This lecture builds a working, quantitative picture of where random noise in an instrumentation circuit actually comes from, and how to combine it correctly. Every noise source discussed is classified by the physical mechanism that produces it, rather than by which component it happens to appear in — the same physical mechanism (e.g. thermal agitation of charge carriers) shows up in resistors, transistors, and interconnects alike.
The lecture organizes every noise mechanism by the physics behind it, not by which component it happens to show up in:
Each branch gets its own noise power spectral density (PSD) — the language that lets noise from completely different physical causes be compared and combined on equal footing:
Present in every resistance, independent of any applied voltage, and dependent only on temperature and resistance:
Two properties matter in practice: for a fixed temperature, noise voltage increases with resistance while noise current decreases with resistance — but noise power is independent of resistance altogether.
Worked example: RMS thermal noise of a 10 kΩ resistor at room temperature (25 °C = 298.15 K), measured through an ideal bandpass filter passing 1–11 kHz (Δf = 10 kHz).
4kBT = 4 × 1.381×10⁻²³ × 298.15 = 1.647×10⁻²⁰ W/Hz
Noise power: P = 4kBT · Δf = 1.647×10⁻²⁰ × 10⁴ = 1.647×10⁻¹⁶ W
VRMS = √(P·R) = 1.28 µV IRMS = √(P/R) = 128 pA
Independent (uncorrelated) noise sources cannot be added directly — only their mean-square values add:
Modeling resistors as Thevenin (series voltage) sources makes this straightforward, since voltage sources in series simply add; the equivalent Norton (parallel current-source) form is algebraically messier for the same result and is a common student pitfall — current noise sources only add directly when the resistors are genuinely in parallel, and voltage noise sources only add directly when the resistors are genuinely in series. Mixing the two up gives a result that looks plausible but is wrong.
The result generalizes cleanly: for any number of resistors at a common temperature T, the combined noise is exactly what a single lumped resistor would produce, using the equivalent series or parallel resistance:
This only holds cleanly when every resistor is at the same temperature — if two resistors in series or parallel sit at different temperatures, the calculation has to track each resistor's contribution separately before combining, since a single equivalent resistance can no longer stand in for both.
A single-pole RC filter has an equivalent noise bandwidth wider than its 3 dB bandwidth by a factor of π/2, which gives a remarkably clean result:
Arises only where charge must cross a potential barrier (a p–n junction being the classic case), since the charge transfer there is discrete rather than continuous — contrast this with a plain wire or resistor, where charge is free to move as a continuum. Its spectral density is proportional to the DC bias current: SI = 2qIDC, and being a counting process it is fundamentally Poisson-distributed, though for the large currents typical of real circuits the central limit theorem makes it converge to Gaussian noise in practice.
Why bother with it at all, given how small it usually is next to thermal noise? Because counter-intuitively, shot noise matters most not when DC current is large, but when a small signal of interest rides on top of a large DC bias — the common situation in most amplifying circuits, where the bias current itself is uninteresting but the shot noise it carries can be comparable to the small signal riding on it. In the high-frequency, low-temperature regime, thermal noise (which fades with temperature) and 1/f noise (which fades with frequency) both shrink away, leaving shot noise — independent of both — to dominate.
Dominates at low frequencies and falls off with increasing frequency, crossing below the frequency-independent thermal/shot noise floor at a device's corner frequency — the lower the corner frequency, the better the device (voltage-noise and current-noise corner frequencies need not coincide). Resistors can exhibit flicker noise too ("excess noise"), though well-made thin-film resistors keep it very low; wirewound and carbon-composition resistors are worse offenders.
Unlike thermal or shot noise, this depends on the actual frequency band chosen, not merely its width — doubling both f1 and f2 changes the noise power even though Δf is unchanged, which is a common trap when porting a bandwidth-only intuition from thermal noise over to 1/f noise.
Sudden, discrete step transitions in offset voltage/current caused by charge carriers trapping and detrapping at material defect sites. Largely a legacy concern in modern semiconductor processes due to cleaner materials and fabrication.