#### Operational Amplifier:

An operational amplifier (Op-amp) is a multistage amplifier and consists of a differential amplifier stage, a high Common Emitter (CE) amplifier stage and Class-B Push-Pull emitter follower.
• It can perform mathematical operations as addition, subtraction, integration and differentiation.
• It has very high input impedance, very low output impedance and very high open loop voltage gain.
• It is a perfect voltage amplifier and is also referred to as Voltage Controlled Voltage Source (VCVS).
• Practical Op-amp: Zin = 2 MΩ, Zout = 100 Ω, and Av = 100000
• Ideal Op-amp: Zin = Infinite, Zout = Zero, and Av = Infinite
• Bandwidth of an Op-amp: The bandwidth of an op-amp depends upon the closed loop gain of the op-amp circuit.

#### Differential Amplifier:

It is a circuit that can accept two input signals and amplifies the difference between these two input signals. First input is called Non-inverting input and Second input is called inverting input. Output is in phase with first input and 180° out of phase with the second input.
• A differential amplifier is sometimes called long tail pair because two transmissions share a common resistor Re.
• The current through this common resistor is called tail current (It).

#### Input Characteristics of an Op-amp:

It consists of input bias current, input offset current and input offset voltage.
1. Input Bias Current: As practically βdc of both transistors are different so base currents will also be slightly different. Input Bias current is defined as the average of the dc base currents.
• Iin(bias) = ( Iβ1 + Iβ2 )/2
2. Input Offset Current: It is defined as the difference of the dc base currents.
• Iin(off) = Iβ1 - Iβ2
3. Input Offset Voltage: It is an input voltage that would produce the output error voltage in a perfect differential amplifier.
• Vin = Verror/Av
• Input offset voltage is generated because of a slight difference in Vbe and Rc of two transistor parameters.

#### Common Mode Gain (Acm):

The common mode signals are equal in amplitude and have the same phase.
• For a Perfectly Symmetrical differential amplifier V1 = V2 and Vout = 0. In practice, differential amplifier is not perfectly symmetrical so there will be some output voltage.
• Differential amplifier is not used in common mode. But most static interference, and other kinds of undesirable pickup are common mode signals.
• If differential amplifier is operating in an environment with a lot of electromagnetic interference, each base acts like a small antenna that pick up an unwanted signal voltage. Differential amplifier does not amplify these unwanted signals as they are common mode signals.
• Since equal voltages Vin(cm), drive both inputs simultaneously, there is almost no current through the wire between emitters.

#### Common Mode Rejection Ratio (CMRR):

The ratio of differential voltage gain to common mode voltage gain is called CMRR.
• The CMRR is the ability of DA to reject common mode signals. The larger the CMRR, the better is DA at eliminating common mode signals.

#### Slew Rate:

It is the change in output voltage divided by the change in time.

• It is a measure of how fast the output voltage can change.
• Since slew rate is a function of time, the slew rate can be used to determine the maximum operating frequency of the op-amp.
• Maximum Operating Frequency, fmax = Slew Rate / ( 2 Π Vp), Where: Vp is the Peak output voltage.

#### Inverting Amplifier:

When the input signal is given to the inverting input of op-amp, it acts as inverting amplifier.
• Feedback resistance Rf provides negative feedback as output is 180° out of phase with input which is being fed back to the input by Rf.
• An op-amp has infinite input impedance, so there will be zero current at the inverting input. Therefore there must be no voltage drop between the inverting and non-inverting inputs.
• This means the voltage at inverting input is zero because the other input is grounded.
• The zero volt at the inverting input terminal  is referred to as virtual ground. It is called as virtual ground as it is at zero volt but not physically connected to the ground.

#### Non-Inverting Amplifier:

When input signal is given to the non-inverting input of an op-amp, It acts as non-inverting amplifier.
• Feedback is almost equal to input voltage. Because of high open loop voltage gain, The difference between V1 and V2 is very small.
• Whenever we analyse a non-inverting amplifier, we can visualise a virtual short between the input terminals of the op-amp.
• Virtual short is a short for voltage but an open for current, and it exists as long as op-amp is operating in the linear region.
• Virtual short causes bootstrapping i.e. Non-Inverting input pulls the inverting input up or down to an equal value.

#### Voltage Follower:

Because of virtual short, It has very high input impedance and very low output impedance.
• It is used as Buffer Amplifier.

#### Op-amp Integrator:

It is a circuit that performs integration of the input signals.
• It is used to produce a Ramp output voltage.

#### Op-amp Differentiator:

It is a circuit that performs differentiation of the input signal.
• It is used to produce Rectangular Output from a ramp input.

#### Reference:

Albert Malvino and David J Bates, “Electronic Principles”, 7th Edition, TATA McGRAW HILL.