EE 2115-01 - Lec 16 - 2026_10_02

Overview

Hiren Trada introduces ideal and practical operational-amplifier behavior, including differential inputs, power-rail limits, saturation, and the role of negative feedback. He derives the non-inverting amplifier's closed-loop gain, \(A_V = 1 + R_2/R_1\), and illustrates it with an LTspice example whose resistor values produce a gain of 26.5.

Key takeaways

The ideal op-amp model assumes infinite input resistance, zero output resistance, infinite open-loop gain, and infinite bandwidth; practical devices approximate these properties but have finite limits.
An op amp amplifies the differential voltage \(V_{IN+}-V_{IN-}\), and its very high open-loop gain makes even a small input difference capable of saturating the output.
Negative feedback controls the output by returning a fraction of it to the inverting input; for a non-inverting amplifier, the closed-loop gain is \(1+R_2/R_1\).
A non-inverting circuit's resistor divider sets the feedback fraction \(F=R_1/(R_1+R_2)\); for large \(A_{OL}\), the gain approaches \(1/F\).
Op-amp output swing is limited by the supply rails and load: the lecture's example calls for at least \(\pm6\) V supplies to produce a 10 V peak-to-peak signal.
The 741's eight-pin package has no ground pin; circuit voltages use a shared external reference, commonly the midpoint between dual supply rails.

Chapters

0:00 Operational Amplifiers: Functions and Input/Output Pins

Operational amplifiers, or op amps, are packaged circuits made from transistors, resistors, and other components.
Op amps can support summation, differentiation, integration, filtering, and amplification; the lecture focuses on amplifier configurations.
The symbol's inputs are the non-inverting \(V_{IN+}\) and inverting \(V_{IN-}\) terminals, alongside the output and \(+V_{DD}\) and \(-V_{SS}\) supply rails.
An op amp can serve as a comparator, but not every comparator is an op amp.

4:35 Four Ideal Op-Amp Assumptions

The ideal model assumes infinite input resistance, so no current enters either input terminal.
It assumes zero output resistance, infinite open-loop gain, and infinite bandwidth.
Open-loop operation means there is no feedback path from the output to an input.
These ideal assumptions simplify analysis of practical op-amp circuits.

7:24 What Ideal Properties Mean in Real Circuits

Infinite input resistance implies zero input current in the ideal model; real op amps still have very high input resistance, commonly in the megaohm range.
Practical output resistance is not zero, and output current is limited rather than infinite.
Real open-loop gain is finite but can exceed 100,000; practical bandwidth also falls as signal frequency rises.
Gain is the output-to-input ratio; a ratio below one describes attenuation rather than amplification.

14:40 Power Rails Supply the Energy for Amplification

An amplifier draws energy from its DC supply rails and uses it to produce an output that follows the input signal's shape.
The output generally cannot reach the supply rails exactly because some voltage is lost inside the device.
The differential input is \(V_{ID}=V_{IN+}-V_{IN-}\); input voltages must stay within the device's allowed supply range to avoid incorrect operation or damage.
The supply rails provide much more current than the inputs, which typically draw only very small currents.

20:05 Output Current, Open-Loop Gain, and Saturation

An op amp can source current from \(V_{DD}\) or sink current toward \(V_{SS}\); output current limits are typically in the tens of milliamps.
Open-loop output follows \(V_{OUT}=A_{OL}(V_{IN+}-V_{IN-})\), making even millivolt-scale input differences significant.
Because \(A_{OL}\) is very large, an uncontrolled differential input drives the output into positive or negative saturation near the supply rails.
The voltage-transfer curve has a steep central region and flat saturated regions where changing the input no longer changes the output.

26:22 741 Pinout, Ground Reference, and Output Swing

The classic 741 is an eight-pin IC containing one op amp, with supply, input, output, offset, and no-connection pins—but no ground pin.
Input and output voltages are measured relative to a common circuit reference, typically the midpoint of dual supplies; \(V_{SS}\) can also be tied to ground.
Output swing depends on the device and load; the example shows limits about 1.5 V from \(V_{DD}\) and 0.75 V from \(V_{SS}\), with differing current capability.
For a desired 10 V peak-to-peak output, Trada recommends at least 12 V total supply, such as dual \(\pm6\) V rails, with extra margin preferred.

31:36 Non-Inverting Amplifier Uses Negative Feedback

The non-inverting configuration applies the signal to \(V_{IN+}\) and feeds a fraction of the output to \(V_{IN-}\) through a resistor divider.
This is a voltage-controlled voltage source: the input voltage controls the output voltage.
Negative feedback reduces the differential input and prevents the very large open-loop gain from immediately driving the output into saturation.
A larger fraction of output fed back to the inverting input results in lower closed-loop gain; a smaller fraction results in higher gain.

36:26 Feedback Applications: Sensors, Equalizers, and Voltage Followers

Op amps can amplify small signals from sensors such as microphones; a function generator supplies test signals in laboratory experiments.
A graphic equalizer can use multiple op-amp circuits, with resistors adjusting gain and capacitors or inductors shaping selected frequency bands.
A voltage follower feeds the entire output back to the input and has a voltage gain of 1, making it useful for isolating a small sensor signal.
For circuit analysis, first identify whether feedback is negative; positive feedback is used in other applications, including oscillators.

43:42 Deriving Non-Inverting Closed-Loop Gain

With negligible input current, the feedback divider sets \(V_{IN-}=F V_{OUT}\), where \(F=R_1/(R_1+R_2)\).
Combining the divider with \(V_{OUT}=A_{OL}(V_{IN+}-V_{IN-})\) gives a closed-loop gain of \(A_{OL}/(1+F A_{OL})\).
When \(A_{OL}\) is much larger than 1, the expression simplifies to \(1/F\), yielding \(V_{OUT}/V_{IN}=1+R_2/R_1\).
The feedback resistor is often labeled \(R_F\), while the other divider resistor may be labeled \(R_I\) or \(R_N\).

48:44 LTspice Gain Example and Course Textbooks

The LTspice example uses an LT1457 with \(\pm5\) V supplies and resistors of 51 kΩ and 2 kΩ.
The non-inverting gain is \(1+51/2=26.5\); \(A_V\) denotes voltage gain, while \(A_{CL}\) denotes closed-loop gain.
Trada notes that the course syllabus lists two legally free textbooks, one available through the library and one available as a free download.

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.