Noise, and where the microvolt goes

You measured a noise floorNoise floor What your instrument records when the input is shorted or connected to a perfectly quiet source; everything smaller than this is invisible to you. Related: Thermal (Johnson) noiseThermal (Johnson) noise The random voltage every resistor produces just by being warm; about 13 nanovolts per root hertz for 10 kilohms, which matters at microvolt levels., CharacterizationCharacterization Measuring what your instrument actually does, such as its noise floor, bandwidth, and rejection, instead of assuming the datasheet.. Glossary entry with the inputs shorted, and a worse one with electrodesElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry in the phantomPhantom A physical stand-in for tissue, such as saline gelatin with embedded wires, used to test an instrument against known signals. Related: CharacterizationCharacterization Measuring what your instrument actually does, such as its noise floor, bandwidth, and rejection, instead of assuming the datasheet. . Glossary entry. The difference is the electrodesElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry. Let’s account for every microvolt: where noise comes from, how sources add, and why in a well-designed EEGElectroencephalography (EEG) Recording the brain's electrical activity from electrodes on the scalp, a few tens of microvolts of blurred, summed cortical activity. Related: Electrocorticography (ECoG)Electrocorticography (ECoG) Recording from electrodes placed on the surface of the brain under the skull, usually during epilepsy surgery evaluation; cleaner and sharper than EEG. , Magnetoencephalography (MEG)Magnetoencephalography (MEG) Recording the tiny magnetic fields produced by cortical currents with superconducting sensors in a shielded room; less blurred by the skull than EEG, and far more expensive. , Volume conductionVolume conduction The spreading of currents from a source through the conductive tissues of the head, which is why one source shows up on many electrodes and why scalp EEG is blurry. , Microvolt (µV)Microvolt (µV) One millionth of a volt. Scalp EEG is tens of microvolts; a AA battery is 1.5 million of them. . Glossary entry system the chip is rarely the limit.

Every resistor hisses

A resistor at room temperature produces a random voltage across itself just from the thermal motion of its electrons. The RMS value is √(4 k T R Δf): Boltzmann’s constant, temperature, resistance, bandwidth. For 10 kΩ over a 40 Hz bandwidth at body temperature that is about 80 nV RMS. For 1 MΩ, about 800 nV. This is thermal noiseThermal (Johnson) noise The random voltage every resistor produces just by being warm; about 13 nanovolts per root hertz for 10 kilohms, which matters at microvolt levels. Related: Noise floorNoise floor What your instrument records when the input is shorted or connected to a perfectly quiet source; everything smaller than this is invisible to you.. Glossary entry and there is no circuit trick that removes it; there is only lowering the resistance or the bandwidth or the temperature.

An electrodeElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry with an impedance of 50 kΩ at 10 Hz is, for noise purposes, a 50 kΩ resistor: about 180 nV RMS over the EEGElectroencephalography (EEG) Recording the brain's electrical activity from electrodes on the scalp, a few tens of microvolts of blurred, summed cortical activity. Related: Electrocorticography (ECoG)Electrocorticography (ECoG) Recording from electrodes placed on the surface of the brain under the skull, usually during epilepsy surgery evaluation; cleaner and sharper than EEG. , Magnetoencephalography (MEG)Magnetoencephalography (MEG) Recording the tiny magnetic fields produced by cortical currents with superconducting sensors in a shielded room; less blurred by the skull than EEG, and far more expensive. , Volume conductionVolume conduction The spreading of currents from a source through the conductive tissues of the head, which is why one source shows up on many electrodes and why scalp EEG is blurry. , Microvolt (µV)Microvolt (µV) One millionth of a volt. Scalp EEG is tens of microvolts; a AA battery is 1.5 million of them. . Glossary entry band, per electrodeElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry, and there are two in every measurement. A dry electrodeDry electrode An electrode used without gel, faster to apply but with higher, less stable impedance and more motion noise; the consumer-headset compromise. Related: Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Active electrodeActive electrode An electrode with a small amplifier or buffer built into it, so the high-impedance signal travels only millimetres before being made robust. . Glossary entry at 1 MΩ is 800 nV each. That is already most of a microvolt before the amplifier has done anything.

The amplifier adds two kinds

A voltage noise, quoted in nanovolts per root hertz, which for a good instrumentation amplifierInstrumentation amplifier A precision differential amplifier with very high input impedance and high CMRR, built from three op-amps and sold as a single chip such as the INA128 or AD8232. Related: Differential measurementDifferential measurement Measuring the difference between two electrodes rather than one electrode against ground, so anything common to both cancels. , Common-mode rejection ratio (CMRR)Common-mode rejection ratio (CMRR) How much better an amplifier responds to a difference between its inputs than to a signal shared by both, in decibels; 100 dB means 100,000 times. , Input impedanceInput impedance How hard the amplifier's inputs are to push current into; it must be far higher than the electrode impedance or the signal is lost in the divider. . Glossary entry is 8 to 10 nV/√Hz, so about 60 nV RMS over 40 Hz. Negligible against the electrodesElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry. And a current noise, in femtoamps or picoamps per root hertz, which flows through the electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. Related: Dry electrodeDry electrode An electrode used without gel, faster to apply but with higher, less stable impedance and more motion noise; the consumer-headset compromise. , Conductive gel or pasteConductive gel or paste Salty gel between electrode and skin that lowers impedance, stabilizes the chemistry, and is the reason research EEG takes half an hour to set up. , Electrochemical impedance spectroscopy (EIS)Electrochemical impedance spectroscopy (EIS) Measuring an electrode's impedance across many frequencies to characterize its interface, standard in electrode development. . Glossary entry and becomes a voltage: current noise times impedance. For the INA128’s 0.3 pA/√Hz through a 50 kΩ electrodeElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry that is 15 nV/√Hz, comparable to its voltage noise; through a 1 MΩ dry electrodeDry electrode An electrode used without gel, faster to apply but with higher, less stable impedance and more motion noise; the consumer-headset compromise. Related: Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Active electrodeActive electrode An electrode with a small amplifier or buffer built into it, so the high-impedance signal travels only millimetres before being made robust. . Glossary entry it is 300 nV/√Hz, which dominates everything. This is why chips meant for dry electrodesDry electrode An electrode used without gel, faster to apply but with higher, less stable impedance and more motion noise; the consumer-headset compromise. Related: Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Active electrodeActive electrode An electrode with a small amplifier or buffer built into it, so the high-impedance signal travels only millimetres before being made robust. . Glossary entry are chosen for low current noise.

The low-frequency rise

Below a few hertz, every amplifier and every electrodeElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry gets noisier, following roughly one over frequency. This 1/f noise1/f noise Noise that grows at low frequencies, present in amplifiers and electrodes, and the reason sub-hertz EEG is hard. Related: Noise floorNoise floor What your instrument records when the input is shorted or connected to a perfectly quiet source; everything smaller than this is invisible to you.. Glossary entry comes from slow fluctuations in materials, in the chip’s transistors and in the electrodeElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry’s chemistry. It is why the noise floorNoise floor What your instrument records when the input is shorted or connected to a perfectly quiet source; everything smaller than this is invisible to you. Related: Thermal (Johnson) noiseThermal (Johnson) noise The random voltage every resistor produces just by being warm; about 13 nanovolts per root hertz for 10 kilohms, which matters at microvolt levels. , CharacterizationCharacterization Measuring what your instrument actually does, such as its noise floor, bandwidth, and rejection, instead of assuming the datasheet. . Glossary entry you measured is dominated by slow wander, why a 0.5 Hz high-pass makes the trace look so much cleaner, and why sub-hertz EEGElectroencephalography (EEG) Recording the brain's electrical activity from electrodes on the scalp, a few tens of microvolts of blurred, summed cortical activity. Related: Electrocorticography (ECoG)Electrocorticography (ECoG) Recording from electrodes placed on the surface of the brain under the skull, usually during epilepsy surgery evaluation; cleaner and sharper than EEG. , Magnetoencephalography (MEG)Magnetoencephalography (MEG) Recording the tiny magnetic fields produced by cortical currents with superconducting sensors in a shielded room; less blurred by the skull than EEG, and far more expensive. , Volume conductionVolume conduction The spreading of currents from a source through the conductive tissues of the head, which is why one source shows up on many electrodes and why scalp EEG is blurry. , Microvolt (µV)Microvolt (µV) One millionth of a volt. Scalp EEG is tens of microvolts; a AA battery is 1.5 million of them. . Glossary entry (which exists and is interesting) is hard to record.

Adding them up

Independent noise sources add as the square root of the sum of squares, not directly. Two 180 nV electrodesElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry and a 60 nV amplifier: √(180² + 180² + 60²) ≈ 260 nV. The biggest source dominates; halving a small source does almost nothing. This is the arithmetic that tells you where to spend effort: a 1 µV-noise chip replaced by a 0.5 µV chip does nothing if the electrodesElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry contribute 2 µV.

Why the breadboard was so bad

None of the above explains a noise floorNoise floor What your instrument records when the input is shorted or connected to a perfectly quiet source; everything smaller than this is invisible to you. Related: Thermal (Johnson) noiseThermal (Johnson) noise The random voltage every resistor produces just by being warm; about 13 nanovolts per root hertz for 10 kilohms, which matters at microvolt levels. , CharacterizationCharacterization Measuring what your instrument actually does, such as its noise floor, bandwidth, and rejection, instead of assuming the datasheet. . Glossary entry of 15 µV, which is what a breadboarded amplifier typically shows. That is not thermal noise; it is pickup. Long, springy, unshielded connections at a high-impedance node act as antennas for the room’s electric field, and the resulting voltage is far larger than any thermal source. The cure is short, soldered, and, for the input node, guarded. That is why the noise floorNoise floor What your instrument records when the input is shorted or connected to a perfectly quiet source; everything smaller than this is invisible to you. Related: Thermal (Johnson) noiseThermal (Johnson) noise The random voltage every resistor produces just by being warm; about 13 nanovolts per root hertz for 10 kilohms, which matters at microvolt levels. , CharacterizationCharacterization Measuring what your instrument actually does, such as its noise floor, bandwidth, and rejection, instead of assuming the datasheet. . Glossary entry of the same circuit falls by a factor of five when it moves from breadboard to soldered board, and why the ADS1299ADS1299 Texas Instruments' 8-channel, 24-bit biopotential front-end chip used in OpenBCI and many research amplifiers. Related: Delta-sigma ADCDelta-sigma ADC A converter that samples very fast with a crude 1-bit decision and averages, achieving 24-bit resolution at modest rates; what the ADS1299 uses. , OpenBCIOpenBCI The open-source EEG hardware company whose Cyton (ADS1299) and Ganglion boards are the default hobby and research-lite amplifiers. . Glossary entry layout rules exist.

Reading a noise floor

Report it as RMS in microvolts over a stated bandwidth, input-referred, with the inputs shorted at the electrodeElectrode The conductor that turns ion currents in tissue into electron currents in a wire; its chemistry and contact quality set the noise you live with. Related: Silver/silver-chloride (Ag/AgCl)Silver/silver-chloride (Ag/AgCl) The standard electrode material for biopotentials, because its chemistry produces a stable, low-noise, low-drift interface with salty gel. , Electrode impedanceElectrode impedance How hard it is to push current through the skin-electrode contact, typically 5 to 50 kilohms with gel and megohms dry, higher at low frequencies. , Half-cell potentialHalf-cell potential The DC voltage that appears wherever a metal meets an electrolyte; two electrodes with different half-cell potentials produce an offset that can swamp the signal. . Glossary entry connector. “0.9 µV RMS, 0.5 to 40 Hz, gainGain How many times an amplifier multiplies its input; 1000× turns 50 microvolts into 50 millivolts, enough for an ADC to see. Related: Instrumentation amplifierInstrumentation amplifier A precision differential amplifier with very high input impedance and high CMRR, built from three op-amps and sold as a single chip such as the INA128 or AD8232. . Glossary entry 24, 250 SPS” is a complete statement; “low noise” is not. Also report peak-to-peak, which is roughly six times RMS for Gaussian noise and is what you see on the trace. And plot the noise spectrumSpectrum A plot of how much of a signal lives at each frequency. Related: Fast Fourier transform (FFT)Fast Fourier transform (FFT) The algorithm that breaks a stretch of signal into the sinusoids that would add up to it, giving amplitude and phase at each frequency. , Power spectral density (PSD)Power spectral density (PSD) The spectrum expressed as power per hertz, the standard way to quantify how strong alpha is. . Glossary entry: its shape tells you which source dominates. A flat floor is thermal or amplifier noise; a rise at low frequency is 1/f; a spikeSpike Shorthand for an action potential as seen by an electrode, a brief blip about a millisecond wide. Related: Action potentialAction potential The brief, all-or-nothing voltage spike a neuron fires, about a millisecond long and about 100 millivolts tall across its membrane. , Spike sortingSpike sorting Deciding which spikes on an electrode came from which neuron, by clustering their waveform shapes. , Extracellular recordingExtracellular recording Recording with an electrode near neurons rather than inside one; you see small, fast blips from nearby cells rather than the full membrane swing. . Glossary entry is pickup at that frequency.