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Lesson 9.5 • Competency 9.3Complete Lesson
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Operational Amplifiers (Op-Amps)

Analyze ideal operational amplifier properties (infinite gain, infinite input impedance, zero output impedance), virtual ground concept, inverting/non-inverting amplifiers, voltage followers, summing amplifiers, and comparators.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • State the 5 golden characteristics of an ideal operational amplifier and deduce the virtual short-circuit concept (V+ ≈ V-).
  • Derive closed-loop voltage gain expressions: Inverting A_v = -R_f / R_in, Non-inverting A_v = 1 + R_f / R_1, and Buffer A_v = 1.
  • Analyze open-loop comparator switching behavior and explain supply rail saturation (+V_sat, -V_sat).

Core Theory & Concepts

The Operational Amplifier (Op-Amp) is a high-gain DC-coupled differential voltage amplifier that forms the cornerstone of modern analogue signal processing. By applying stable negative feedback through external resistors, highly precise and temperature-independent amplifier circuits can be built.

Inverting Amplifier Gain

Because input current into the inverting terminal is zero, current through R_in equals current through R_f, yielding V_out = -(R_f / R_in) V_in.

A_v = -\frac{R_f}{R_{\text{in}}}, \quad V_{\text{out}} = -\frac{R_f}{R_{\text{in}}} V_{\text{in}}

Non-Inverting Amplifier Gain

Feedback voltage to the inverting terminal must match V_in at the non-inverting terminal, producing closed-loop gain A_v = 1 + (R_f / R_1).

A_v = 1 + \frac{R_f}{R_1}, \quad V_{\text{out}} = \left(1 + \frac{R_f}{R_1}\right) V_{\text{in}}

Rail Saturation

An Op-Amp output cannot exceed its DC supply voltages. When the calculated linear output exceeds ±V_s, the output clips to the saturation rails.

-V_{\text{sat}} \le V_{\text{out}} \le +V_{\text{sat}}

Common Misconceptions

Misconception

An Op-Amp can output 50 V if supplied by ±12 V rails as long as the theoretical gain is 100.

Physical Clarification:The output is strictly limited by the physical supply rails (typically 1–2 V below rails, or rail-to-rail). It clips at saturation.

Syllabus Topic Outline

Competency 9.3
  • 1Op-Amp symbol, inverting (-) and non-inverting (+) inputs, power supply rails (±V_s)
  • 2Ideal Op-Amp properties: A_OL = ∞, R_in = ∞, R_out = 0, bandwidth = ∞
  • 3Virtual ground and virtual short principles under negative feedback
  • 4Inverting amplifier: derivation of V_out = -(R_f / R_in) V_in
  • 5Non-inverting amplifier and voltage follower buffer circuits
  • 6Inverting summing amplifier and open-loop voltage comparators

Practice Problems

1
Competency 9.3 • intermediate

In an inverting Op-Amp circuit, R_in = 10 kΩ and R_f = 50 kΩ. If input voltage V_in = +1.2 V with supply rails at ±15 V, calculate the output voltage V_out in Volts.

V