# Differential amplifier common mode gain

• paulmdrdo
In summary, the conversation discusses the derivation of equations 10-8 and 10-9 for a differential amplifier. The speaker is struggling with the derivation and asks for help. Another person suggests setting R2'/R1' = R2/R1 for the differential amplifier to make sense. For sensitivity analysis, the suggestion is to add an error term to a single resistor and recalculate the common mode gain, which may result in discrepancies from the original result.
paulmdrdo
Summary:: Differential amplifier common mode gain derivation of forumlas

I'm having a hard time deriving for equations 10-8 -10-9.

I tried adding equation's 18-6 and 18-7 but cannot proceed with the derivation. I need help on this. Thank you!

It's kind of a confusing section, much appears to be left out.

For this to be a differential amp, you would have to set R2'/R1' = R2/R1. Then the difference mode gain is R2/R1 and the common mode gain is 0. If you don't do this, I don't think the premise makes sense.

Then for the sensitivity analysis, I would pick any single resistor and add in an error term eg. R2 → R2 + ΔR. Then recalculate the common mode gain. You may find some discrepancies from their result because of how you introduce the component value error term.

## 1. What is a differential amplifier common mode gain?

A differential amplifier common mode gain is a measurement of the amplifier's ability to reject common mode signals, which are signals that are present on both of its input terminals. It is a ratio of the output voltage to the common mode voltage at the input.

## 2. Why is the common mode gain important in differential amplifiers?

The common mode gain is important because it determines the amplifier's ability to distinguish between the desired signal and any unwanted noise or interference that may be present on both input terminals. A higher common mode gain means better rejection of common mode signals, resulting in a cleaner output signal.

## 3. How is the common mode gain calculated?

The common mode gain is calculated by dividing the output voltage by the common mode voltage at the input. It is usually expressed in decibels (dB) and can be calculated using the formula: CM Gain = 20log(Vout/Vcm).

## 4. What factors can affect the common mode gain of a differential amplifier?

The common mode gain of a differential amplifier can be affected by various factors such as the amplifier's design, component tolerances, and external noise sources. It can also be affected by the amplifier's power supply voltage and temperature.

## 5. How can the common mode gain be improved in a differential amplifier?

The common mode gain can be improved in a differential amplifier by using high-quality components, minimizing external noise sources, and implementing proper shielding and grounding techniques. Additionally, using a higher power supply voltage and maintaining a stable temperature can also help improve the common mode gain.

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