Unit 5: Operational Amplifiers and Applications - Subjective Questions

An Operational Amplifier (Op-Amp) is a high-gain, direct-coupled (DC) differential amplifier that amplifies the difference between two input voltages.

Basic features:

• Very high open-loop voltage gain ( to )
• Very high input impedance ( to )
• Very low output impedance ( few )
• Two inputs: inverting () and non-inverting ()
• Wide bandwidth and good frequency response

Why operational:
It was originally used to perform mathematical operations such as addition, subtraction, integration, differentiation, and multiplication in analog computers. With suitable feedback components, the same device can perform these operations, hence the name.

Output relation:

An Op-Amp internally consists of four main stages connected in cascade:

1. Input Stage (Dual-Input Balanced-Output Differential Amplifier):

• Provides high input impedance and high CMRR
• Amplifies the difference of the two input signals

2. Intermediate Stage (Dual-Input Unbalanced-Output Differential Amplifier):

• Provides additional voltage gain
• Converts the double-ended output into a single-ended signal

3. Level Shifter (Level Translator) Stage:

• Since the Op-Amp is directly coupled, a DC voltage builds up. This stage shifts the DC level down toward zero to prevent output distortion.

4. Output Stage (Complementary Push-Pull Amplifier):

• Provides low output impedance and high current-driving capability
• Increases output voltage swing

Block flow:

The IC 741 is available in an 8-pin Dual-In-line Package (DIP). The pin assignments are:

Notes:

• Pins 1 and 5 are connected to a potentiometer whose wiper goes to for offset nulling.
• Typical supply is .

Characteristics of an Ideal Op-Amp:

• Infinite open-loop gain:
• Infinite input impedance: (no input current is drawn)
• Zero output impedance: (acts as an ideal voltage source)
• Infinite bandwidth: amplifies all frequencies equally
• Infinite CMRR: rejects common-mode signals completely
• Infinite slew rate: output responds instantly
• Zero offset voltage: output is zero when both inputs are equal

Comparison with practical Op-Amp (e.g., 741):

CMRR is a measure of an Op-Amp's ability to reject signals common to both inputs while amplifying the difference signal.

Definition:
It is the ratio of differential-mode gain () to common-mode gain ():

Expressed in decibels:

Explanation of terms:

• = gain for the difference between two inputs
• = gain for the signal common to both inputs (e.g., noise, hum)

Significance:

• A high CMRR means better rejection of noise, temperature drift, and interference common to both inputs.
• Ideal Op-Amp: ; Practical 741: .
• Essential in instrumentation where small differential signals ride on large common-mode noise.

Slew Rate (SR) is defined as the maximum rate of change of output voltage per unit time, expressed in :

Cause:

• It is caused by the limited charging current available for the internal compensating capacitor. The capacitor cannot charge/discharge faster than , limiting how fast the output can change.

Effect on performance:

• For large-amplitude, high-frequency signals, the output cannot follow the input, causing slew-rate distortion (a sine wave becomes triangular).

Relation to maximum frequency (full-power bandwidth):
For a sinusoidal output ,

For the 741, .

A differential amplifier can be configured in four ways depending on the number of inputs and outputs:

1. Dual-Input, Balanced-Output:

• Two input signals applied to both transistors; output taken between two collectors.
• Highest performance; used as the input stage of Op-Amps.

2. Dual-Input, Unbalanced-Output:

• Two inputs applied; output taken from one collector with respect to ground.
• Converts differential to single-ended signal.

3. Single-Input, Balanced-Output:

• One input applied; output taken between the two collectors.

4. Single-Input, Unbalanced-Output:

• One input applied; output taken from one collector w.r.t. ground.
• Simplest configuration.

Key output relation (differential):

The dual-input balanced-output configuration provides the best CMRR and is preferred for the Op-Amp input stage.

In an inverting amplifier, the input signal is applied to the inverting terminal () through resistor , the non-inverting terminal () is grounded, and feedback resistor connects the output to the inverting input.

Derivation (using virtual ground concept):
Since (grounded) and the Op-Amp has infinite gain, . Hence node A is a virtual ground.

Input current:

Since no current enters the ideal Op-Amp, all current flows through :

Setting :

Voltage gain:

The negative sign indicates a phase shift between input and output.

In a non-inverting amplifier, the input signal is applied directly to the non-inverting terminal (). The output is fed back to the inverting terminal () through resistor , and connects the inverting input to ground.

Derivation:
Using the virtual short concept, .

The feedback network forms a voltage divider:

Since :

Voltage gain:

Key points:

• Output is in phase with input (no phase inversion).
• Gain is always .
• Very high input impedance.

Virtual Short:
Because an ideal Op-Amp has infinite open-loop gain, the differential input voltage must be nearly zero for a finite output:

Thus the two input terminals are at the same potential even though no current flows between them. This is called a virtual short.

Virtual Ground:
When the non-inverting terminal is grounded (), the virtual short forces . So the inverting node behaves as if it is grounded, without being physically connected to ground. This is the virtual ground.

Importance:

• Simplifies analysis of feedback circuits (inverting amp, summing amp, integrator).
• Allows use of KCL at the input node assuming and zero input current.
• Makes gain expressions depend only on external resistors, independent of Op-Amp gain.

A summing amplifier produces an output proportional to the sum of several input voltages. Inputs are applied through resistors to the inverting terminal; is the feedback resistor and the terminal is grounded.

Derivation (virtual ground at node A, ):
Applying KCL:

Output:

Case 1 — Equal weights ():

Case 2 — Averaging amplifier:
If (where = number of inputs), then

which gives the average of the inputs.

A difference amplifier amplifies the difference between two input signals while rejecting the common-mode component. Signal is applied through to the inverting input, and through to the non-inverting input, with to ground and as feedback.

Derivation:
Using superposition:

Due to (inverting, ):

Due to (non-inverting):
Voltage at terminal:

For and :

When all resistors are equal ():

This directly subtracts the two inputs.

A Voltage Follower (unity-gain buffer) is a special case of the non-inverting amplifier where the output is directly connected to the inverting input (, ).

Working:
Due to the virtual short, , and since the output equals :

Voltage gain:

So the output follows the input exactly (unity gain, no phase inversion).

Characteristics:

• Very high input impedance
• Very low output impedance
• Unity gain

Applications:

• Impedance matching / buffering between high-impedance source and low-impedance load
• Isolation between circuit stages
• Preventing loading effect on sensitive signals
• Used as a buffer in sample-and-hold and ADC circuits

An integrator produces an output proportional to the integral of the input signal. It uses an input resistor and a feedback capacitor connected to the inverting terminal.

Derivation (virtual ground ):
Input current:

This current charges the capacitor:

Equating:

Integrating:

Interpretation:

• Output is the time integral of the input, scaled by .
• A square wave input gives a triangular output.

Limitations:

• At DC (zero frequency), the capacitor acts as open circuit, giving very high gain and causing output saturation due to offset/bias currents.
• Remedy: A large resistor is placed across to limit low-frequency gain (practical integrator).

A differentiator produces an output proportional to the rate of change (derivative) of the input signal. It uses an input capacitor and a feedback resistor at the inverting terminal.

Derivation (virtual ground ):
Current through capacitor:

This flows through :

Output:

Interpretation:

• Output is proportional to the slope of the input.
• A triangular input produces a square-wave output.

Drawbacks:

• Gain increases with frequency ( decreases), making the circuit noise-sensitive and prone to high-frequency instability.
• Remedy: A small series resistor with (and sometimes a feedback capacitor) is added to limit high-frequency gain (practical differentiator).

A Comparator is an Op-Amp operated in open-loop (or with positive feedback) that compares an input voltage with a reference voltage and produces a digital-level output ( or ).

Basic operation:

Non-Inverting Comparator:

• Input applied to terminal, reference to terminal.
• Output goes HIGH when .

Inverting Comparator:

• Input applied to terminal, reference to terminal.
• Output goes LOW when .

Zero-Crossing Detector:

• A comparator with .
• The output switches state each time the input signal crosses zero volts.
• Converts a sine wave into a square wave.

Applications: Waveform generators, ADCs, level detectors, and Schmitt triggers.

Comparison of Inverting vs Non-Inverting Amplifiers:

Summary: The inverting amplifier inverts and can attenuate or amplify, while the non-inverting amplifier preserves phase and always amplifies with gain and offers higher input impedance.

An Op-Amp datasheet specifies key parameters needed for reliable design:

Important parameters:

• Supply Voltage (): Operating supply range (e.g., to ).
• Input Offset Voltage (): Small DC voltage needed at input to make output zero ( for 741).
• Input Bias Current (): Average current into inputs ().
• Input Offset Current (): Difference between the two input bias currents.
• Open-Loop Gain (): .
• CMRR: .
• Slew Rate: .
• Gain-Bandwidth Product (GBW): .
• Input/Output Impedance, Output Voltage Swing, Power Dissipation.

Importance of reading datasheets:

• Ensures the device operates within safe supply and temperature limits.
• Helps select the right Op-Amp for bandwidth, accuracy, and speed requirements.
• Allows prediction of errors from offset, bias current, and slew-rate limitations.
• Prevents design failures and improves reliability.

Given:

• Slew rate,
• Peak amplitude,

Formula (full-power bandwidth):

Calculation:

Effect of exceeding :

• If the signal frequency exceeds at this amplitude, the output cannot change fast enough to follow the input.
• This causes slew-rate distortion: the sinusoidal output becomes distorted into a triangular waveform, reducing the effective amplitude and introducing harmonic distortion.

Given:

• ,
• ,

Output equation for inverting summer:

Step 1 — Compute gain factors:

Step 2 — Substitute values:

Result:

The weighted contributions of the two inputs cancel exactly, giving zero output.