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Microvolt
Phase 1: First contactExplainer14 min

Why so small?

Microvolts, gain, and why the amplifier measured a difference between two electrodes instead of one electrode against ground. And the reason for the third electrode.

AssumesProject B: One channel of youSpineAnalog / mixed-signal hardware

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The alpha rhythm you saw was about fifty . The hum your body picks up from the room is about ten to a hundred millivolts, a thousand times bigger. And your amplifier still showed you alpha. It did that with three ideas: , which made everything bigger; a , which made everything shared between two electrodes disappear; and a third electrode that actively cancelled what was left. Let’s see each one work.

How small, exactly

Signal Typical size on the skin
Scalp EEG (alpha, eyes closed) 20 to 60 µV
Scalp EEG (an ERP, before averaging) 1 to 10 µV
EOG (eye movement) about 15 µV per degree; hundreds of µV for a big look
ECG on the chest about 1 mV
Surface EMG, clenched 0.1 to 5 mV
Extracellular spike, needle near a nerve 50 to 500 µV
60 Hz hum on a body in a normal room 10 to 100 mV, sometimes volts
A AA battery 1,500,000 µV

Two things to notice. EEG is the smallest thing on the list. And the hum is bigger than everything you want to measure, sometimes by ten thousand times.

Gain

An like the Arduino’s measures 0 to 5 volts in 1024 steps, so each step is about 5 millivolts. Fifty microvolts is a hundredth of a step. Invisible. Multiply by 2000 and alpha becomes 100 millivolts, twenty steps. That is what gain is for, and that is all gain is for: matching the signal to the converter. It does nothing about the hum, which it also multiplies by 2000.

The difference

Here is the trick. The hum is picked up by your whole body, so it is very nearly the same at every point on your head. Alpha is generated under one spot and is different at different points. Measure the difference between two electrodes and the hum, being the same on both, cancels, while alpha, being different, survives. A signal that appears equally on both inputs is called . A signal that appears as a difference is called differential. An is a chip built to amplify the second and ignore the first, and how well it ignores the first is its .

Single-ended versus differentialSimulated signal
This interactive needs JavaScript. If you are reading a printout, the caption describes what it shows.
Figure 1. Two electrodes on a body full of 60 Hz. The top trace is one electrode measured against the amplifier's ground: hum, and nothing else. The bottom is the difference between the two electrodes, amplified. Play with the sliders.
Try this
  1. Slide the CMRR from 80 dB down to 40. Watch the hum reappear in the bottom trace.
  2. Put CMRR back to 120 dB. Now slide the electrode impedance mismatch to 100 percent. The hum comes back even though the amplifier is perfect. Read the readout.
  3. Turn on the driven-right-leg circuit and watch what happens to the hum before it reaches the amplifier.

The readout in Figure 1 is worth staring at. A CMRR of 100 dB means the amplifier treats a common-mode signal as a hundred thousand times smaller than a differential one. Ten millivolts of hum becomes a tenth of a microvolt. That would be the end of the story, except for the second experiment you just did.

Why perfect amplifiers still hum

The two electrodes do not have the same . One has more paste, or sits on drier skin, or has a half-detached edge. Now the common-mode hum, pushing current through two unequal impedances into the amplifier’s (very large but finite) input impedance, produces two slightly different voltages at the two inputs. A difference. The amplifier, correctly, amplifies it. The hum has been converted from common mode to differential before the chip ever saw it, and no CMRR can remove it.

This is the physics behind the debugging advice “re-paste the electrodes.” It is also why the of a biopotential amplifier is enormous (10 gigohms for the INA128): the bigger it is compared to the electrode impedance, the smaller the conversion.

The third electrode

You could try to reject the hum. Or you could make it smaller before it arrives. The circuit measures the common-mode voltage (that is what the split gain resistor gave you), inverts it, amplifies it, and drives it back into the body through a third electrode. The body’s hum is now being actively pushed toward zero by a feedback loop. Typical gain: another 30 to 40 dB of rejection, which is the difference between a trace that is mostly hum and one where you have to look for it.The name is from electrocardiography, where the third electrode was traditionally on the right leg. In EEG it goes on the forehead or an earlobe; the physics does not care.

Without a third electrode you have no reference for the body at all, and the common-mode voltage can float wherever the room’s fields push it, including outside the amplifier’s supply rails, at which point it stops working entirely. So the third electrode does two jobs: it gives the body a reference, and it cancels hum. Every clinical EEG, ECG, and EMG system has one.

Deep dive Decibels, since everyone uses them 3 min

A decibel is a ratio on a logarithmic scale. For voltages, 20 dB is a factor of 10, 40 dB is 100, 60 dB is 1000, 100 dB is 100,000, 120 dB is a million. Amplifier CMRR is quoted in dB. Filter attenuation is quoted in dB. Signal-to-noise ratio is quoted in dB. The advantage is that gains and attenuations along a chain simply add: 40 dB from the amplifier’s CMRR plus 35 dB from the DRL is 75 dB of hum rejection, a factor of about 5,600.

Deep dive What sets the amplifier's own CMRR 4 min

Inside an instrumentation amplifier are three op-amps and a set of precisely matched resistors. The common-mode rejection comes from the matching: if the resistors that set the difference are equal to one part in ten thousand, the CMRR is about 80 dB. Laser-trimmed chips like the INA128 reach 120 dB at DC. But the matching gets worse with frequency because of tiny stray capacitances, so CMRR at 60 Hz is typically 20 dB lower than the DC number on the datasheet’s first page. That is exactly where you need it most, which is one reason the DRL is not optional.

Deep dive Why the reference electrode is not the ground electrode 3 min

Three electrodes, three jobs. The active electrode sits over the thing you want (O1). The is the other input of the difference (the earlobe); everything you see is active minus reference, so a “quiet” reference matters and there is no truly quiet spot on the head. The or DRL electrode gives the body a voltage reference and cancels hum; it is not part of the difference at all. Beginners connect the reference to ground and wonder why the hum is terrible. In Phase 2 you will meet , which are just different choices of what to subtract from what.

Recall
What is a common-mode signal and why does a differential amplifier reject it?
A signal that appears equally on both inputs, such as hum picked up by the whole body. A differential amplifier outputs the difference between inputs, so anything identical on both cancels.
Recall
Your amplifier has 120 dB CMRR but the trace is full of hum. What is the most likely cause?
Electrode impedance mismatch. Unequal electrode impedances convert the common-mode hum into a small differential voltage before the amplifier, which it then correctly amplifies. Re-paste the electrodes.
Recall
What two jobs does the third (DRL) electrode do?
It gives the body a voltage reference so the common-mode voltage stays within the amplifier's range, and it actively cancels hum by driving the inverted common-mode signal back into the body.
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