EE 2115-01 - Lec 18 - 2026_10_07

Overview

Hiren Trada reviews ideal op-amp assumptions—negligible input current, virtual short, and virtual ground—and applies them with Ohm’s law, KCL, and current division to analyze a multi-resistor feedback circuit. He then compares that calculation with a Y-to-delta simplification and LTspice verification, before introducing the summing amplifier and pointing students to free Canvas textbooks and upcoming practice problems.

Key takeaways

For an op-amp operating with negative feedback, negligible input current and near-equal input voltages allow the inverting node to be treated as a virtual ground when the non-inverting input is grounded.
A virtual short is an analytical approximation: the op-amp inputs are at nearly the same potential but are not physically connected.
In the three-resistor feedback example, the virtual-ground node makes R1 and R3 parallel; Ohm’s law, current division, and KCL then determine the inverting gain.
A Y-to-delta conversion can reduce a T-feedback analysis to a standard inverting-amplifier form when grounded branches carry no current.
LTspice supports the virtual-ground approximation in the example: the inverting input remains within about 0.7 mV of 0 V.
Multiple signals applied through separate resistors to one op-amp input form a summing amplifier; equal 1 V DC inputs produce a 2 V DC sum in the unity-gain illustration.

Chapters

0:00 Course Resources and Upcoming Op-Amp Practice

Hiren Trada plans to post practice problems on Zener diodes, comparators, and op-amps.
Two free textbooks linked on Canvas provide additional reading and practice problems; one is a legal download and one is licensed through the library.
Students can ask questions by email or during office hours.

2:46 Virtual Short and Virtual Ground in an Op-Amp

An op-amp’s very large input resistance means negligible current flows between its input terminals.
With negligible current, the voltage drop between the inputs is approximately zero, so the terminals are treated as a virtual short—not a physical connection.
When the non-inverting input is grounded, the virtual short makes the inverting input approximately 0 V, creating a virtual ground.

4:09 Setting Up the Three-Resistor Feedback Analysis

The example uses a 10 kΩ input resistor and a feedback network containing 10 kΩ and two 100 kΩ resistors.
Trada labels the feedback elements R1, R2, and R3, then uses the virtual-ground node to identify R1 and R3 as parallel branches.
The op-amp input current is assumed to be zero, so currents entering the inverting node must balance under KCL.

10:25 Using Current Division and KCL to Find Inverting Gain

The parallel combination of R1 and R3 is placed in series with R2 to find the total feedback-path current using Ohm’s law.
Current division determines the portion of that total current flowing through R1; the example gives a fraction of approximately 0.91.
Applying KCL at the virtual-ground node relates the input current to the R1 current and yields an inverting transfer relationship.
The negative sign in the derived gain indicates that the output is inverted relative to the input; assumed current directions do not change the final result.

18:00 Replacing T Feedback with a Y-to-Delta Equivalent

A T-shaped feedback network can be transformed into an equivalent pi/delta network using a Y-to-delta resistor conversion.
With the virtual-ground and physical-ground connections, two branches have no voltage across them and carry no current, so they can be omitted from the simplified analysis.
The remaining resistor makes the circuit equivalent to a standard inverting amplifier, with gain expressed as −R2/R1.
Trada presents this conversion as an alternative to the longer KCL and current-division calculation, not as a required problem-solving method.

24:10 LTspice Checks and the Summing-Amplifier Preview

LTspice plots show the inverting input staying within roughly 0.7 mV of ground while the non-inverting input is grounded.
The output waveform is amplified and agrees approximately with the gain predicted by circuit analysis; students can also test the transformed resistor network in LTspice.
Adding multiple input voltages through separate resistors at the same inverting node creates a summing amplifier.
For the stated unity-gain illustration, inputs of 1 V DC and 1 V DC combine to produce a 2 V DC summed output.

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.