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# Resistors network matching for fully-differential amplifiers

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#### Junus2012

Dear friends,

When we talk about the feedback resistor matching of the fully-differential amplifier, say the circuit below

I have found the concept of the feedback matching little bit differernt when I reas the manuals from Texas Instrument and from Analog Devices, may be I am not getting the point correctly ofr sure. So up to my understanding,

Matching for the FDA means matching the ratio of RF2/I2 to be equal to the ratio of RF1/RI1. Therefore, I can match RF2 and RI2 in one group, say at the top of the amplifier, and match the RF1 with RI1, say at the bottom of the amplifier.

However, if matching means that I have to match RF2 with RI2 with RF1 with RI1, the story will be different and more difficult with regard to the connectivity, then in this case I have to put all of these resistors in one matching array.

Regards

Regards, Dana

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• CMR Analysis IA.pdf
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Junus2012

### Junus2012

Points: 2
Thank you very much Dana for sharing this very nice and helpful document,

I am sad that I am still not extracting the answer of my question from the document

You are essentially asking if you need to match the upper with the lower resistors. Apparently you didn't attempt to answer the question yourself, e.g. to what would be the effect of changing the absolute resistance of RI1 and RF1.

But without assuming amplifier properties like input current or common mode input impedance, the question can't be answered. In case of an ideal amplifier, there's no effect.

Junus2012

### Junus2012

Points: 2
The mathcad sim seems to imply only the ratio, or feedback fraction, is
of concern. But then the practical aspect, what if the resistors are not
in thermal equilibrium, or equal in parasitic C loading. In other words
not in same array, clearly the potential for unbalanced gains thru Inv and
Noninv path would pose a problem. Or as FVM points out......

Just the AC effects due to unbalanced magnitude of R x Cparasitic causes issues.

Regards, Dana.

Last edited:
Hi,

A way of being certain is (sorry) grabbing diff amp gain formulas from somewhere and a bit of time spent on calculatoring through four cases of Vin times gains when: the four resistor values are equality + equality /equality + equality, equality + equality/inequality + inequality, equality +inequality/equality + equality, etc. Those four numbers/results will answer your question.
--- Updated ---

... dohhh, or much quicker and viewable on a graph by just simulating four diff amps with their various gain networks' resistor matches and mismatches.

Last edited:
Junus2012

### Junus2012

Points: 2

This is from Analog Devices,

It shows if the two feedback ratios are perfectly matched (independently), then we have no common to fully differential gain as seen from Eq (3), or Eq (1).

But this for sure doesn't mean that I am going to choose different values for Rf1 from Rf2 or Rs1 from Rs2, because it will not satisfy the balanced condition. I will choose them equally in absolute value but during matching, I want to match the upper resistors and the down resistors individually to reduce the layout complexity or not necessary complications.

Just consider please for the case of high order fully differential active filters, I don't believe that people are matching the upper components with the bottom components.

Thank you for your discussions and help
Regards

Keep in mind thats a DC discussion you are showing. But if you have
unmatched Rf or Ri pairs, even though fdbk factor is matched, for
the Rf/Ri pairs, that means that AC considerations, eg. poles and zeros
created by parasitic C, will result in degradation of AC CM performance.

All because for AC case its absolute values of R's that matter when
considering AC CM performance.

Regards, Dana.

Last edited:
Junus2012

Points: 2