AC Coupling (removing DC drift) 3-Amp INA Instrumentation Amplifier (DC restoration)

While clearing out my old data, I came across the teaching materials I’ve helped rewritten as a teaching assistant of Biomedical Electronics Lab (Stanford EE122A).

It’s a generic concept in electronics that often used in EKG/ECG circuits to remove the baseline drift on the fly so the analog signal won’t drift off the rails (exceed the dynamic range limited by the op-amps) before the post-processing filter (whether it’s analog or digital) kicks in to remove the DC component.

This concept is called ‘DC restoration’, which is often not taught in standard electronics textbooks. Instead it’s detailed in one of the instrumentation amp (INA) Burr-Brown (now TI) application notes.

It’s a slick trick but the rationale wasn’t very well explained even in the application note itself. It was presented as a feedback design but it doesn’t tell you intuitively what was fed back and why INA chips, and why the reference pin is the right injection point.

Most textbooks don’t even teach the existence of the reference pin (they always short the reference to the ground without explaining). Application notes talk about the REF pin, but they often jump too quickly into cookbook recipes and equations (likely because customers just want quick answers) so they never tell you the thought process.

This blog post shares my intuition of DC-restoration that’s exposed to EE122A students after I’ve updated the lab document. Hope electronic hobbyists and industry people will find it useful.

Before we get to DC restoration, we must see that the purpose of a 3-amp INA is basically a non-inverting buffer stage (primarily done to increase input impedance) followed by a single difference amp (output) stage.

Non-inverting configuration has higher input impedance as the input goes directly to the high impedance non-inverting (+) input pin without taking material current from the input (loading), so there’s no good reason to lose this property by doing inverting op-amp configuration twice.

Most practical INA chips assign some of the user-adjustable gains at the buffer stage because ‘mirrored-ground’ (superposition) allows one resistor to program the gains for the 2 buffer amps without adding more mismatch, but conceptually the first stage’s primary purpose is a buffer. The rest of the gains can be hard-coded by manufacturing with matched ‘resistors’ inside the IC, mostly at the output difference amp stage.

But for illustration (so not to drown the readers in math), let’s assume the design choice of assigning the gains at the input buffer stage and make the output stage a unity gain difference amplifier (V_pV_n), which I use small letters (n, p) to denote the outputs of the buffer stage internal to the INA chip.

The REF pin (the part of R_4 exposed in Figure 6 above) is often advertised as an offset adjustment pin. This is just one of the many uses if you really understand the idea behind the 1-amp difference amplifier configuration.

The slightly more shallow perspective (more modular or system perspective that I’ve shared with EE122A students) is that if you look at an standard 3-amp INA configuration in regular textbooks like this,

Understanding CMR and instrumentation amplifiers - EDN

the entire sub-circuit (3 amp INA) is floating so it has absolutely no idea what the reference (‘ground’) would have been if we did not ARBITRARILY define it through R_4 by tying it to the CM ground, by forcing REF pin (V_{REF}) to be 0V (relative to the common mode ground shared with the inputs)!

In other words, we now have an INA ‘ground’ and a Common Mode (CM) ground, which they do not have to be the same unless we force them to be equal by shorting the REF pin to the CM ground.

This means whatever voltage V_{REF} we set the REF pin to be, it’s the baseline of the system (amplifier) and the whole output shifts moves up and down by whatever V_{REF} relative to common mode ground we are feeding into the REF pin for the moment.

The DC restoration takes advantage of the user-definable baseline (INA ‘ground’) by extracting a low-frequency (drift) portion of the output signal V_o with an INVERTING low-pass filter (LPF) with frequency response L(\omega), and re-define it as the INA’s ‘ground’ level. This is the LPF:

e.g. if the signal’s baseline drifted up by 1V, a -1V is generated by the inverting LPF and the INA ‘ground’ respond by moving from 0V down to -1V, which pulls the entire signal down by 1V, cancelling the 1V increase in baseline. All the voltages used here are relative to the common mode ground.

As with any AC coupling circuit, there is no precise definition of what ‘DC’ or ‘baseline’ is. It’s up to the experimenter to consider what cutoff frequency in the LPF is close enough. Technically DSP engineers can call a running window of trimmed-median the baseline if they wanted to.

The feedback (how fast the INA ‘ground’ is readjusted) is as responsive as the phase delay introduced by the LPF’s time constant. If you only consider anything below 0.00001Hz to be DC, you have to pay a price for the long delay catching up to the changes which might or might not be considered a baseline drift (it’s an application specific context).

I also have an alternate view of DC restoration which does not use the concept of INA ‘ground’ (not taught in EE122A). This is based on seeing the final stage op-amp (1-amp INA) not just as a simple difference amplifier, but as a 3-input arithmetic circuit (summing and subtractions) through super-position (setting one input to 0V at a time and add the results up).

This is the gut of a 1-amp INA difference amplifier

We can break it down into a (1 input) inverting amplifier plus a summing (2 inputs) non-inverting amplifier.

The equations for inverting amplifier and non-inverting amplifiers are not symmetric! The core part of the feedback gain in EITHER CONFIGURATION are ALWAYS set at the feedback branch which ONLY goes to the inverting input (-), aka R_1 and R_2!

  1. Inverting amplifier portion do not care about the resistors at the non-inverting input (+), but
  2. Non-inverting amplifier portion’s gain is determined by the 2 resistors at the inverting input (-)! The resistors at the non-inverting inputs (+) never boost the amplifier gains! They only attenuate signal from external sources (like voltage dividers). The gain boost happens ONLY at the inverting branch!

Why? By superposition (short out other inputs you are not considering)

  1. Inputs to R_3 (V_p) and R_4 (V_{REF}) shorted to the common ground gives an inverting amplifier. They don’t matter to V_n. The gain to V_n is -\frac{R_2}{R_1}.
  2. Input to R_1 (V_n) shorted to the common ground gives a non-inverting amplifier, which the gain boost (1+\frac{R_2}{R_1}) is relative to voltage V_+ showing up at the non-inverting input (+), which is the result of attenuating V_p through R_3 and V_{REF} through R_4.

The output contributions, if R_1=R_2 and R_3=R_4,

  1. [Inverting amplifier gain of -1 relative to V_n] contributes -V_n to the output
  2. [Non-inverting amplifier gain of 2 relative to V_+] if R_4 is set to ground through V_{REF}, R_3 and R_4 forms a 1:1 potential divider which halves V_p to give \frac{V_p}{2} at V_+. Doubling (2x gain) the halved input gives an overall gain of 1, therefore contributing V_p to the output

So the overall output equation is V_p - V_n if V_{REF} is grounded to 0V.

The intuition for DC restoration is to untie the REF pin (going to R_4) from CM ground and treat it as equals to V_p pin (going through R_3, so instead of a potential divider, they form a non-inverting summing amplifier:–r1-q34558104

So the DC restoration circuit can be seen as a 3-input arithmetic amplifier that gives the equation V_{REF}+V_p-V_n and you can subtract the baseline by setting V_{REF} to be whatever baseline your inverting LPF feedback branch judged. The overall AC-coupled system response is \frac{1}{1+L(\omega)}.

Note that ALL 3 inputs (V_p, V_n, V_{REF}) should be driven from sources with low output impedance. V_p and V_n is the outputs of a buffer op-amp so they already have good low impedance outputs feeding to the last stage. We’ll need to do the same for V_{REF} by using an op-amp to lower the output resistance whether it is an active low pass filter or active potential divider, because V_+ do not see V_p differently from V_{REF}. Noise showing up from high resistance output driving REF pin do not simultaneously appear on V_n, so it’s not canceled and therefore it’s worsening the common mode rejection (CMR).


Descriptive names for logic operations on a pair (x, y)

It reads as “The output is TRUE only when the reduction (x,y)\rightarrow z meets the description of the operations below”

0 inputs:

  • Constant: gives the same hard-coded result regardless of inputs

1 input:

  • Transfer: Hardwired to one of the inputs
  • Complement: NOT

2 inputs (symmetric):

  • Comparison: different (XOR), identical (NXOR or equivalence)
  • Arithmetic: AND, OR and its complements NAND, NOR

2 inputs (asymmetric):

  • Inhibition: ONLY 1 followed by 0 is an inhibition. It’s a WHITE-list: anything else is not an inhibition (starting with 0 doesn’t inhibit)
  • Implication: ANYTHING GOES as long as 1 is be followed by 1. It’s a BLACK-list: anything else qualifies as an implication (starting with 0 does not break the implication)

Implication is the complement of Inhibition, as the only case that breaks an implication is inhibition.

This ‘operator’ instead of truth-table view is more often used in electrical engineering than in computer science. There are many names for the same thing, but I put in some thought to find the intuitive words to make it easy to understand and remember

WARNING: Those there are tempting faint similarities between logic and set theory, there’s no direct tight duality between the two. Whitelist/Blacklist in inhibition/implication do not make sense with set-diff/subset as we are talking about a one-shot relationship here in logic, while set theory talks about the relationship between elements picked after it is quantified by “for all” vs “there is”. i.e. Truth table do not mix with sets


Oh! Humanity

Onion used to my favorite satire newspaper before it was taken over by the wokes. When I was in college, some teaching assistants read us an article as a treat before starting a session. Here’s one of my favorite headlines. Here’s one of my favorite

Newborn Loses Faith In Humanity After Record 6 Days
It took me 7 years. I guess I was slow.

I grew up in Hong Kong and I can tell you for sure that you are going to have a very hard time surviving there if you are not a hardcore cynic. People are very harsh to each other but most are sticklers to the rules and contracts to the letter (they believe in the rule-OF-law), to the extent that some might find them inflexible or outright cruel (this is especially true with bus drivers in Hong Kong nowadays) .

In other words, people there feel comfortable taking advantage of others, but 99.9% of time they do it within legal boundaries (like exploiting scenarios not considered when the contracts are drafted) as they are not bold legal risk takers. It’s not a forgiving city because Hongkong is geographically too close to the land of crooks so every sign of kindness we show are seen as signs of weakness ready to be exploited. Kindness just doesn’t pay in Hong Kong.

Socialist (Chinese Communist Party) is a shit-magnet, identifying the nastiest people in any population. Hong Kong Protests in 2019 showed me people aren’t predominantly bad. I might have picked up a little bit of faith in humanity again after seeing the spirits of the freedom-fighters. The scumbags I should have hated with passions are now wagging their tails and licking the boots of the Chinese Communist Party.