Analog Electronics - Operational Amplifiers Complete Study Notes

Introduction

An operational amplifier (Op-Amp) is an integrated circuit that amplifies the difference between two input voltages and produces a single output. From signal point of view, the Op-Amp has two input terminals and one output terminal as shown in figure below.

 Characteristics of Ideal Op-Amp

The ideal Op-Amp senses the difference between two input signals and amplifies this difference to produce an output signal. The output terminal voltage is the voltage at the output terminal measured with respect to ground.

The ideal Op Amp equivalent is shown in figure below.

Here,

A_OL = open loop gain

1. It has infinite input impedance and zero output impedance.
2. The common mode gain is zero (or) equivalently, common mode rejection ratio is infinite.
3. The open loop gain of ideal op-amp is infinite
4. The ideal op-amp has infinite bandwidth and infinite slew-rate.
5. We stated that if the open loop gain (A_OL) is very high, then the two input V₁ and V₂ must be nearly equal. Since, if V₂ is at ground potential, voltage V₁ must also be approximately zero volts as shown below.                                                                                                                                                                                   

              Figure : Voltage Controlled Voltage Source

 Transfer Characteristics of Op-Amp

 Feedback in Op-Amp

 Negative Feedback:

             Figure: Non-Inverting Amplifier

So, for any input V_i in the range of “mV” or 0V, output V₀ will be very close to 0.

Positive Feedback: 

Figure: Positive Feedback Amplifier

 Note: Multi vibrator works in open or closed loop of positive feedback.

Virtual-Ground and Comparator

• Virtual ground theory is applicable only in “Negative feedback”. It is not applicable in positive feedback and open loop.
• Comparator theory is applicable for open loop and positive feedback.

Table: Comparison between Negative feedback and Open-loop

 Slew-Rate

Slew rate is defined as the maximum rate at which amplifier output can change. It is expressed in Volts per microsecond (V/μs) i.e.

Here, ∆V₀ = Small change in output voltage in a small interval ∆t.

In terms of input voltage, slew rate can be expressed as:

Here, A_CL = closed loop gain,

        ∆V_i = Small change in input voltage in a small interval ∆t

 Differential and Common Mode operation

 Differential Inputs:

When separate inputs are applied to the op-Amp, the resulting difference signal is the difference between the two inputs

i.e.

V_d = V_i1 – V_i2

Here, V_i1, V_i2 = inputs to the op-Amp.

 Common Inputs:

If there is no difference between the input signals, a common signal element due to the two input signals can be defined as the average of the sum of the two signals.

Here, V_i1, V_i2 are the inputs to the Op-Amp.

 Output-Voltage:

Since, any signal applied to an Op-Amp is generally have both in phase and out of phase components, the resulting output can be expressed as:

V₀ = A_dV_d + A_cV_c

Here,

A_d = differential voltage

V_c = Common voltage

A_d = Differential gain of the amplifier

A_c = common mode gain of the amplifier

Common Mode Rejection Ratio: (CMRR)

CMRR is defined as the ratio of differential voltage gain to the common mode gain.

Applications of Operational amplifiers

• Inverting Amplifier
• Non-inverting Amplifier
• Differentiator
• Differential Amplifier
• Voltage follower
• Selective inversion circuit
• Current-to-voltage converter
• Active rectifier
• Integrator
• Comparator
• Filters
• Voltage comparator
• Signal Amplifier

 Inverting-Amplifier:

 Non-Inverting Amplifier

The voltage gain for the non-inverting amplifier is given by:

 Voltage Adder:

 Inverting Adder:

 Non-Inverting Adder:

 Voltage Subtractor Circuit

A Voltage Subtractor circuit consist of an inverting amplifier and a summing amplifier. Output of the inverting amplifier is given by:

 Difference Amplifier:

Consider the difference amplifier shown below:

Applying Superposition, we consider only one input at a time as shown in below figures

When only V₁ is present,

 Differentiator circuit:

 Integrator circuit:

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