Common Mode Rejection Ratio (CMRR) is a measure of how effectively a differential amplifier rejects common mode signals. It is defined as the ratio of the differential voltage gain to the common mode voltage gain.

Given:
Differential voltage gain = 50 dB
Common mode voltage gain = 2 dB

To find the CMRR, we can convert the gains from decibels to linear scale using the formula:

Gain (linear scale) = 10^(Gain (dB)/20)

Therefore, the differential voltage gain in linear scale is:
Differential voltage gain = 10^(50/20) = 316.23

The common mode voltage gain in linear scale is:
Common mode voltage gain = 10^(2/20) = 1.58

Now, we can calculate the CMRR using the formula:
CMRR = Differential voltage gain / Common mode voltage gain

CMRR = 316.23 / 1.58 = 200

Since the CMRR is a ratio, it is usually expressed in decibels. To convert the CMRR from linear scale to decibels, we use the formula:

CMRR (dB) = 20 log10(CMRR)

CMRR (dB) = 20 log10(200) = 46.02 dB

Therefore, the correct answer is option C) 48 dB.

Explanation:
The common mode rejection ratio (CMRR) is a measure of how well a differential amplifier can reject common mode signals. A high CMRR indicates good rejection of common mode signals, while a low CMRR indicates poor rejection.

In this case, the differential voltage gain is 50 dB, which means that the amplifier amplifies the difference between the two input voltages by a factor of 316.23. The common mode voltage gain is 2 dB, which means that the amplifier amplifies the average of the two input voltages by a factor of 1.58.

The CMRR is calculated by dividing the differential voltage gain by the common mode voltage gain. In this case, the CMRR is 316.23 / 1.58 = 200.

To express the CMRR in decibels, we use the formula CMRR (dB) = 20 log10(CMRR), which gives us 46.02 dB. Therefore, the correct answer is option C) 48 dB.