An Operational Amplifier, or op-amp for short, is fundamentally a voltage amplifying device designed to be used with external feedback components such as resistors and capacitors between its output and input terminals. These feedback components determine the resulting function or “operation” of the amplifier and by virtue of the different feedback configurations whether resistive, capacitive or both, the amplifier can perform a variety of different operations, giving rise to its name of “Operational Amplifier”.

An Operational Amplifier is basically a three-terminal device which consists of two high impedance inputs. One of the inputs is called the Inverting Input, marked with a negative or “minus” sign, ( – ). The other input is called the Non-inverting Input, marked with a positive or “plus” sign ( + ).

A third terminal represents the operational amplifier's output port which can both sink and source either a voltage or a current. In a linear operational amplifier, the output signal is the amplification factor, known as the amplifier's gain ( A ) multiplied by the value of the input signal.

Fig.1 Operational Amplifier

Common Mode Gain

Common-mode voltage gain refers to the amplification given to signals that appear on both inputs relative to the common (typically ground). … This means the output is unaffected by voltages that are common to both inputs.

Voltage applied to both input is common, it is referred as common mode voltage V_cm. The common mode voltage V_cm can be DC, AC and a combination of AC and DC.

Fig.2 Common Mode Gain circuit
V_cm = (V₁ + V₂)/2
V_ocm = A_cm × V_cm
A_cm = V_ocm / V_cm

Differential Mode Gain

Instead of applying superposition theorem with V₁ and V₂ separately, a better way is to first combine V₁ and V₂ in a different format, viz. (V₁ - V₂). This is known as the differential mode input - V_d.

Differential mode component: V_d = (V₁ - V₂)

Gain = V_OUT / (V₁ - V₂)

Gain = V_OUT / V_d

This gain is known as the Differential Gain (A_d) as it is based on the differential input alone.

The common-mode rejection ratio (CMRR)

The common-mode rejection ratio (CMRR) is defined as the ratio of differential voltage gain A_d to the common-mode voltage gain A_CM.
i.e. CMRR = A_d / A_CM
Fig.3 The common-mode rejection ratio circuit

Slew Rate

Slew rate is defined as the maximum rate of change of output voltage caused by a step input voltage and is expressed in volts per microseconds.

Fig.4 Slew Rate Op-Amp circuit

V_s = V_mSin ωt

V_o = V_m Sin ωt
dV_o / dt = V_m ω Cos ωt
SR = dV_o/dt |_max V/µs

But, Slew rate:

Put max value of Cos ωt in the equation:

SR = V_m ω    Where (ω = 2πf)

SR = V_m 2πf

Slew rate indicates how rapidly the output of an op-amp can change in response to changes in the input frequency.