A. Agarwal & J. H. Lang, Foundations of Analog and Digital Electronic Circuits, Morgan Kaufmann, 2005 — nonlinear devices and diode analysis.
Circuit-level nonlinear constitutive laws, load-line/operating-point thinking and local linearization.
AE-00
Course overview
Diodes & nonlinear circuits
Linear circuit methods remain essential, but a diode introduces a constitutive law whose slope changes with operating point. AE-00 builds nonlinear reasoning carefully: first the physical/terminal I–V law, then controlled approximations and local linearization, rectification, clamps/limiters and finally systematic nonlinear bias-point analysis.
5 chapters5 available · 0 plannedintermediate
Prerequisites
- CT-01 — Thévenin/Norton
- DY-01 — first-order dynamics
- KCL/KVL and DC analysis
By the end of the course
- Analyze a nonlinear I–V law and its operating point.
- Choose a diode approximation with an explicit validity range.
- Analyze rectifiers, clamps and limiters while preserving sign references.
- Linearize a diode locally around a Q-point.
- Recognize when a simple model is no longer adequate.
Syllabus
Five readings from the physical I–V law to practical nonlinear circuits.
Linear circuit methods remain essential, but a diode introduces a constitutive law whose slope changes with operating point. AE-00 builds nonlinear reasoning carefully: first the physical/terminal I–V law, then controlled approximations and local linearization, rectification, clamps/limiters and finally systematic nonlinear bias-point analysis.
- 01→
The diode I–V law
Treat the diode first as a two-terminal nonlinear constitutive element, then connect its exponential I–V relation to the minimum p–n junction physics needed to understand where it comes from. Define voltage/current references, derive the ideal Shockley form under stated assumptions, separate the ideality-factor compact extension from the ideal law, introduce thermal voltage and logarithmic slope, explain reverse-bias and breakdown limits, reject a universal 0.7 V threshold, and solve a resistor–diode operating point by load-line and numerical intersection.
185–235 min · Intermediate · available - 02→
Piecewise & small-signal diode models
Turn the exponential diode law into controlled circuit approximations instead of folklore. Derive the ideal-diode complementarity model, constant-drop and piecewise-linear forward models, quantify their error against the exponential law, then linearize the exact I–V relation around a declared Q-point to obtain gd and rd. Keep large-signal and incremental variables separate, state the amplitude condition behind local linearization, and explain when junction/diffusion capacitances must be added for dynamic small-signal work.
180–230 min · Intermediate · available - 03→
Rectifiers
Use diode state logic to derive AC-to-unidirectional conversion rather than memorizing waveforms. Analyze the resistive-load half-wave rectifier, derive its average and RMS output, extend the same reasoning to a full-wave bridge and its two-diode conduction paths, then add a reservoir capacitor and derive the small-ripple approximation ΔV≈Iload/(fripple C) with explicit assumptions. Separate output ripple from diode/source pulse current, voltage stress and safety limits.
190–245 min · Intermediate · available - 04→
Clamps & limiters
Separate two diode waveform operations that are often confused. A limiter clips selected amplitude regions by switching a diode into conduction; a clamper uses a diode plus capacitor to translate a waveform’s DC level while approximately preserving peak-to-peak span. Derive upper, lower and biased limiters with explicit source resistance and current limiting, then derive an ideal/constant-drop positive clamper from capacitor charge and show how finite off-state time constant causes droop.
185–235 min · Intermediate · available - 05→
Nonlinear DC bias point
Turn nonlinear circuit biasing into a systematic equation-solving problem. Start from topology, references and device models, formulate scalar or vector residuals F(x)=0, prove uniqueness for the simple resistor–diode load-line case, derive Newton and the Jacobian for coupled diode networks, add damping and convergence checks, search for multiple admissible roots when the circuit allows them, then recover the small-signal model from the Jacobian evaluated at Q. Finish with independent KCL, power, model-domain and perturbation checks.
195–250 min · Intermediate · available
Reference backbone
References used
The course deliberately combines circuit-level nonlinear analysis with enough semiconductor-device physics to explain where the diode models come from and where they fail.
MIT OpenCourseWare 6.002 — nonlinear analysis / diode materials.
General circuit treatment of nonlinear elements, graphical operating points and diode approximations.
MIT OpenCourseWare 6.012 — p-n junction diode I–V characteristics and diode circuit models.
Physical basis of the p-n junction exponential law, forward/reverse bias and large-/small-signal diode models.
A. S. Sedra & K. C. Smith, Microelectronic Circuits — diode chapters.
Practical diode circuits, exponential model, bias points, piecewise models, rectifiers, limiters and incremental resistance.
B. Razavi, Fundamentals of Microelectronics — diode physics and circuit analysis chapters.
Bridge from device I–V physics to circuit operating-point and small-signal reasoning.
B. G. Streetman & S. Banerjee, Solid State Electronic Devices — p-n junction diode chapters.
Semiconductor transport assumptions and physical interpretation behind the ideal diode equation.
C. T. Kelley, Solving Nonlinear Equations with Newton's Method, SIAM, 2003.
Newton linearization, Jacobians, damping/globalization and convergence diagnostics for nonlinear equation systems.