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In the question, he told me from the begging that it is an ideal op amp .. so A(cm) =0 !! How can I find the CMRR then !!

I tried to analyze the circuit to be sure!! And i got the same !

the question

my steps

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    \$\begingroup\$ what is your question? The single ended gain of each input is combined into differential and common mode gain. If each side is not the same gain, then there is imbalance and thus a CM gain. Also if not ideal tolerance R ratios of 5:1 there is a CM error and gain. Also since gain is integrated in compensated real OA's CMRR degrades with rising frequency at the same rate. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Oct 3 '16 at 16:22
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Hint - it may be an ideal op-amp but the overall circuit is not ideally suited to reject common mode voltages applied to both input nodes simultaneously. You have to work out what change in output voltage results from a change in input voltage. When you do part (b) you will then see that the overall circuit is no longer ideal.

A(cm) =0 !! I tried to analyze the circuit to be sure!! And i got the same !

Then you did it incorrectly but that image you posted is too small for my old eyes to read.

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  • \$\begingroup\$ I reuploaded my answer again .. and i didn't find the mistake !! \$\endgroup\$ – Hashim Oct 3 '16 at 16:39
  • \$\begingroup\$ I'm struggling to read and cross ref one circuit to the other but I made a mistake in my original answer that I've corrected. Originally I said that (b) is ideal - I misread the numbers and I meant to say (b) is not ideal. (a) is ideal. \$\endgroup\$ – Andy aka Oct 3 '16 at 16:51
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    \$\begingroup\$ Your answer does appear to be correct, Vo = -5Va + 5Vb i.e. perfect common mode rejection. \$\endgroup\$ – Andy aka Oct 3 '16 at 16:54
  • \$\begingroup\$ Wonderful, but does that mean there is no value for CMRR !? I mean what should be my final answer for this part !? \$\endgroup\$ – Hashim Oct 3 '16 at 16:58
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    \$\begingroup\$ The rejection ratio for part (a) is infinite but for part (b) it isn't. \$\endgroup\$ – Andy aka Oct 3 '16 at 17:01
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Hint: Try using superposition. Figure out what the output response is if only \$V_a\$ is nonzero, then what is the response if only \$V_b\$ is nonzero. Then you can figure out what happens if the two inputs change by the same amount.

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