Determining CMRR for an op amp with two electrode inputs

[engineer23]

Homework Statement

I have an op amp with two electrode inputs. Each input has 5V of common 60 Hz noise. The size of the signal I want to measure is 9 mV. Signal to noise ratio needs to be 10 to 1.

Homework Equations

I know that CMRR = 20 log (DMG/CMG), where DMG is differential mode gain and CMG is common mode gain.

SNR = range of signal/range of noise

The Attempt at a Solution

I know that CMG is equal to the ratio of Vout to Vcommon. Is Vcommon 10 V since I have two 5V inputs? Or would it be the average (5V)? How do I get Vout? Where does the frequency come into play?

Also, SNR = 10 and range/size of signal is 9 mV = .009 V, so range of noise = .0009 V.

What is the equation for DMG?


Can anyone direct me to a good internet reference that explains these ideas? The class I am in does not use a textbook.

Thanks!

 

[KataKoniK]

Hi there,

I can definitely help you with your questions about op amps and signal to noise ratio.

First, let's start with the common mode gain (CMG). This is the ratio of the output voltage to the common mode voltage. In your case, since you have two 5V inputs, the common mode voltage would be 5V. So, to find the CMG, you would divide the output voltage (Vout) by 5V.

Next, let's look at the differential mode gain (DMG). This is the ratio of the output voltage to the differential input voltage. In your case, the differential input voltage would be 9 mV. So, to find the DMG, you would divide the output voltage (Vout) by 9 mV.

Now, let's talk about the frequency. The 60 Hz noise is the frequency of the common mode signal. This means that it is the same for both inputs. To eliminate this noise, you can use a high-pass filter with a cutoff frequency of 60 Hz. This will filter out the 60 Hz noise and leave only the differential signal.

To find the SNR, you would use the equation SNR = range of signal/range of noise. In your case, the range of signal would be 9 mV and the range of noise would be 0.009 V (since it is 10 times smaller than the signal). This means that your SNR is 1000 (or 30 dB).

To achieve a 10 to 1 signal to noise ratio, your DMG would need to be 10. This means that your Vout would need to be 90 mV (since 9 mV x 10 = 90 mV). So, to achieve this, you would need to adjust your op amp's gain accordingly.

I hope this helps and feel free to ask any other questions you may have. As for internet references, I recommend checking out websites like All About Circuits or Electronics Tutorials for more in-depth explanations and examples. Good luck with your project!

 

[piercas]

The common mode rejection ratio (CMRR) is a measure of how well an op amp can reject common mode noise, which is noise that is present on both inputs. In order to determine the CMRR for your specific op amp with two electrode inputs, you will need to know the differential mode gain (DMG) and the common mode gain (CMG).

To calculate the CMRR, you can use the equation CMRR = 20 log (DMG/CMG). The DMG is the ratio of the output voltage (Vout) to the difference between the two input voltages (Vin1 - Vin2). The CMG is the ratio of the output voltage to the average of the two input voltages (Vin1 + Vin2)/2.

In your case, the common mode noise is 60 Hz and has an amplitude of 5V. The signal you want to measure is 9 mV, which is much smaller than the common mode noise. This means that the common mode noise will have a larger impact on the output voltage, making it difficult to accurately measure the signal. In order to achieve a SNR of 10 to 1, the output voltage should be at least 90 mV.

To calculate the DMG, you will need to know the input voltage (Vin1 - Vin2) that corresponds to an output voltage of 90 mV. This can be found by using the equation for DMG: DMG = Vout/(Vin1 - Vin2). Once you have the DMG, you can then calculate the CMRR using the equation CMRR = 20 log (DMG/CMG).

The frequency of the noise does not come into play when calculating the CMRR, as it is a measure of the op amp's ability to reject common mode noise at all frequencies. However, it is important to consider the frequency when designing a circuit to minimize common mode noise.

I recommend doing some research on op amp CMRR and differential mode gain to gain a better understanding of these concepts. Some useful resources include textbooks on analog circuits and online articles and tutorials on op amp design and applications.