What's the common-mode gain of the following...?

Question

An op-amp data sheet specificies a CMRR of 300,000 and an Aol of 95,000. What is the common-mode gain?

Answer 1

0.3166

Which is found using:

CMR = 20log(Ad/Ac)

109.5 = 20log(95000/Ac)

Ac = 0.3166

BTW:

109.5 = 20log(300000)

.

Answer 2

My guess is Aol is voltage gain, open loop.

So any signal will be multiplied by 95 000.

The common mode rejection ratio is 300 000, so 1/300000 of the common mode signal gets amplified by 95000 to give 0.316 for a common mode gain.  A gain less than 1 is really a loss, and if you take 20 times log of (0.316) you'll get the power reduction of the common mode input as -10 dB.