detection systems face limitations in capacity and range.

    Purpose of the Study:

    • To investigate phase detection in photonic communication systems affected by spontaneous emission noise.
    • To determine the optimal nonlinear phase shift for minimizing phase noise.
    • To identify the range limitations imposed by current phase detection techniques.

    Main Methods:

    • Analysis of amplitude-to-phase noise conversion due to the nonlinear Kerr effect.
    • Modeling of photonic communication systems with linear optical amplifiers.

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  • Evaluation of phase detection performance under varying nonlinear phase shifts.
  • Main Results:

    • Optimal phase noise performance is observed when the nonlinear phase shift approaches 1 radian.
    • Amplitude-to-phase noise conversion is a significant limiting factor.
    • State-of-the-art systems achieve error-free operation at multigigabit rates but are range-limited.

    Conclusions:

    • The nonlinear Kerr effect and spontaneous emission noise fundamentally limit the range of photonic communication systems.
    • A nonlinear phase shift of approximately 1 radian offers optimal phase noise performance.
    • Current phase detection technologies restrict system reach to a few thousand kilometers.