I was given the following question on a homework assignment dealing with op-amps.


"Given an input of 0.1V DC with a gain of 10 and a common mode voltage of 0.009, what is the common mode output with a CMRR of 70dB? What is the total output voltage?"

So far, the only thing I have been able to calculate is the common mode gain, which has gotten me nowhere. I'm not even sure that part is correct, as I assume the gain of 10 the instructor gave us is a closed loop gain, and I was under the impression that open-loop gain was used in the following equation:


CMRR=20log(differential V gain/CM gain)
70 =20log(10/CM gain)
3.5 =log(10/CM gain)
10(to 3.5 power) =(10/CM gain)
CMgain=10/10(to3.5)
=0.0032



I have spent hours researching this question and am obviously missing something. Can anyone please help me figure out where I went wrong? Thanks!!

 

Well...

Homework questions...professors and books really need to get it together. No circuit, no mention of supplies (single, dual), or configuration. However, since the gain is stated to be positive then I think it would be safe to say that the configuation is either a non-inverting or difference configuration. I vote for non-inverting.

A non-inverting op-amp with a gain of 10 and an input of 100mV will produce a 1V output ideally. You have a common mode voltage of 9mV and a CMRR of 75 dB.

So all you need to do is convert 75dB into an absolute number: 10^(75/20) and divide 9mV by the result.

Your final answer will be 1V + x, where x is the additional voltage offset from the common mode voltage.

 

Thank you so much! I really appreciate your time on this one-our professor makes me feel completely stupid if I ask him anything, although I don't believe he means to do so. The assignment was hand-written by the professor and photocopied, and my class has had to make a lot of assumptions on various parts of it! Thanks again!