A. S. Sedra & K. C. Smith, Microelectronic Circuits — differential amplifiers, op-amps and feedback chapters.
Differential pairs, common-mode response, op-amp models and feedback-amplifier analysis.
AE-03
Course overview
Differential pairs, op-amps & feedback
AE-03 moves from matched transistor pairs to operational-amplifier abstractions and then to feedback as a loop problem. Differential/common-mode behavior, non-ideal op-amp parameters, negative feedback, loop gain and stability are kept connected rather than taught as unrelated formula sets.
5 chapters5 available · 0 plannedintermediate → advanced
Prerequisites
- AE-02 — single-stage amplifiers & active loads
- AE-01 — BJT/JFET/MOSFET
- AC-02 — transfer functions
By the end of the course
- Analyze a differential pair in differential and common modes.
- Move from transistor differential stages to ideal/non-ideal op-amp abstractions.
- Derive negative-feedback configurations from the loop structure itself.
- Relate loop gain to closed-loop gain without using the virtual-short shortcut outside its scope.
- Develop stability intuition before the detailed frequency-domain treatment in AE-04.
Syllabus
Five readings from differential pairs to loop-stability intuition.
AE-03 moves from matched transistor pairs to operational-amplifier abstractions and then to feedback as a loop problem. Differential/common-mode behavior, non-ideal op-amp parameters, negative feedback, loop gain and stability are kept connected rather than taught as unrelated formula sets.
- 01→
Differential pair
Build BJT and MOS differential pairs from matched-device laws, a shared tail current and explicit differential/common-mode variables. Derive current steering, the symmetric operating point, differential small-signal gain, common-mode response with finite tail resistance, CMRR and the role of active loads. Keep single-ended and differential outputs distinct and connect every gain formula to the actual circuit and bias point.
220–280 min · Intermediate → advanced · available - 02→
Ideal & non-ideal op-amps
Build the operational-amplifier abstraction from a differential-input, single-ended-output voltage amplifier before using any virtual-short shortcut. Define the open-loop law vo=A(s)(v+−v−), then separate ideal assumptions from real limits: finite open-loop gain, finite input/output resistance, input offset and bias currents, common-mode range, CMRR, output swing/current limits, slew rate and frequency dependence. Show explicitly that v+≈v− is a consequence of stable negative feedback with large loop gain and unsaturated operation — not an intrinsic op-amp law.
210–270 min · Intermediate → advanced · available - 03→
Negative feedback
Treat negative feedback as a physical comparison process before invoking op-amp shortcuts. Identify the error signal, returned output fraction and net loop sign, then analyze canonical non-inverting and inverting op-amp circuits with real resistor networks. Derive their ideal closed-loop gains only after checking the conditions that justify the virtual-short approximation, and show how feedback trades raw gain for accuracy, linearity and controlled impedances without removing saturation or stability limits.
210–270 min · Intermediate → advanced · available - 04→
Loop gain & closed-loop gain
Quantify the correction mechanism introduced in chapter 03. Start from the subtractive loop e=xs−βxo and forward relation xo=Ae, define the loop gain L=Aβ under an explicit sign convention, derive the exact closed-loop gain A/(1+Aβ), then connect large loop gain to finite-gain error, desensitization, noise gain, input/output resistance changes and the frequency range over which ideal op-amp formulas remain accurate. Keep stability margins for chapter 05.
220–290 min · Advanced · available - 05→
Stability intuition
Keep the loop gain complex and ask when negative feedback stops behaving as a correction mechanism. Start from the characteristic denominator 1+L(s), interpret the critical point −1, define gain crossover, phase margin and gain margin, connect poor margin to peaking/ringing, and show why extra poles, capacitive loading and frequency-dependent feedback networks can erode stability. Use Bode/Nyquist intuition without turning 45° or 60° into universal design laws.
230–300 min · Advanced · available
Reference backbone
References used
Device-level differential analysis is anchored in microelectronics texts and MIT 6.012; op-amp and feedback chapters then use MIT 6.071J and Roberge’s feedback text alongside standard circuit references.
B. Razavi, Fundamentals of Microelectronics — differential amplifiers and feedback chapters.
Large- and small-signal differential-pair reasoning, active loads, CMRR and feedback intuition.
P. R. Gray, P. J. Hurst, S. H. Lewis & R. G. Meyer, Analysis and Design of Analog Integrated Circuits.
Differential stages, bias sources, common-mode behavior and integrated op-amp building blocks.
MIT OpenCourseWare 6.012 — Lectures 19–22 on differential amplifier stages and analysis.
Large-signal transfer, differential/common-mode small-signal analysis, active loads and integrated-amplifier metrics.
MIT OpenCourseWare 6.071J — operational-amplifier lecture notes.
Ideal/non-ideal op-amp models and basic negative-feedback configurations.
J. K. Roberge, Operational Amplifiers: Theory and Practice / MIT RES.6-010.
Feedback-system modeling, loop gain, stability and compensation foundations.