Noise and Interference in Instrumentation — Part 1: Introduction

This opening lecture sets up the toolkit that Part 2 builds on: how to represent noise sources in a circuit, how to quantify them, when it's valid to simply add them together, how they propagate through a frequency-dependent system, and how to compare a system's own noise contribution against a standard reference.

1. Where noise comes from

• Inherent (transmitted) noise — noise already present in the physical quantity a sensor measures, originating before the signal ever reaches the instrument.
• Intrinsic noise — generated inside the instrument itself; every practical component contaminates the signal it carries (e.g. thermal noise in a resistor, shot noise in a diode).
• Interference — noise coupled in from external sources sharing no intrinsic connection to the signal of interest (e.g. powerline hum, solar flares, lightning) — separate from intrinsic noise, though how much of it couples in can itself depend on the system's design.

Modeling noise this way — rather than treating it as an unstructured nuisance — enables design optimization: informed source/load matching, component choice, filtering and bandwidth decisions, and a realistic uncertainty floor for measurements.

2. Modeling a noisy device

For a simple two-terminal (1-port) device — a resistor, a non-ideal capacitor or inductor, a diode, a battery — the noise it generates can be modeled with a single source applied to an otherwise ideal, noiseless version of the device:

The two forms are equivalent (Thevenin ↔ Norton), but one is often more convenient depending on the device: a series voltage source suits a resistor, while a diode's current-driven physics often makes a current source the more natural choice.

3. Multi-terminal devices: the input-referred noise model

A 3- or 4-terminal (2-port) device — a transistor, an op-amp — can't be modeled with a single noise source: a BJT alone has separate noise contributions from its base, base–emitter junction and collector–emitter junction, and every device topology places them differently. Rather than track each source individually, every noise source inside the 2-port device is collapsed into one equivalent series voltage source AND one parallel current source at the input — the input-referred noise model. This lets noise calculations proceed agnostic to whatever is actually inside the device.

4. Quantifying noise: RMS, mean, variance and PSD

Noise voltage/current has zero mean by definition — so the quantity that actually matters is its power, via the RMS value. But real systems only ever pass a limited band of frequencies, so noise power needs a frequency-resolved description: the power spectral density (PSD), the average noise power measured through a very narrow bandpass filter centered at each frequency, normalized per Hz of bandwidth.

This is exactly why Part 2's thermal-noise formulas multiply a flat PSD by a bandwidth Δf to get a power: it's this integral, simplified for the white-noise case.

5. When can noise powers simply add?

Not automatically. Writing the instantaneous power of two combined noise voltages through a resistance R and averaging over time produces a cross term alongside the two individual power terms:

That cross term vanishes — leaving the simple P_AVG = P_1,AVG+P_2,AVG rule used throughout Part 2 — only when the two sources are genuinely independent (their instantaneous product averages to zero over time). When sources are correlated, the cross term survives and the simple sum under-counts the true noise power.

6. Noise through a frequency-dependent system

A linear system with transfer function H(f) scales a noise PSD at its input by the squared magnitude of the transfer function:

So a real (rounded-off) filter passes exactly as much noise power as an ideal "brick-wall" filter whose width — the effective noise bandwidth — is π/2 times the filter's own −3 dB cutoff frequency, not the cutoff frequency itself. This equal-area argument is why a filter's noise bandwidth is always somewhat wider than its "advertised" 3 dB bandwidth would suggest.

7. Noise figure: comparing against a standard reference

To judge how much noise a system itself adds — independent of whatever noise its input signal already carries — every source resistance is assigned a standardized reference noise, using a fixed reference temperature T₀ = 290 K (the maximum available thermal noise power a source resistance can deliver, by the maximum power transfer theorem):

The noise factor F is independent of the input signal itself and depends only on the system's intrinsic noise characteristics — which is what makes it a fair way to compare the noise performance of two different systems. Expressed in decibels, NF = 10log₁₀(F).