The Common Mode Rejection Ratio (CMRR) is a measure of how well a differential amplifier can reject common mode signals. It is defined as the ratio of the differential mode gain to the common mode gain.

Formula: CMRR = Differential Mode Gain / Common Mode Gain

Given that the differential mode gain is 50 and the common mode gain is 0.2, we can calculate the CMRR as follows:

CMRR = 50 / 0.2 = 250

Therefore, the CMRR of the differential amplifier is 250.

Explanation:

To understand how the CMRR of a differential amplifier is calculated, let's look at the different types of signals that can be present at the input of the amplifier.

1. Differential mode signal:

A differential mode signal is a signal that is applied between the two input terminals of the differential amplifier. This type of signal is amplified by the differential gain of the amplifier.

2. Common mode signal:

A common mode signal is a signal that is applied to both input terminals of the differential amplifier in-phase. This type of signal is rejected by the differential gain of the amplifier.

3. Noise:

Noise is an unwanted signal that can be present at the input of the differential amplifier. It can be either differential or common mode.

The CMRR of a differential amplifier is a measure of how well it can reject common mode signals and noise. A higher CMRR indicates better rejection of common mode signals and noise.

In the given problem, the differential gain of the amplifier is 50, which means that it amplifies the differential mode signal by a factor of 50. The common mode gain of the amplifier is 0.2, which means that it attenuates the common mode signal by a factor of 0.2.

Using the formula for CMRR, we can calculate that the CMRR of the amplifier is 250. This means that the differential amplifier is good at rejecting common mode signals and noise, as the differential mode signal is amplified 250 times more than the common mode signal.

CMRR = Adm / Acm = 50/0.2 = 250