EE 2115-03 - Lec 17 - 2026_10_05

Overview

Hiren Trada explains how negative feedback controls op-amp gain, then develops inverting and non-inverting amplifier analysis using ideal-op-amp assumptions, voltage dividers, KCL, and Ohm’s law. The lecture shows how a loaded, two-stage divider made from 51 kΩ, 2 kΩ, and two 1 kΩ resistors produces an effective feedback fraction of 1/104, and derives the standard gains −R2/R1 and 1 + R2/R1.

Key takeaways

Negative feedback lets an op amp avoid open-loop saturation by driving its input-terminal difference toward zero and setting gain through the feedback network.
A 51 kΩ resistor in series with an effective 1 kΩ lower branch returns about 1/52 of the output; halving that signal again with equal 1 kΩ resistors gives 1/104 feedback.
The ideal closed-loop gain is −R2/R1 for an inverting amplifier and 1 + R2/R1 for a non-inverting amplifier; the negative sign represents waveform inversion.
Negligible op-amp input current allows KCL to equate currents through the input and feedback resistors, making Ohm’s law a direct route to amplifier gain.
Virtual short means the input-terminal voltages are approximately equal under negative feedback, while virtual ground is the special case where one grounded input keeps the other near 0 V.

Chapters

0:00 Op-Amp Feedback: From Open-Loop Saturation to Controlled Gain

An ideal op amp has infinite input resistance, zero output resistance, infinite open-loop gain, and infinite bandwidth; practical devices approximate these properties.
Open-loop gain can drive the output beyond the available supply rails, so an op amp typically uses negative feedback to set a usable closed-loop gain.
Directly feeding the output to the inverting input creates a unity-gain voltage follower; feeding back only a fraction of the output allows larger gains.

5:00 Why a Single Feedback Divider Can Be Impractical

A feedback divider using 51 kΩ and 2 kΩ produces a gain of about 26.5 in the non-inverting configuration.
A target gain near 100 from one divider may require a much larger resistor ratio, such as 100 kΩ to 1 kΩ.
Very large resistance values can reduce current, and practical designs may be limited to available resistor values or benefit from using equal-valued on-chip resistors.

7:00 Building a Multi-Stage Feedback Divider

Trada introduces cascaded voltage-divider stages to reduce the returned feedback fraction without relying on one extreme resistor ratio.
The first divider creates an intermediate voltage Vx; a second divider made from two equal 1 kΩ resistors halves Vx before it reaches the inverting input.
Additional divider stages can further reduce the feedback signal and increase the resulting closed-loop gain.

13:00 Accounting for Divider Loading and the 1/104 Feedback Fraction

The added 1 kΩ + 1 kΩ stage is a 2 kΩ load in parallel with the original 2 kΩ resistor, giving an effective lower resistance of 1 kΩ.
With 51 kΩ in series with that effective 1 kΩ, the first divider returns approximately 1/52 of its input voltage.
The second equal-resistor stage halves that fraction again, producing an overall feedback fraction of 1/104 and a corresponding gain near 104.
For a 50 mV input amplitude, a gain near 104 predicts an output amplitude of about 5.2 V; LTspice can verify the result.

19:00 How Negative Feedback Brings Op-Amp Inputs Toward Equality

Negative feedback drives the op amp to reduce the difference between its inverting and non-inverting input voltages.
The two input voltages are not exactly equal at every instant in a real circuit because the response takes finite time.
The op amp amplifies the differential input; a common signal at both inputs is rejected in the idealized analysis.

23:30 Deriving the Inverting Gain with a Weighted Divider

The inverting configuration applies Vin through the input resistor to the inverting terminal and grounds the non-inverting terminal.
The feedback-node voltage is a weighted combination of Vin and Vout, derived using superposition and the assumption of negligible op-amp input current.
Using the large open-loop-gain approximation gives the standard inverting gain: Vout/Vin = −R2/R1.
The minus sign indicates that the output waveform is inverted relative to the input.

29:00 Checking Inversion in LTspice and Applying KCL

An LTspice example powered from +10 V and −10 V shows an amplified, inverted response to a small input signal.
A second derivation defines currents through R1 and R2, assumes negligible current enters the op-amp input, and applies KCL to set the resistor currents equal.
With the non-inverting terminal grounded, negative feedback holds the inverting node near 0 V, yielding Vout/Vin = −R2/R1 through Ohm’s law.

37:00 Deriving Non-Inverting Gain and Reviewing the Standard Forms

For a non-inverting amplifier, Vin is applied to the positive terminal and feedback forces the negative terminal toward the same voltage.
The voltage across R1 is approximately Vin, so IR1 = Vin/R1; zero input current makes IR2 equal IR1.
Adding the voltage across R2 to the voltage across R1 gives Vout/Vin = 1 + R2/R1.
The standard closed-loop gains are 1 + R2/R1 for non-inverting amplifiers and −R2/R1 for inverting amplifiers.

43:00 Virtual Short, Virtual Ground, and a Circuit-Analysis Checklist

With negative feedback and high open-loop gain, the two input terminals are treated as having nearly equal voltage even though they are not physically connected; this is the virtual-short approximation.
If the non-inverting input is physically grounded, the inverting input is approximately 0 V by virtual ground, a useful condition for analyzing inverting amplifiers.
For an unfamiliar circuit, first identify negative feedback, then determine whether the input enters the inverting or non-inverting terminal.
The closing exercise identifies an inverting amplifier with its non-inverting input grounded and asks students to determine whether a resistor affects the output; Trada recommends analyzing it rather than relying only on LTspice.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Hiren Trada.