Operational Amplifiers

Why it matters

Operational Amplifiers (Op-Amps) are fundamental components in analog electronics, widely used in signal conditioning, filtering, and mathematical operations such as addition, subtraction, integration, and differentiation. Their versatility and precision make them essential in various applications, from audio equipment to instrumentation and control systems.

Key ideas

• Definition: An operational amplifier is a high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output.
• Ideal Op-Amp Characteristics:
  • Infinite open-loop gain
  • Infinite input impedance
  • Zero output impedance
  • Infinite bandwidth
  • Zero offset voltage
• Practical Op-Amp Characteristics: While ideal characteristics are theoretical, practical Op-Amps have very high gain, high input impedance, low output impedance, and wide bandwidth.
• Common Configurations:
  • Inverting Amplifier: Provides phase inversion and gain determined by external resistors.
  • Non-Inverting Amplifier: Offers gain without phase inversion.
  • Voltage Follower: Provides unity gain with high input impedance and low output impedance.
  • Summing Amplifier: Combines multiple inputs into a single output.
  • Differential Amplifier: Amplifies the difference between two input voltages.

Formulas

These closed-loop formulas assume stable negative feedback and linear unsaturated operation. Then ideal input currents are zero and V+ ≈ V−. A virtual short is not valid in saturation or with positive feedback. Check output swing, common-mode range, bandwidth and slew rate.

• Inverting Amplifier Gain: A_v = -R_f / R_in
  • A_v: Voltage gain (unitless)
  • R_f: Feedback resistor (Ohms)
  • R_in: Input resistor (Ohms)
• Non-Inverting Amplifier Gain: A_v = 1 + (R_f / R_in)
  • A_v: Voltage gain (unitless)
  • R_f: Feedback resistor (Ohms)
  • R_in: Input resistor (Ohms)

Worked example

Problem: Calculate the output voltage of an inverting amplifier with R_f = 100 kΩ, R_in = 10 kΩ, and an input voltage of 0.2 V, with the non-inverting input grounded and adequate ±12 V supply rails.

1. Identify the formula: Use the inverting amplifier gain formula: A_v = -R_f / R_in
2. Calculate the gain: A_v = -100 kΩ / 10 kΩ = -10
3. Calculate the output voltage: V_out = A_v * V_in = -10 * 0.2 V = -2 V

Final Answer: −2 V, provided the chosen op-amp supports the input range, output swing and load.

Common mistakes

• Confusing inverting and non-inverting configurations.
• Ignoring the sign of the gain in inverting amplifiers.
• Miscalculating resistor values or units.
• Assuming ideal characteristics in practical scenarios without considering limitations.

For GATE EC

Questions often involve analyzing Op-Amp circuits to determine gain, input/output impedance, or output voltage. Practice solving problems with different configurations and understanding the impact of non-ideal characteristics.

Quick check

1. What is the voltage gain of a voltage follower?
2. How does an inverting amplifier affect the phase of the input signal?
3. What is the primary function of a differential amplifier?

Answers: 1. 1 (unity gain), 2. Inverts the phase, 3. Amplifies the difference between two input voltages.