How to obtain the CMR formula about component mismatch in the Application SBAA188

Andrea Verdecchia

My question is simple and maybe stupid, but I'd like to know how obtain the Equation 2 from the Figure 2 in the Application SBAA188. I don't understand how to simplify to that form.

over 6 years ago

0 Ryan Andrews over 5 years ago

TI__Guru 57296 points

Hello Andrea,

Thanks for your post!

The formula simply calculates the best-case CMR assuming the tolerance of the resistors and capacitors used in the input antialiasing filters. The terms "delta-R / R" and "delta-C / C" can be replaced with the component tolerance in decimal format (i.e. for 5% resistors, substitute 0.05 for "delta-R / R"). The other terms on the right are frequencies in Hz, where "f" is the frequency for which you want to calculate the CMR, and "fC" is the nominal -3 dB cutoff frequency of the R-C low-pass filter (fc = 1 / (2 * pi * R * C)).

Best Regards,

0 Andrea Verdecchia over 5 years ago in reply to Ryan Andrews

Prodigy 120 points

Hi Ryan, thanks for your reply.

I understood the concept of the formula but I'm asking how to reach that final formula. I know that maybe can be complicated to explain to me. I tried but my last result is a fractional expression and so i think that there are some simplifications which I'm not taking into account. For simplicity I attach my calculus. I know it's a strange request but if you could help me i will very grate.

Best regards.Notes_180424_095436_107.pdf

0 Ryan Andrews over 5 years ago in reply to Andrea Verdecchia

TI__Guru 57296 points

Hi Andrea,

Sorry, but I do not know how that formula was originally derived.

Best Regards,

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How to obtain the CMR formula about component mismatch in the Application SBAA188