Circuits & Systems Classroom

An interactive classroom and knowledge base for analog and mixed-signal circuits and systems, spanning amplifiers, data converters, PLLs, noise, feedback, and signal analysis.

Interactive illustrations

The web/ folder holds Circuits & Systems Classroom, published at https://circuits-and-systems.tokenzhang.com. It combines selected interactive lessons on data converters and PLLs with an external Bode-plot tool. The ADCToolbox reference manual remains at https://adctoolbox.tokenzhang.com/doc/. See web/README.md for development and deployment.

Contents

Basic Amplifier Topologies

Single-Transistor-Amplifier-Configurations.md

Reference guide for the three fundamental MOSFET amplifier topologies (Common Source, Common Gate, Common Drain). Includes voltage gain, input/output impedance analysis, and typical applications for each configuration.

5T-Differential-Amplifier-Analysis.md

Complete mathematical analysis of 5-transistor differential amplifiers including differential/common-mode gains, CMRR, PSRR, noise analysis (thermal and flicker), frequency response (poles, zeros, transfer function), and pole-zero doublet settling time analysis.

Miller-Compensated-Two-Stage-Amplifier.md

Classical two-stage operational amplifier with Miller compensation. Comprehensive reference covering DC gain equations, dominant/non-dominant poles, RHP zero analysis, GBW calculations, phase margin design, slew rate, settling time, noise analysis, CMRR/PSRR, and complete design procedure with sizing equations.

Dynamic and Advanced Amplifiers

Ring-Amplifier.md

Ring amplifier (Ringamp) topology using dynamically stabilized inverter stages. Covers working principle, dead-zone design, bandwidth/power equations, dead-zone degeneration (DZD), multi-stage configurations, and state-of-the-art pipelined ADC applications.

Floating-Inverter-Amplifier.md

Floating Inverter Amplifier (FIA/FIDA) with floating supply reservoir. Includes gain formulas, common-mode stability, reservoir capacitor sizing, cross-coupled body biasing (CCBB) for enhanced gain, and applications in DTDSM and SAR ADCs.

Floating-Charge-Transfer-Amplifier.md

Floating Charge Transfer (FCT) amplifier with complementary common-gate topology and cross-coupled capacitor biasing (C³B). Covers charge conservation equations, PVT-robust gain, filter-embedded Pipe-SAR ADC architecture achieving 172 dB Schreier FoM.

Noise Reduction Techniques

kTC-Noise-Cancellation.md

Thermal noise cancellation achieving up to 70% noise power reduction using auxiliary capacitors. Includes basic cancellation, presampling techniques (>5× sampling rate improvement), design equations, capacitor sizing, and applications in high-resolution SAR ADCs and ΔΣ modulators.

Correlated-Double-Sampling.md

Correlated Double Sampling (CDS) for removing offset, reset noise, and 1/f noise. Covers frequency response, noise shaping, reset noise cancellation, switched-capacitor implementation, Correlated Multiple Sampling (CMS), and comparison with other techniques.

Correlated-Level-Shifting.md

Correlated Level Shifting (CLS) for gain enhancement achieving effective gain A² from opamp with gain A. Enables >60 dB performance from 30 dB opamps. Includes sequential CLS (SCLS), noise analysis, pipelined SAR ADC applications, and look-ahead CLS techniques.

Sampling and Data Conversion

Current-Integration-Sampling.md

Current integration sampling for converting current signals to voltage. Covers fundamental equations, integrating ADC architectures (dual-slope, incremental ΔΣ, multi-slope), photodiode integrators, noise analysis (kT/C, shot noise), jitter performance comparison with voltage sampling, and design equations.

Analysis and Calculations

Amplifier-Bandwidth-Calculations.md

Comprehensive guide to amplifier bandwidth theory including gain-bandwidth product (GBW) fundamentals, closed-loop bandwidth calculations, gain-bandwidth tradeoffs, and multi-stage bandwidth analysis with visual comparisons.

Phase-Noise-Calculations.md

Bidirectional conversion formulas between phase noise and amplitude noise, including definitions, step-by-step derivations, direct formulas, and worked examples for high-speed applications.

Comparator-Noise-Calculation.md

Statistical analysis of comparator noise using Gaussian distribution theory. Covers probability density/cumulative distribution functions, noise sigma extraction formulas (inverse CDF method), visualization of noise impact on decision probability, and figures of merit (FoM₁, FoM₂) for comparator performance evaluation.

Capacitance-AC-Simulation.md

Practical method for extracting capacitance values from AC simulation results using current-frequency relationships. Includes derivation from I = jωCV, formulas for imaginary current component analysis, and ready-to-use Virtuoso Calculator expressions for automated capacitance extraction.

Source Degeneration Analysis

Degenerated-Resistor-Noise.md

Complete noise analysis comparing non-degenerated vs source-degenerated resistor configurations. Covers transistor and resistor noise contributions, output current/voltage noise PSD derivations, frequency-dependent behavior, noise ratio calculations, and numerical examples showing noise contribution breakdown for different γ and gₘRₛ values.

Degenerated-Resistor-Current-Noise.md

Focused current noise analysis for source-degenerated circuits. Derives output current noise PSD for both cases, includes sanity checks for limiting cases (Rₛ→0 and gₘRₛ≫1), and provides simplified noise ratio formulas for design calculations.

Degenerated-Resistor-Charging-Time.md

Charging time comparison between RC charging and constant-current source degeneration. Includes time-to-Vdd/2 derivations, equivalence conditions for matched speed, design tables mapping gₘ/Rₛ/Rₗ values, effective transconductance calculations, and output resistance boosting analysis.

Directories

code/

Python scripts for generating figures and visualizations.

figures/

Generated plots and images referenced in the documentation.

reference/

Local reference materials including LaTeX source documents and papers.