Operational Amplifier

Unit IX: Operational Amplifier (Op-Amp)

Duration: 4 Hours | Credit: ELX 133.3

Introduction to Operational Amplifiers

An operational amplifier (op-amp) is a high-gain, general-purpose electronic amplifier. It is one of the most versatile analog integrated circuits and forms the building block for countless analog applications including amplifiers, filters, oscillators, and signal processing circuits.

Op-Amp Structure and Terminals

Pin Configuration (8-Pin DIP Package)

• Pin 1: Offset Null (null input offset voltage)
• Pin 2: Inverting Input (-)
• Pin 3: Non-Inverting Input (+)
• Pin 4: Negative Supply Voltage (-V_CC)
• Pin 5: Offset Null (null input offset voltage)
• Pin 6: Output
• Pin 7: Positive Supply Voltage (+V_CC)
• Pin 8: NC (No Connection)

Common Op-Amp ICs

• LM741: General-purpose op-amp, classic design
• LM358: Single supply, low cost, popular
• TL072: JFET input, low noise, audio applications
• OPA2134: Audio grade, excellent specifications
• LM6171: High-speed, 2.5 GHz gain-bandwidth

Ideal Op-Amp Characteristics

Ideal vs Real Op-Amps

Op-Amp Operating Principle

Differential Amplifier

The op-amp is fundamentally a differential amplifier:

V_out = A₀ × (V₊ - V_-) = A₀ × V_d

Where:

• A₀: Open-loop voltage gain (100,000 to 1,000,000)
• V_d: Differential input voltage (V₊ - V_-)

Golden Rules of Ideal Op-Amps (Negative Feedback)

When negative feedback is applied:

1. Rule 1: The output voltage adjusts to make the differential input voltage zero (V₊ = V_-)
2. Rule 2: No current flows into the input terminals (I₊ = I_- = 0)

These rules simplify circuit analysis enormously!

Negative Feedback

Importance of Negative Feedback

• Stabilizes gain (makes it independent of op-amp open-loop gain)
• Reduces distortion
• Increases bandwidth
• Improves input and output impedance characteristics

Closed-Loop Gain with Feedback

A_CL = A₀ / (1 + β A₀)

Where β is the feedback factor. When A₀ is very large:

A_CL ≈ 1 / β

Inverting Amplifier

Circuit Configuration

• Input signal to inverting input through resistor R_in
• Non-inverting input connected to ground
• Feedback resistor R_f from output to inverting input

Voltage Gain

A_v = V_out / V_in = -R_f / R_in

Key features:

• Negative gain (180° phase shift)
• Input impedance = R_in
• Very simple and practical amplifier
• Gain determined by resistor ratio (independent of op-amp gain)

Applications

• Audio amplifier (with capacitor for AC coupling)
• Transimpedance amplifier (photodiode amplifier)
• Summing amplifier

Non-Inverting Amplifier

Circuit Configuration

• Input signal to non-inverting input
• Feedback network divider from output through R₂ to ground
• R₁ from divider tap to inverting input

Voltage Gain

A_v = V_out / V_in = 1 + (R_f / R₁)

Key features:

• Positive gain (no phase inversion)
• Input impedance approaches infinity (very high)
• Can't have gain less than 1
• Output impedance very low
• Excellent buffer/follower with unity gain

Special Op-Amp Configurations

Unity Gain Buffer (Voltage Follower)

Non-inverting amplifier with no feedback network:

• Gain = 1 (unity)
• Output = Input (follows input)
• Very high input impedance
• Very low output impedance
• Used for impedance matching and isolation

Summing Amplifier (Inverting Summer)

Multiple inputs through separate resistors to the inverting input:

V_out = -(R_f/R₁ × V₁ + R_f/R₂ × V₂ + ... + R_f/R_n × V_n)

Integrator

Feedback element is a capacitor (not a resistor):

• V_out is proportional to integral of input voltage
• Used in analog computers, analog-to-digital converters
• Low frequency response (blocked by coupling capacitor)
• Output ramps up or down with constant input

Differentiator

Input element is a capacitor (not a resistor):

• V_out is proportional to derivative of input voltage
• Used for edge detection, transient response
• High frequency noise can be problematic
• Requires series resistor for stability

Comparator

Op-amp used without negative feedback (open-loop):

• Compares two input voltages
• Output is saturated (full positive or negative)
• Used as zero-crossing detector, window detector
• Very fast switching

Op-Amp Frequency Response

Gain-Bandwidth Product (GBP)

GBP = A_CL × f_-3dB = A₀ × f₀

Where f_-3dB is the bandwidth at -3dB gain reduction

Slew Rate

Maximum rate of change of output voltage:

• Typical values: 0.5 - 13 V/μs
• Limits the rate of change (causes distortion at high frequencies with large amplitudes)
• Higher slew rate required for audio and video applications

Bandwidth Considerations

• Bandwidth inversely proportional to closed-loop gain
• Higher gain = Lower bandwidth
• Trade-off between gain and bandwidth
• Compensation techniques (external capacitors) improve stability

Op-Amp Practical Considerations

Input Offset Voltage

• Voltage required at input to bring output to zero
• Typical: 0.5 - 5 mV
• Can be nulled using offset trim potentiometer
• Temperature drifts over time

Bias Current

• Current flowing into input terminals
• BJT input op-amps: 20 - 500 nA
• JFET input op-amps: 1 - 100 pA
• Causes voltage drops across input resistances

Power Supply Requirements

• Dual supply: ±5V to ±15V (±12V typical)
• Single supply: +5V to +30V (requires biasing)
• Bypass capacitors (0.1μF and 10μF) required close to supply pins

Frequency Compensation

Stability and Phase Margin

• Op-amp can oscillate if feedback is not properly compensated
• Phase margin > 45° required for stability
• External capacitor across feedback resistor for low-frequency compensation
• Resistor in series with compensation capacitor for high-frequency compensation

Op-Amp Applications Summary

Key Takeaways

• Op-amp is a high-gain differential amplifier with voltage output control
• Negative feedback makes gain depend on passive components, not op-amp
• Golden rules: V₊ = V_- and I₊ = I_- = 0 simplify analysis
• Inverting gain: A_v = -R_f/R_in
• Non-inverting gain: A_v = 1 + R_f/R₁
• Frequency response limited by gain-bandwidth product
• Proper compensation and bypass capacitors essential for stability
• Op-amps form basis of analog signal processing circuits