Noise, Distortion, and Stochastic Methods in Electronics
Noise Sources and Spectral Densities
Thermal and shot noise
Thermal noise in resistive elements is modeled by a white spectral density proportional to , while shot noise arises from discrete charge transport and has spectral density proportional to . These mechanisms set fundamental lower bounds on resolution and dynamic range in amplifiers and sensors.
Common noise mechanisms
| Noise type | Typical origin |
|---|---|
| Thermal noise | Random motion of carriers in resistors and channels |
| Shot noise | Discrete carriers crossing a barrier |
| Flicker noise | Defect and trapping processes |
| Random telegraph noise | Discrete trap occupancy changes |
Research relevance
At small dimensions, low-frequency noise and device-to-device fluctuations can dominate over classical thermal limits, especially in precision analog, biomedical, and quantum-readout circuits.
Nonlinearity and Distortion Metrics
Small-signal vs large-signal behavior
Real circuits are nonlinear, so distortion appears when an input excites higher-order terms in the transfer function. Metrics such as total harmonic distortion, intermodulation products, and third-order intercept points are used to quantify spectral purity.
Which noise source is most directly associated with discrete charge crossing a junction or barrier?
Shot noise comes from the discrete nature of charge and is especially relevant in currents through barriers or junctions.
Correct answer: Shot noise
What is the approximate one-sided thermal noise voltage spectral density of a resistor?
A resistor at temperature has thermal noise spectral density approximately in one-sided voltage form.
Correct answer: 4k_BTR
Modeling caution
Noise formulas depend on definitions of one-sided versus two-sided spectra and on whether quantities are expressed as current, voltage, or power spectral density.