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Say you have differential signals that are perfectly phase and amplitude balanced, but obviously 180 degrees out of phase

V+= Asin(2pif*t)+ Vcommon_mode_noise

V-= -Asin(2pif*t)+ Vcommon_mode_noise

The output code of a differential ADC is determined by Vo=(V+ - V-):

V+-V-= 2Asin(2pif*t) +(Vcmn-Vcmn)

V+ - V-= 2Asin(2pif*t)

Looks like a CMRR of infinity to me, although I know there's something I'm missing.

In cases where that makes a difference, I'm looking at an AD9655.

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    \$\begingroup\$ 100% is impossible unless you decided that was just less than the least significant bit or no contribution to SNR. \$\endgroup\$ Jun 15, 2021 at 20:05

5 Answers 5

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A theoretical perfect differential ADC (or differential amplifier) will reject 100% of common-mode noise regardless of magnitude or bandwidth.

Now compare the CMRR specification on the datasheet of a real differential ADC.

Here is the typical rejection from the datasheet of the AD7675:

enter image description here

There is no guaranteed CMRR specification.

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  • \$\begingroup\$ Very interesting. I still don't understand exactly WHY the CMRR isnt perfect. But what is also interesting is that my ADC doesn't specify its CMRR, how would I know what it is then? \$\endgroup\$
    – Max W
    Jun 15, 2021 at 19:51
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    \$\begingroup\$ Can you link the datasheet? No components are perfect, there will always be some mismatch and even if you could null it out at one frequency (for example) it would not be zero at other frequencies. \$\endgroup\$ Jun 15, 2021 at 20:01
  • \$\begingroup\$ analog.com/media/en/technical-documentation/data-sheets/… \$\endgroup\$
    – Max W
    Jun 15, 2021 at 21:08
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    \$\begingroup\$ I don't see a specification. It's intended to be driven with a differential-output ADC driver or transformer with a fairly narrow common-mode voltage range. If it's important to you, you may wish to try the manufacturer's forum or possibly look at other parts. This is a pretty expensive part, apparently not very popular, a bit long in the tooth, and only has a Rev 0 datasheet. They do list it as "recommended for new designs" however. \$\endgroup\$ Jun 15, 2021 at 21:48
  • \$\begingroup\$ It is for a new design, but it will be interesting to see how we figure out its CMRR. Thanks. \$\endgroup\$
    – Max W
    Jun 15, 2021 at 22:03
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Usually the common mode rejection ratio (CMRR) will be specified in the datasheet. So far I have never seen one that was infinite.

If nothing else there will always be some slight common mode capacitance from input to output that will allow common mode noise to couple directly (and passively) into the output. No matter how good the silicon designer is.

One way to think about it is, imagine a PCB with the footprint for differential to common mode amplifier on it. Even if you don't install the IC, there is a tiny amount of capacitance from pad to pad, so a common mode signal will still couple to the output. The IC may have additional coupling above and beyond the pad-to-pad capacitance. So I don't think you will ever find a common mode rejection ratio of infinity.

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100% is impossible unless you decided that was just less than the least significant bit or no contribution to SNR or unless the CM is very low to begin with. CM chokes rarely operate more than two f decades with design attenuation. So only at low freq, can you achieve this.

The irony of INA’s is when they have 110 CMRR from laser trimmed resistors, people slap on a pair of wires to the input and think they’re good when wire imbalances will degrade it down to 40 dB or much worse easily without careful selection and using guard signals to block the CM noise to reduce the wire stray capacitance.

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In theory yes, but circuits built with real-world components will have some imperfections such as precision and tolerances so in practice differential ADCs don't reject 100% of common mode.

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  • \$\begingroup\$ So do the precision and tolerances of the components driving my ADC determine the CMRR? If so could you give an example. \$\endgroup\$
    – Max W
    Jun 15, 2021 at 19:52
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    \$\begingroup\$ Well, which ADC you mean? And if you try to make a differential amplifier, let's say with an op-amp and resistors, surely you can't have resistors with exactly identical resistance, or an op-amp with ideal mathematical function. \$\endgroup\$
    – Justme
    Jun 15, 2021 at 20:28
  • \$\begingroup\$ I'm using an AD9655. \$\endgroup\$
    – Max W
    Jun 15, 2021 at 21:11
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Since you are asking, WHY?

Assume you have 0 volts differential but different common mode voltage on the inputs.

You charge the input cap to 0 volts, but when it is switched from the input pins over to the ADC, the switches will cause different amounts of charge injection depending on the difference between the input pin common mode voltage and the ADC common mode voltage.

Since the switches are not exact replicas, the charge injection dependence will vary slightly between the switches.

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