Define slew rate and CMRR.

Slew Rate:

The slew rate (SR) of an operational amplifier (op-amp) is defined as the maximum rate of change of its output voltage with respect to time. It is an important parameter that characterizes the op-amp's ability to respond to rapidly changing input signals. The slew rate is typically specified in volts per microsecond (V/µs).

Mathematically, the slew rate can be expressed as:

SR = \frac{\Delta V_{out}}{\Delta t}

where:

• ΔVout is the change in output voltage
• Δt is the corresponding change in time

The slew rate is limited by the internal design of the op-amp, primarily by the slew rate of the input stage and the slew rate of the output stage. The input stage slew rate is determined by the charging and discharging time constants of the input transistors, while the output stage slew rate is determined by the charging and discharging time constants of the output transistors.

A high slew rate is desirable in many applications, such as high-speed signal processing, video amplifiers, and data converters. A high slew rate allows the op-amp to accurately amplify and reproduce fast-changing signals without introducing distortion.

CMRR:

The common-mode rejection ratio (CMRR) of an operational amplifier (op-amp) is a measure of its ability to reject common-mode signals, which are signals that appear on both the inverting and non-inverting inputs of the op-amp. A high CMRR is desirable because it ensures that the op-amp will amplify the differential signal (the difference between the two input signals) while rejecting the common-mode signal.

The CMRR is typically expressed in decibels (dB) and is calculated using the following formula:

CMRR = 20 \log_{10}\left(\frac{A_d}{A_{cm}}\right)

where:

• Ad is the differential-mode gain of the op-amp
• Acm is the common-mode gain of the op-amp

A high CMRR is important in many applications, such as instrumentation amplifiers and differential amplifiers. A high CMRR helps to minimize the effects of noise and interference that may be present in the common-mode signal.

CMRR is affected by several factors, including the design of the op-amp, the operating frequency, and the feedback network. In general, a higher CMRR can be achieved by using op-amps with a low input offset voltage and a high open-loop gain.