Phase 2: Build the instrumentExplainer15 min

Instrumentation amplifiers, properly

What is inside the chip you have been trusting. Three op-amps, four matched resistors, and the numbers that decide whether the board records brain or room.

AssumesWhy so small?Project A: The ADS1299 boardSpineAnalog / mixed-signal hardware

You are skimming: the title, the first figure, and the short version. Switch to Read in the header for the full page, or Deep to open every deep dive.

You have used an instrumentation amplifier as a black box with two inputs and a gain resistor. Inside the INA128, and inside each of the ADS1299’s eight channels, is the same three-op-amp circuit that has been the standard since the 1970s. Let’s open it, see where the common-mode rejection comes from, and see why the three numbers on the datasheet’s first page (CMRR, input impedance, and noise) are the three that decide whether a design records brain or room.

Where rejection comes fromSimulated signal

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Figure 1. The same playground as Phase 1, with the numbers this page explains. Notice that above about 100 dB of CMRR, the electrode mismatch slider matters and the CMRR slider does not.

Why not one op-amp

An ordinary op-amp with four resistors can subtract two voltages. Two things make it useless for electrodes. Its input impedance is set by the resistors, in the tens of kilohms, comparable to the electrodes themselves, so most of the signal is lost in the divider and any mismatch between the two sides turns common mode into a difference. And its CMRR depends on matching four external resistors to a part in ten thousand, which you cannot do with a parts drawer.

The three-op-amp circuit

Two input op-amps, each configured as a follower with gain, share a single gain resistor between their inverting inputs. Because a follower’s input is the op-amp’s own input pin, the input impedance is the op-amp’s: gigohms. Because the two share one gain resistor, a common-mode voltage appears identically at both outputs and is not amplified at all, while a differential voltage is amplified by 1 + 2R/R_gain. The first stage therefore boosts the difference and leaves the common mode at gain 1, which is where most of the rejection comes from.

The third op-amp is a plain difference amplifier with four resistors that subtracts the two first-stage outputs. Its resistors are matched by laser trimming inside the chip, and since the differential signal arriving at it has already been amplified while the common mode has not, its matching only needs to reject a common-mode signal that is already small relative to the signal.

The gain resistor you connect externally is R_gain. With the INA128’s internal resistors of 25 kΩ, the gain is 1 + 50 kΩ / R_gain, which is the formula on the datasheet’s first page and the reason 500 Ω gave you about 100.

The three numbers

CMRR. Quoted at DC, typically 100 to 120 dB. It falls with frequency because the two input paths have slightly different stray capacitances, and at 60 Hz it is usually 20 dB worse. As Figure 1 shows, once the chip is above about 100 dB the electrodes, not the chip, set the system’s rejection.

Input impedance. Gigohms in parallel with a few picofarads. The resistive part is so high it does not matter. The capacitive part does: a few picofarads at 60 Hz is a few gigohms, and a mismatch between the two inputs’ capacitances is a mismatch in impedance, which converts common mode to differential exactly as an electrode mismatch does. This is why input traces on the ADS1299 board are laid out symmetrically.

Noise. Quoted as a voltage noise density in nanovolts per root hertz, plus a 1/f corner. The INA128’s 8 nV/√Hz over a 40 Hz bandwidth is about 50 nV RMS, negligible. What is not negligible is the 1/f rise below a few hertz, and the current noise flowing through a high electrode impedance. The noise explainer adds these up.

Predict before you look

You raise the first-stage gain from 10 to 1000. What happens to the system's CMRR?

It gets better, by roughly the same factor, until something else limits it. The first stage amplifies the difference and not the common mode, so the ratio between them at the second stage improves with first-stage gain. This is why instrumentation amplifiers are usually run at as much gain as the signal range allows. In the ADS1299, that is gain 24 for EEG.

The ADS1299’s version

Each of the eight channels is a programmable-gain instrumentation amplifier feeding a 24-bit converter. The gain is set by register (1 to 24). The inputs have a common-mode range that must include the body’s potential, which is what the bias drive holds in place. There is a multiplexer in front of each channel that can route the electrode, a shorted input (for noise measurement), the internal test signal, the supply (for monitoring), or the bias reference, all in software. Reading that multiplexer’s options in the datasheet tells you exactly which measurements the designers expected you to make during bring-up, and you made them.

Stop here if you like. Three op-amps, one gain resistor, three numbers. The deep dives are for the design review.

Deep dive Input protection and why the series resistors are there 3 min

The few-kilohm resistors in series with each input, together with the op-amp’s internal clamp diodes, limit the current from a static discharge or a defibrillator pulse (in clinical designs) to something the chip survives. They also form a low-pass with the input capacitance that keeps radio frequencies out. Their cost: their own thermal noise (a few nanovolts per root hertz for a kilohm) and a tiny extra impedance mismatch if they are not matched. Use 1 percent parts and keep them equal.

Deep dive Right-leg drive as a feedback loop 4 min

The bias amplifier senses the common-mode voltage (the average of the inputs), inverts it with high gain, and drives the body. It is a negative feedback loop, and like every feedback loop it can oscillate if the gain is too high at a frequency where the phase shift through the body and the cable reaches 180 degrees. Designs add a capacitor in the feedback path to roll the gain off at high frequencies, and the series resistor both limits current for safety and adds phase margin. If your DRL “sings” at a few kilohertz, that is what happened.

Deep dive Chopper-stabilized and other modern tricks 3 min

Newer front ends chop the input (swap the two inputs back and forth at tens of kilohertz) so that the amplifier’s own 1/f noise and offset are modulated up and out of band and then removed. The signal you want is demodulated back. This is how sub-microvolt noise floors at 1 Hz are achieved in modern implantable and wearable chips. The ADS1299 does not chop; the Intan and newer TI parts do. Knowing the word is enough for now.

Recall

Where does most of an instrumentation amplifier's common-mode rejection come from?

The first stage: two followers sharing one gain resistor amplify the difference by 1 + 2R/R_gain while passing the common mode at unity gain, so the ratio improves by the first-stage gain before the difference amplifier ever sees it.

Recall

Why does a mismatch of a few picofarads between the two input capacitances matter?

At 60 Hz a few picofarads is gigohms of impedance; a mismatch between inputs is an impedance mismatch that converts common-mode hum into a differential signal, just as electrode mismatch does.

Recall

Why does a biopotential chip put a multiplexer in front of each channel?

So the input can be switched in software to a shorted input (noise floor), the test signal (framing and scaling check), the supply (monitoring), or the electrode, which are exactly the bring-up measurements the designers expect.

Explain it to your roommate

Explain what this page was about to your roommate in three sentences. No jargon they would not know.